tag:blogger.com,1999:blog-34544900017725747702024-03-18T08:22:51.581-04:00eat play mathA blog by a veteran math teacher who tries to learn new things. Most posts are about teaching math and problem-solving, but sometimes, it's just about life.Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.comBlogger130125tag:blogger.com,1999:blog-3454490001772574770.post-9597996320708413662023-05-06T16:05:00.005-04:002023-05-06T16:10:16.315-04:00Best Desmos Conics Projects of 2022 - 2023<p> </p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn9LgP89ofzS4V1UxtyTEbfL2ddUFJUMbLt11osSpArMG_93nfnF6dDIUDdHU79K6YQcwJbcuVqRfPzMy5nFysmYQw_kP41bbso9LgCXr6bawaY8b1KW7nGyQ0PaeemK_nqFHEvLX1F5BOi7zAZzXWIeHELHRB3gH9WXvsXKChxySEPWZaRR0jBfTn8A/s1038/Screen%20Shot%202023-05-06%20at%204.06.06%20PM.png" style="margin-left: 1em; margin-right: 1em;"><br /><div class="separator" style="clear: both; text-align: center;"><br /></div></a><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgn9LgP89ofzS4V1UxtyTEbfL2ddUFJUMbLt11osSpArMG_93nfnF6dDIUDdHU79K6YQcwJbcuVqRfPzMy5nFysmYQw_kP41bbso9LgCXr6bawaY8b1KW7nGyQ0PaeemK_nqFHEvLX1F5BOi7zAZzXWIeHELHRB3gH9WXvsXKChxySEPWZaRR0jBfTn8A/s1038/Screen%20Shot%202023-05-06%20at%204.06.06%20PM.png" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEhgbU7XOu8V5Q8G7q4fdCl0td_csfI4vWFhp_oE19yNpEqIuyy4gUFDoV176dsLHb-gtt8kUFHoo1c7ouVDmn5Zav9cMH9isZe458IiURd-w1DGiYDjh7ySZEaBBkS4lvMejaVzcAen9QPgETfQoXZzofU3bzColCw0xFNtzaVA5firy4X6xsa-aFSMQA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="394" data-original-width="656" height="192" src="https://blogger.googleusercontent.com/img/a/AVvXsEhgbU7XOu8V5Q8G7q4fdCl0td_csfI4vWFhp_oE19yNpEqIuyy4gUFDoV176dsLHb-gtt8kUFHoo1c7ouVDmn5Zav9cMH9isZe458IiURd-w1DGiYDjh7ySZEaBBkS4lvMejaVzcAen9QPgETfQoXZzofU3bzColCw0xFNtzaVA5firy4X6xsa-aFSMQA" width="320" /></a></div><br /></div><br />I'm finally getting around to posting these projects! <a href="https://docs.google.com/document/d/1rV7VQQTC_f_tyPUEVGXUsz9TgxA8ktY4mOmEDoD2UcI/edit?usp=sharing">Here</a> is the link to the assignment and past projects.<p></p><p><br /></p>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/wvlzdgrmj4?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/ywaqz4xv8t?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/xg7dzl2urs?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/39ymowveq6?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/ouhwgulxqz?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/1rjmbhfhhk?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/wbnlwaxz3f?embed" style="border: 1px solid #ccc;" width="500"></iframe>Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com0tag:blogger.com,1999:blog-3454490001772574770.post-90937028035716549042023-05-06T15:43:00.001-04:002023-05-06T16:11:50.395-04:00Unit Circle Project 2022-2023<p> Here are the best projects from 2023 along with the <a href="https://docs.google.com/document/d/1vJK6wEBZDY-nkAe5guVisNIEpPBwJN3o5fZxe1MoJb4/edit?usp=sharing">instructions</a> and <a href="http://eatplaymath.blogspot.com/search/label/unit%20circle%20project">links to prior years</a>.</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiABbu7pHLdII_vIpu-lznN-SxNJAzIJsHmcadKA7LuJRU-SKgeeOQAkRCpjfeuz35C7pU9NN5tlzaClHGghikAKI-4LlPVFGDmIKU3fTYv_bBYeywZlWJYQ7V4GFz_BqWjtBm5j_jLx8rWhiSaKs35lgxX9FS0iDtkvJs-paMwGrhtD3cwK_Mi8CLo-A" style="margin-left: 1em; margin-right: 1em;"></a><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiABbu7pHLdII_vIpu-lznN-SxNJAzIJsHmcadKA7LuJRU-SKgeeOQAkRCpjfeuz35C7pU9NN5tlzaClHGghikAKI-4LlPVFGDmIKU3fTYv_bBYeywZlWJYQ7V4GFz_BqWjtBm5j_jLx8rWhiSaKs35lgxX9FS0iDtkvJs-paMwGrhtD3cwK_Mi8CLo-A" style="margin-left: 1em; margin-right: 1em;"></a><a href="https://blogger.googleusercontent.com/img/a/AVvXsEjf_XnujYtJotVbO6Xy0fJgT1a82kUF0T_qlrv3IPwBRA7mWnOrlAa8H0nxr2wqT9fUAO-Jhcr08PEzAn4Eev1XJrKE6ptWW27zMALTCD01Ddp8WdGaRHMSbyOvimKTq2l312Ldw_KHTsHSTju9VGrEyRmgujeq3P57QtyqgR6LMoK0PzsZ6lZm_N680w" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="3024" data-original-width="4032" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEjf_XnujYtJotVbO6Xy0fJgT1a82kUF0T_qlrv3IPwBRA7mWnOrlAa8H0nxr2wqT9fUAO-Jhcr08PEzAn4Eev1XJrKE6ptWW27zMALTCD01Ddp8WdGaRHMSbyOvimKTq2l312Ldw_KHTsHSTju9VGrEyRmgujeq3P57QtyqgR6LMoK0PzsZ6lZm_N680w" width="320" /></a></div><br /><img alt="" data-original-height="1278" data-original-width="1170" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEiABbu7pHLdII_vIpu-lznN-SxNJAzIJsHmcadKA7LuJRU-SKgeeOQAkRCpjfeuz35C7pU9NN5tlzaClHGghikAKI-4LlPVFGDmIKU3fTYv_bBYeywZlWJYQ7V4GFz_BqWjtBm5j_jLx8rWhiSaKs35lgxX9FS0iDtkvJs-paMwGrhtD3cwK_Mi8CLo-A" width="220" /></div><div class="separator" style="clear: both; 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margin-right: 1em;"><img alt="" data-original-height="4032" data-original-width="3024" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgqMjuCwm2yzy449xGngP-d1Fw99itZ7KmMQj6visCaBfRDA997715QWYj1OWHGw_v4I1lcUk3OhB1t5bQIYQqUySoSXXimofkQnHNh_s5_OnYl4PwLvbDI5US4OalPzDA5d9yq7n_iHGlBTKC6sTfrevPD2geNLjsi4liHw26DwyQrYNQkmNiDfeN7Mg" width="180" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEgvy2Q1RtZITY2SdS6vXg0He5CqGmuNYHp1WrH9BPnt_pgxjNtUmOR0t4bfXCQeaWyi44lCbUwksgFtU6jdEE0IljwDMv9ntrIT9U4dgC5XH5V1_sS1LNV8rs_45a2BPlx9zfbOTp9JsnB9Lema5tyzmkoUnWIn97VRfqMZGoA3J8fdsXkVbx618dZvAA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="4032" data-original-width="3024" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEgvy2Q1RtZITY2SdS6vXg0He5CqGmuNYHp1WrH9BPnt_pgxjNtUmOR0t4bfXCQeaWyi44lCbUwksgFtU6jdEE0IljwDMv9ntrIT9U4dgC5XH5V1_sS1LNV8rs_45a2BPlx9zfbOTp9JsnB9Lema5tyzmkoUnWIn97VRfqMZGoA3J8fdsXkVbx618dZvAA" width="180" /></a></div><div class="separator" style="clear: both; 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margin-right: 1em;"><img alt="" data-original-height="3024" data-original-width="4032" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEimQvAV3g4JEWBBwv_luXiGdcC25PcQ0nJAvdox7nCUUl6D2BCDRponCPw0Ju3Vg_D9687VYqEB2URkOOt92PDAo13MbOqn4eD5mTOLHvsHIFD6ETPn9JnBhXb8QB63hJANMUeaYxdWJFqAtdqZ7CURKIO9HoRMJhxLeGr7GvpC-ufreHvqAwyhS8iGqg" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiPA079khUb4ZlTi_mMrMDocqjlzWzUd3wJYMOjiCN2rDKqQ-dcc5Euchb3_5bb6UsuIzmx2nvtqWXT9fDzkzIVtJVx-o24xUTe27c2iiImjRiVjWkVwE8eC6ji_URuY1GjXL_MzgGF8a8UYXhTMntz_vC0c3S_pNyADyer73LXxtp___licyglNKVJng" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="4032" data-original-width="3024" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEiPA079khUb4ZlTi_mMrMDocqjlzWzUd3wJYMOjiCN2rDKqQ-dcc5Euchb3_5bb6UsuIzmx2nvtqWXT9fDzkzIVtJVx-o24xUTe27c2iiImjRiVjWkVwE8eC6ji_URuY1GjXL_MzgGF8a8UYXhTMntz_vC0c3S_pNyADyer73LXxtp___licyglNKVJng" width="180" /></a></div><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/a/AVvXsEiakcgNBnKQrUD6VaLqUMcb9mPwzDSQXwfCfn7aPIZVUWhOtYUp9B97VbGYsed_tRLYqDY9awhwu0_GE-JqGnb4YT4AT56A8nVq2y1Qu86KNTW-KQg4QJPAJlVYRI3qQyRtN-BLTPMBLFOTuchTqGmtprGGOEWwX4H37cqTVF_xBzmItHB0VsU3VQJPWA" style="margin-left: 1em; margin-right: 1em;"><img alt="" data-original-height="1478" data-original-width="1250" height="240" src="https://blogger.googleusercontent.com/img/a/AVvXsEiakcgNBnKQrUD6VaLqUMcb9mPwzDSQXwfCfn7aPIZVUWhOtYUp9B97VbGYsed_tRLYqDY9awhwu0_GE-JqGnb4YT4AT56A8nVq2y1Qu86KNTW-KQg4QJPAJlVYRI3qQyRtN-BLTPMBLFOTuchTqGmtprGGOEWwX4H37cqTVF_xBzmItHB0VsU3VQJPWA" width="203" /></a></div><br /><br /></div><br /><br /><br /><p></p>Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com1tag:blogger.com,1999:blog-3454490001772574770.post-38418302165231394312021-12-30T10:02:00.000-05:002021-12-30T10:03:22.635-05:00Desmos Alternate Assessment Project 2021 Conics and Parent FunctionsOne of my favorite projects to do with my Honors Algebra 2 students is the Desmos alternate assessment that brings together everything students learned in the first semester. Students know how to graph all of the parent functions and conics, and their task was to create a drawing on Desmos that puts it all together. I love this project because it incorporates student identities and interests, which is essential according to <a href="https://selfdeterminationtheory.org/theory/">Self-Determination Theory</a> and <a href="https://www.edutopia.org/article/getting-started-culturally-responsive-teaching">Culturally Responsive Teaching</a>. This year, I shared all projects in a <a href="https://padlet.com/lisawiner/x0ln629xss93kaw7">Padlet</a> so that students could easily see everyone else's. Students had to use their knowledge of domain and range to limit the functions and also had to think about how to create the perfect size and shape by, for example, figuring out the center, "a," and "b" for an ellipse. Many incorporated different colors and animations. <div><br /></div><div>Here are some of my favorites this year:</div><div><br /></div>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/vywkdwtr3z?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/iayh2zqzei?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/cp3r30e5du?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/ziklhyglnj?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/dqrgriq2vy?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/4gxyopwipk?embed" style="border: 1px solid #ccc;" width="500"></iframe>
<iframe frameborder="0" height="500" src="https://www.desmos.com/calculator/mnqrpmfhdz?embed" style="border: 1px solid #ccc;" width="500"></iframe><div><br /></div><div>Here is the Padlet of all of the projects.<br /><div><br /></div><div><div><div class="padlet-embed" style="background: rgb(244, 244, 244); border-radius: 2px; border: 1px solid rgba(0, 0, 0, 0.1); box-sizing: border-box; overflow: hidden; position: relative; width: 684px;"><p style="margin: 0px; padding: 0px;"><br class="Apple-interchange-newline" /><iframe allow="camera;microphone;geolocation" frameborder="0" src="https://padlet.com/embed/x0ln629xss93kaw7" style="display: block; height: 608px; margin: 0; padding: 0; width: 100%;"></iframe></p><div style="margin: 0px; padding: 8px; text-align: right;"><a href="https://padlet.com?ref=embed" style="border: none; display: block; height: 16px; line-height: 1; margin: 0px; padding: 0px;" target="_blank"><img alt="Made with Padlet" height="16" src="https://padlet.net/embeds/made_with_padlet.png" style="background: none; border: none; box-shadow: none; display: inline; margin: 0px; padding: 0px;" width="86" /></a></div></div></div><div><br /></div>Here are my students' <a href="https://eatplaymath.blogspot.com/2020/12/desmos-conics-projects-2020-with.html">2020 projects</a>, <a href="http://eatplaymath.blogspot.com/2019/12/conic-sections-projects-using-desmos.html">2019 projects</a>, and <a href="http://eatplaymath.blogspot.com/2017/03/a-great-conics-project-using-desmos.html">2018 projects</a>. <a href="https://docs.google.com/document/d/1Mlmek2blkPhwBSUxqiLehOHFKCOcDABG/edit?usp=sharing&ouid=112803049209111533292&rtpof=true&sd=true">Here</a> is the project outline, based on <a href="http://mrsumerton.weebly.com/uploads/7/9/7/5/7975495/conic_project_final_2015.pdf">a project by Mr. Sumerton.</a> If you do incorporate this project, please be sure to include an Honor statement that attests to the fact that students have not copied any of the equations or pictures. I am blown away by the number of projects I see online posted by their teachers that are blatantly copied. Please be aware of this; if there is no statement or discussion about this, students may be tempted to take the easy way out. The critical part of this activity is each individual's unique learning opportunity to create something from scratch using math. They are so proud of themselves! As they should be!!</div></div>Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com8tag:blogger.com,1999:blog-3454490001772574770.post-23946372708550706002020-12-19T10:54:00.004-05:002021-01-04T10:49:00.660-05:00Desmos Conics projects 2020 with Animation and Short Video Explanations for Students including how to change colors<p>Well, some good came from 2020 this year, and that is my student Desmos projects. I've posted my students' conics project in <a href="http://eatplaymath.blogspot.com/2019/12/conic-sections-projects-using-desmos.html">2019</a> and <a href="http://eatplaymath.blogspot.com/2017/03/a-great-conics-project-using-desmos.html">2018</a>, but what turned out great this year was that they couldn't be printed, so students actually worked more on discovering animations. Below are some of the best ones. But first the rules...<b>Students <span style="font-family: times;">must have at least one ellipse, circle, parabola, hyperbola, and another parent function as a minimum. </span></b></p><p>What did students learn/solidify? The student was able to:</p><p></p><ul style="text-align: left;"><li><b>Plan a unique design from start to finish using what they learned about graphs in an Algebra 2 Honors class</b></li><li><b>Predict shapes and locations based on the transformations of the graphs we learned in class</b></li><li><b>Generalize what they have learned about transformations on graphs to what they haven't yet learned, such as y=asinbx + c.</b></li><li><b>Construct pictures by analyzing and synthesizing their own piecewise shapes </b></li><li><b>Illustrate knowledge of domain and range by limiting their graphs </b></li><li><b>Demonstrate knowledge of inequalities through shading and domain and range restrictions</b></li></ul><div>For some more than others:</div><div><ul style="text-align: left;"><li><b>Infer from examples of how to apply animation </b></li><li><b>Explain how to animate and use shading arrangements (see student video links at the end)</b></li></ul></div><p>Twin artists first drew their concepts and then "desmofied" them. </p><p><span></span></p><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><a href="https://lh3.googleusercontent.com/-NURnvBSmZoY/X94NHn5SyCI/AAAAAAAAbG4/27QTpBYpXh0PXwNmxK7_WgIYynoHHJ3VACLcBGAsYHQ/image.png" style="clear: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img alt="" data-original-height="649" data-original-width="495" height="240" src="https://lh3.googleusercontent.com/-NURnvBSmZoY/X94NHn5SyCI/AAAAAAAAbG4/27QTpBYpXh0PXwNmxK7_WgIYynoHHJ3VACLcBGAsYHQ/image.png" width="183" /></a><a href="https://lh3.googleusercontent.com/-DXCJGgP5hjQ/X94M_q9N2lI/AAAAAAAAbG0/XziG396mcikTXw9clbbWa7avpWrzT5NjQCLcBGAsYHQ/image.png" style="clear: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img alt="" data-original-height="785" data-original-width="576" height="240" src="https://lh3.googleusercontent.com/-DXCJGgP5hjQ/X94M_q9N2lI/AAAAAAAAbG0/XziG396mcikTXw9clbbWa7avpWrzT5NjQCLcBGAsYHQ/image.png" width="176" /></a><p></p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://lh3.googleusercontent.com/-Kcbp4jzvfyY/X94OgnYl48I/AAAAAAAAbHI/6ZCBHV5qI0cIYo5mqmVmRKDU5osKMC1ywCLcBGAsYHQ/image.png" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img alt="" data-original-height="447" data-original-width="485" height="240" src="https://lh3.googleusercontent.com/-Kcbp4jzvfyY/X94OgnYl48I/AAAAAAAAbHI/6ZCBHV5qI0cIYo5mqmVmRKDU5osKMC1ywCLcBGAsYHQ/image.png" width="260" /></a></div><br /><a href="https://lh3.googleusercontent.com/-GADQWx_mRIs/X94Opnop2nI/AAAAAAAAbHM/86HckP8PlE409ox4BzcNe8Vxo3bh3zRaQCLcBGAsYHQ/image.png" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img alt="" data-original-height="735" data-original-width="482" height="240" src="https://lh3.googleusercontent.com/-GADQWx_mRIs/X94Opnop2nI/AAAAAAAAbHM/86HckP8PlE409ox4BzcNe8Vxo3bh3zRaQCLcBGAsYHQ/image.png" width="157" /></a><p></p><p>The shoes had 199 lines of equations and the skater had 378 lines of equations/points.</p><p>Some animations, with the help of Twitter!</p><p></p><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-AARd24kb51g/X94WfEoeTGI/AAAAAAAAbH0/bRs1aFwovKcf1I7Bypp5-BgbIWDeuQx9gCLcBGAsYHQ/s638/The%2BGrinch.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="330" data-original-width="638" src="https://1.bp.blogspot.com/-AARd24kb51g/X94WfEoeTGI/AAAAAAAAbH0/bRs1aFwovKcf1I7Bypp5-BgbIWDeuQx9gCLcBGAsYHQ/s320/The%2BGrinch.gif" width="320" /></a></div><blockquote class="twitter-tweet"><p dir="ltr" lang="en">From <a href="https://twitter.com/quantgal67">@quantgal67</a>: Okay, I was doing something similar, trying to make water move. So I played around with this and here is a link to a little how-to video and a <a href="https://twitter.com/Desmos?ref_src=twsrc%5Etfw">@Desmos</a> graph:<br />video:<a href="https://t.co/nUQK998QPK">https://t.co/nUQK998QPK</a><br />desmos: <a href="https://t.co/DXpCtRa6Kj">https://t.co/DXpCtRa6Kj</a></p>— Laurie Hailer, M.A., M.Ed. (@quantgal67) <a href="https://twitter.com/quantgal67/status/1338259519323815936?ref_src=twsrc%5Etfw">December 13, 2020</a></blockquote><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-bP8GUOLMC6k/X94WP9_Mj1I/AAAAAAAAbHw/zFr4Up5fTVAzRIaXlkB25zEldw92jcHOQCLcBGAsYHQ/s638/Conics%2BProject%2B-%2BTennis%2BMatch%2B%25281%2529.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="330" data-original-width="638" src="https://1.bp.blogspot.com/-bP8GUOLMC6k/X94WP9_Mj1I/AAAAAAAAbHw/zFr4Up5fTVAzRIaXlkB25zEldw92jcHOQCLcBGAsYHQ/s320/Conics%2BProject%2B-%2BTennis%2BMatch%2B%25281%2529.gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-MmDroxgGVZs/X94XiQnUVxI/AAAAAAAAbIA/9kcqE10kOj4nMikkf1RYA5rFzzFhrCJrACLcBGAsYHQ/s638/Kirby%2BGraph.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="330" data-original-width="638" src="https://1.bp.blogspot.com/-MmDroxgGVZs/X94XiQnUVxI/AAAAAAAAbIA/9kcqE10kOj4nMikkf1RYA5rFzzFhrCJrACLcBGAsYHQ/s320/Kirby%2BGraph.gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-Zd-VezvGM_Q/X94YDs5vVhI/AAAAAAAAbII/_3PDEBonwmIH_H_jWHbTP94TpmsOH6drwCLcBGAsYHQ/s638/Thunderbird%2BDrawing.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="330" data-original-width="638" src="https://1.bp.blogspot.com/-Zd-VezvGM_Q/X94YDs5vVhI/AAAAAAAAbII/_3PDEBonwmIH_H_jWHbTP94TpmsOH6drwCLcBGAsYHQ/s320/Thunderbird%2BDrawing.gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-nKZXJ4aMQMI/X94Yqrx6OpI/AAAAAAAAbIU/hpKVWUxCT84VZ0DmeJJBdQ79DLU9CVQHACLcBGAsYHQ/s638/Truck%2BFor%2BDesmos%2BProject.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="330" data-original-width="638" src="https://1.bp.blogspot.com/-nKZXJ4aMQMI/X94Yqrx6OpI/AAAAAAAAbIU/hpKVWUxCT84VZ0DmeJJBdQ79DLU9CVQHACLcBGAsYHQ/s320/Truck%2BFor%2BDesmos%2BProject.gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-7s8nPledzw4/X94ZcrE2tMI/AAAAAAAAbIc/MTh4GvuvrDkjA2GmSjJ_7A3t-ubYJ_FjQCLcBGAsYHQ/s638/Conics%2BProject.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="330" data-original-width="638" src="https://1.bp.blogspot.com/-7s8nPledzw4/X94ZcrE2tMI/AAAAAAAAbIc/MTh4GvuvrDkjA2GmSjJ_7A3t-ubYJ_FjQCLcBGAsYHQ/s320/Conics%2BProject.gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-NCjqipc29T4/X94ar5yGTtI/AAAAAAAAbIw/Q8AML6XY8vQnKz82iXNzd2AApcwkWWD-gCLcBGAsYHQ/s616/Conics%2BProject%2BAlgebra%2B2%2BH%2B%25281%2529.gif" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="480" data-original-width="616" src="https://1.bp.blogspot.com/-NCjqipc29T4/X94ar5yGTtI/AAAAAAAAbIw/Q8AML6XY8vQnKz82iXNzd2AApcwkWWD-gCLcBGAsYHQ/s320/Conics%2BProject%2BAlgebra%2B2%2BH%2B%25281%2529.gif" width="320" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: left;">This student recreated a painting of a bird that she did. The first picture is the overlay and the second picture is without it. </div><div class="separator" style="clear: both; text-align: left;"><div class="separator" style="clear: both; text-align: center;"><div class="separator" style="clear: both; text-align: center;"><br /></div></div><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-PpnwnOmZKkk/X94bamDZ5QI/AAAAAAAAbJQ/KBsvGI6onK4zV4uMiVxOcBMOoI8TH-OlwCLcBGAsYHQ/s518/Screen%2BShot%2B2020-12-19%2Bat%2B10.24.51%2BAM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="518" data-original-width="407" height="320" src="https://1.bp.blogspot.com/-PpnwnOmZKkk/X94bamDZ5QI/AAAAAAAAbJQ/KBsvGI6onK4zV4uMiVxOcBMOoI8TH-OlwCLcBGAsYHQ/s320/Screen%2BShot%2B2020-12-19%2Bat%2B10.24.51%2BAM.png" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-wbLv6Q4Zq54/X94balapeJI/AAAAAAAAbJM/wvGySmO-2DgOrM90S5N6dn5JNCFi6s7_wCLcBGAsYHQ/s432/Screen%2BShot%2B2020-12-19%2Bat%2B10.24.59%2BAM.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="432" data-original-width="380" height="320" src="https://1.bp.blogspot.com/-wbLv6Q4Zq54/X94balapeJI/AAAAAAAAbJM/wvGySmO-2DgOrM90S5N6dn5JNCFi6s7_wCLcBGAsYHQ/s320/Screen%2BShot%2B2020-12-19%2Bat%2B10.24.59%2BAM.png" /></a></div><div class="separator" style="clear: both; text-align: left;"><br /></div><div class="separator" style="clear: both; text-align: left;">Finally, here are some short student-made videos that you may want to use for your classes.</div><ul style="text-align: left;"><li><a href="https://drive.google.com/file/d/1yr08shQq1Ru2fz-pMQzTjj-2ahQa1Bun/view?usp=sharing">Student made video on how to <b>animate in the shape of absolute value.</b></a></li><li><a href="https://drive.google.com/file/d/1xdUarPRFEry1Gjb70j5sPP-qhIX1jVVp/view?usp=sharing">Student made video on how to <b>arrange order of shading on Desmos </b>(so one object pops in front of another) </a></li><li><a href="https://drive.google.com/file/d/1lkcoE5REKmD2RJBz2cRWsufOJtQ1l1tA/view?usp=sharing">Student made video on how to <b>shade between two graphs</b></a></li><li><a href="https://drive.google.com/file/d/10at6w6vYrRHYB854uctOWdkO7QfcaYqI/view?usp=sharing">Student made video on how to <b>rotate an ellipse</b></a><br /></li><li><a href="https://drive.google.com/file/d/1tagNquAKL58etSuebiY8Wh3oxsH-HcOp/view?usp=sharing">Student made video on how to <b>add different colors to DESMOS</b></a><br /></li></ul></div><div><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><div class="separator" style="clear: both; text-align: center;"><br /></div><br /><br /> <p></p> <script async="" charset="utf-8" src="https://platform.twitter.com/widgets.js"></script></div>Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com3tag:blogger.com,1999:blog-3454490001772574770.post-2021615484886167292020-08-07T09:54:00.001-04:002020-08-07T09:54:30.821-04:00How I'm Organizing My Class Notes for Distance Learning<p>I am just finishing my first year as an <a href="http://bulletin.miami.edu/graduate-academic-programs/education-human-development/teaching-learning/applied-learning-sciences-edd/">Applied Learning Sciences Ed.D. candidate</a> at the University of Miami. For my course, Design for Workplace Related Learning, I designed a 3-day professional development on the transitioning to distance learning, specifically for math teachers entitled <span style="font-family: "Times New Roman", serif; font-size: 12pt;"><i>Finding the Remote Control in the Math Classroom. </i>After hours of research, getting Google level 2 certification, and meeting with a focus group of math teachers from my school who told me what they needed, I curated three days of professional development on the following objectives (note, if it's in italics, it means it's specific to math teachers):</span></p><p><span style="font-family: "Times New Roman", serif; font-size: 12pt;">Math teachers should be able to:</span></p><p class="MsoListParagraphCxSpFirst" style="font-family: "Times New Roman", serif; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";"><span style="font-size: 12pt;">o</span><span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span><span style="font-family: "Times New Roman"; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> In <a href="https://classroom.google.com/">Google Classroom</a>, c</span></span>r<span style="font-size: 12pt;">eate a class template, add topics, schedule announcements to be used in the math classroom.<o:p></o:p></span></p><p class="MsoListParagraphCxSpMiddle" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><i>Create a </i><i style="color: purple; position: relative; top: 0.5pt; vertical-align: baseline;"><a href="https://jamboard.google.com/" style="color: purple; position: relative; top: 0.5pt; vertical-align: baseline;">Jamboard</a>,</i><i> </i><a href="https://whiteboard.fi/" style="color: purple; position: relative; top: 0.5pt; vertical-align: baseline;"><i>Whiteboard.fi</i></a><i> and <a href="https://padlet.com/">Padlet</a> assignment for math collaboration<o:p></o:p></i></p><p class="MsoListParagraphCxSpMiddle" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><i>Create a math quiz using </i><a href="https://docs.google.com/forms/u/0/?tgif=d" style="color: purple; position: relative; top: 0.5pt; vertical-align: baseline;"><i>Google Forms</i></a><i> and </i><a href="https://chrome.google.com/webstore/detail/equatio-math-made-digital/hjngolefdpdnooamgdldlkjgmdcmcjnc?hl=en" style="color: purple; position: relative; top: 0.5pt; vertical-align: baseline;"><i>Equatio</i></a><i> to be used on the first day of class for a check for understanding.<o:p></o:p></i></p><p class="MsoListParagraphCxSpLast" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span>Use the laptop to type or speak an annotation (using <a href="https://chrome.google.com/webstore/detail/mote-voice-notes-feedback/ajphlblkfpppdpkgokiejbjfohfohhmk?hl=en-US" style="color: purple; position: relative; top: 0.5pt; vertical-align: baseline;">mote</a>) without error.<o:p></o:p></p><p class="MsoListParagraphCxSpFirst" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><i>Scan multiple documents and upload them as one PDF to </i><a href="https://classroom.google.com/" style="color: purple; position: relative; top: 0.5pt; vertical-align: baseline;"><i>Google Classroom</i></a><i> using the Notes App so that homework and quizzes can be uploaded with one document only for ease of math grading.<o:p></o:p></i></p><p class="MsoListParagraphCxSpMiddle" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><i>Annotate a “math quiz” using the iPad and Apple pencil and return it to a “student” without error.<o:p></o:p></i></p><p class="MsoListParagraphCxSpLast" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><i>Upload a video in <a href="https://edpuzzle.com/">EdPuzzle</a> and include three questions to check for understanding, incorporating the math feature in at least one.<o:p></o:p></i></p><p class="MsoListParagraphCxSpFirst" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><i>Create a <a href="https://www.youtube.com/watch?v=ZUDoniqrUmQ">Bitmoji virtual classroom</a> with at least one interactive activity relating to math.<o:p></o:p></i></p><p class="MsoListParagraphCxSpMiddle" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span>Choose one of the building relationship activities from this <a href="https://docs.google.com/presentation/d/1qIIyltsGWQ0r6Ly2uN8p0Y9-14sm4eMGcRlvC6h5lDI/edit?usp=sharing">choiceboard</a> and tailor it specifically to the learner’s own classroom and post it in Google Classroom for the first week of school.<o:p></o:p></p><p class="MsoListParagraphCxSpLast" style="font-family: "Times New Roman", serif; font-size: 12pt; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><span style="font-family: "Courier New";">o<span style="font-family: "Times New Roman"; font-size: 7pt; font-stretch: normal; font-variant-east-asian: normal; font-variant-numeric: normal; line-height: normal;"> </span></span><i>Create a digital choice board for students that includes at least four virtual activities in math.</i></p><p><span style="font-family: Times New Roman, serif;">Now, after doing all this research and using an instructional systems design (ISD) approach to create professional development for my teachers, it was time for me to put my money where my mouth is. How was I going to design my notes for my students who are all starting remotely?</span></p><p>In comes <a href="https://slidesmania.com/">Slidesmania</a>. You have to know I've created my notes twice already for just the first day...thinking about how to open, creating a bitmoji classroom to mimic my exact in person classroom, thinking about <a href="http://udlguidelines.cast.org/">UDL</a>, meeting with our learning specialist, etc., etc., but <a href="https://slidesmania.com/free-digital-notebooks-with-sections-for-google-slides-editable-colors/">these digital notebooks using Google Slides</a> won out anything else I've researched. </p><p>Why? Look how cool it is! </p><p></p><div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-hvHGOT-C9rY/Xy1Y52Vy-MI/AAAAAAAAZHs/Qh4wgiVeSIUd2GMwyzQ0pyIrfdFw0xhBACLcBGAsYHQ/s960/swmloJpIFRXsODkWy12cpBA%2B%25281%2529.png" imageanchor="1" style="display: block; padding: 1em 0px;"></a><a href="https://1.bp.blogspot.com/-PNGKqJ3zXEY/Xy1YFW382PI/AAAAAAAAZHk/E9q14wYTHZEubcDkpZrI4pi5EwcnGt1CgCLcBGAsYHQ/s960/swmloJpIFRXsODkWy12cpBA.png" imageanchor="1" style="display: inline !important; padding: 1em 0px;"><img border="0" data-original-height="720" data-original-width="960" src="https://1.bp.blogspot.com/-PNGKqJ3zXEY/Xy1YFW382PI/AAAAAAAAZHk/E9q14wYTHZEubcDkpZrI4pi5EwcnGt1CgCLcBGAsYHQ/s640/swmloJpIFRXsODkWy12cpBA.png" width="640" /></a><img border="0" data-original-height="720" data-original-width="960" src="https://1.bp.blogspot.com/-hvHGOT-C9rY/Xy1Y52Vy-MI/AAAAAAAAZHs/Qh4wgiVeSIUd2GMwyzQ0pyIrfdFw0xhBACLcBGAsYHQ/s640/swmloJpIFRXsODkWy12cpBA%2B%25281%2529.png" width="640" /><div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-AOdJxG1RsH8/Xy1aaY1LGnI/AAAAAAAAZH4/TlpPDZk2p00D08gylsFDKk5-i0wGza5lwCLcBGAsYHQ/s960/swmloJpIFRXsODkWy12cpBA%2B%25282%2529.png" imageanchor="1" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="720" data-original-width="960" src="https://1.bp.blogspot.com/-AOdJxG1RsH8/Xy1aaY1LGnI/AAAAAAAAZH4/TlpPDZk2p00D08gylsFDKk5-i0wGza5lwCLcBGAsYHQ/s640/swmloJpIFRXsODkWy12cpBA%2B%25282%2529.png" width="640" /></a><a href="https://1.bp.blogspot.com/-AOdJxG1RsH8/Xy1aaY1LGnI/AAAAAAAAZH4/TlpPDZk2p00D08gylsFDKk5-i0wGza5lwCLcBGAsYHQ/s960/swmloJpIFRXsODkWy12cpBA%2B%25282%2529.png" imageanchor="1" style="display: block; padding: 1em 0px;"><span style="color: black;">Note that the first page of notes is my bitmoji classroom, with a plexer puzzle that will be on the board each day as well as the topic. This will be on the screen as students sign in, just as if they are walking into class. </span></a><div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-pgJkIdWbPBk/Xy1cOS48i5I/AAAAAAAAZIQ/BICqMGBBxLMfUoYmYOQOg-hMMb5RbCYuwCLcBGAsYHQ/s591/Screen%2BShot%2B2020-08-07%2Bat%2B9.50.17%2BAM.png" imageanchor="1" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="591" data-original-width="447" src="https://1.bp.blogspot.com/-pgJkIdWbPBk/Xy1cOS48i5I/AAAAAAAAZIQ/BICqMGBBxLMfUoYmYOQOg-hMMb5RbCYuwCLcBGAsYHQ/s0/Screen%2BShot%2B2020-08-07%2Bat%2B9.50.17%2BAM.png" /></a></div></div></div><p></p><p>Also, I've shown my first 24 pages of notes...I can add to them as I want, can give students a PDF version with links and slides hidden that they are not ready for so that they can print or use on Notability, if they have it. </p><div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-fdmxbI3oVcs/Xy1cZkpIEKI/AAAAAAAAZIY/6qOJArJo8egNBRzbPhwfgDT7pPTxez3XACLcBGAsYHQ/s994/Screen%2BShot%2B2020-08-07%2Bat%2B9.45.23%2BAM.png" imageanchor="1" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="659" data-original-width="994" src="https://1.bp.blogspot.com/-fdmxbI3oVcs/Xy1cZkpIEKI/AAAAAAAAZIY/6qOJArJo8egNBRzbPhwfgDT7pPTxez3XACLcBGAsYHQ/s640/Screen%2BShot%2B2020-08-07%2Bat%2B9.45.23%2BAM.png" width="640" /></a></div><br /><div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-QN6uxGm0JIs/Xy1cZinpfaI/AAAAAAAAZIU/aNwBC6FHBcAzr-_NK0tJIPXyr2KLeiCnQCLcBGAsYHQ/s980/Screen%2BShot%2B2020-08-07%2Bat%2B9.46.02%2BAM.png" imageanchor="1" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="659" data-original-width="980" src="https://1.bp.blogspot.com/-QN6uxGm0JIs/Xy1cZinpfaI/AAAAAAAAZIU/aNwBC6FHBcAzr-_NK0tJIPXyr2KLeiCnQCLcBGAsYHQ/s640/Screen%2BShot%2B2020-08-07%2Bat%2B9.46.02%2BAM.png" width="640" /></a></div><br /><div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-m4QfGKdYphE/Xy1cZuyhlbI/AAAAAAAAZIc/zqiNMaWj-kYxVGuWr_k80vkgiaEs9BrfQCLcBGAsYHQ/s983/Screen%2BShot%2B2020-08-07%2Bat%2B9.49.56%2BAM.png" imageanchor="1" style="display: block; padding: 1em 0px;"><img border="0" data-original-height="655" data-original-width="983" src="https://1.bp.blogspot.com/-m4QfGKdYphE/Xy1cZuyhlbI/AAAAAAAAZIc/zqiNMaWj-kYxVGuWr_k80vkgiaEs9BrfQCLcBGAsYHQ/s640/Screen%2BShot%2B2020-08-07%2Bat%2B9.49.56%2BAM.png" width="640" /></a></div><p>What are you doing that will make Distance Learning organized for your students? Please share in the comments below!</p><div class="separator" style="clear: both;"><div class="separator" style="clear: both;"><a href="https://1.bp.blogspot.com/-AOdJxG1RsH8/Xy1aaY1LGnI/AAAAAAAAZH4/TlpPDZk2p00D08gylsFDKk5-i0wGza5lwCLcBGAsYHQ/s960/swmloJpIFRXsODkWy12cpBA%2B%25282%2529.png" imageanchor="1" style="display: block; padding: 1em 0px;"><p><br style="color: black;" /></p></a></div><a href="https://1.bp.blogspot.com/-hvHGOT-C9rY/Xy1Y52Vy-MI/AAAAAAAAZHs/Qh4wgiVeSIUd2GMwyzQ0pyIrfdFw0xhBACLcBGAsYHQ/s960/swmloJpIFRXsODkWy12cpBA%2B%25281%2529.png" imageanchor="1" style="display: block; padding: 1em 0px;"><br /></a></div><p><span style="font-family: "Times New Roman", serif; font-size: 12pt;"><br /></span></p><p><span style="font-family: "Times New Roman", serif; font-size: 12pt;"><br /></span></p><p class="MsoListParagraphCxSpFirst" style="font-family: "Times New Roman", serif; margin: 0in 0in 0in 71.9pt; text-indent: -0.25in;"><br /></p><p></p>Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com3tag:blogger.com,1999:blog-3454490001772574770.post-6971838719608584612020-04-29T09:38:00.000-04:002020-04-29T10:04:29.313-04:00Unit Circle Projects 2020, Quarantine Edition!<div class="separator" style="clear: both; text-align: center;">
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<a href="http://2.bp.blogspot.com/-i5ygzBNyPMI/XqbeivrDpgI/AAAAAAAAGh0/p5VF7fp-MTcgXK3OE-BwpZC_JCcbZTswACK4BGAYYCw/s1600/Unit%2Bcircle%2Bproject%2B%2528due%2Bat%2B11_59pm%2529%2B%2528Apr%2B24%252C%2B2020%2Bat%2B12_26%2BPM%2529%2B%25281%2529.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://2.bp.blogspot.com/-i5ygzBNyPMI/XqbeivrDpgI/AAAAAAAAGh0/p5VF7fp-MTcgXK3OE-BwpZC_JCcbZTswACK4BGAYYCw/s320/Unit%2Bcircle%2Bproject%2B%2528due%2Bat%2B11_59pm%2529%2B%2528Apr%2B24%252C%2B2020%2Bat%2B12_26%2BPM%2529%2B%25281%2529.png" width="240" /></a><a href="http://1.bp.blogspot.com/-T47A26U1h9o/Xqbep75dtyI/AAAAAAAAGh8/xdiLP5-q_6M3Rrz9NnJrDhqvnPs0aVplwCK4BGAYYCw/s1600/Unit%2Bcircle%2Bproject%2B%2528due%2Bat%2B11_59pm%2529%2B%2528Apr%2B25%252C%2B2020%2Bat%2B11_01%2BPM%2529.png" imageanchor="1"><img border="0" height="320" src="https://1.bp.blogspot.com/-T47A26U1h9o/Xqbep75dtyI/AAAAAAAAGh8/xdiLP5-q_6M3Rrz9NnJrDhqvnPs0aVplwCK4BGAYYCw/s320/Unit%2Bcircle%2Bproject%2B%2528due%2Bat%2B11_59pm%2529%2B%2528Apr%2B25%252C%2B2020%2Bat%2B11_01%2BPM%2529.png" width="240" /></a><br />
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Every year, my students create a unit circle project. It's all described <a href="http://eatplaymath.blogspot.com/2018/04/my-best-unit-circle-projects-2018.html">here</a>, in a previous blog post with lots of links to former projects as well. However, this year, due to COVID-19, the rules for the project was not to buy anything for the project itself (i.e., posterboard, markers, etc.), but to ONLY use what you have around the house. The results were amazing. I also normally don't allow baking for the projects, but this year, that was fine...and boy did I get some delicious looking projects! I clearly I have some artistic and creative students!<br />
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Here they are:<br />
<a href="http://1.bp.blogspot.com/-cPL2pK_12OE/Xqbe_qkKeUI/AAAAAAAAGiY/oLBWMCIBZ4c1ILSKjVJwNff2gCbttl0mACK4BGAYYCw/s1600/side%2Bview.jpeg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="320" src="https://1.bp.blogspot.com/-cPL2pK_12OE/Xqbe_qkKeUI/AAAAAAAAGiY/oLBWMCIBZ4c1ILSKjVJwNff2gCbttl0mACK4BGAYYCw/s320/side%2Bview.jpeg" width="240" /></a><a href="http://2.bp.blogspot.com/-w3rgnFBgj8E/Xqbe-ItBwfI/AAAAAAAAGiQ/JM2T_couZBQJf8f6CehYexSAZFOrwzrdwCK4BGAYYCw/s1600/giant%2Bfrench%2Bmacaron%2Bunit%2Bcircle.jpeg" imageanchor="1"><img border="0" height="301" src="https://2.bp.blogspot.com/-w3rgnFBgj8E/Xqbe-ItBwfI/AAAAAAAAGiQ/JM2T_couZBQJf8f6CehYexSAZFOrwzrdwCK4BGAYYCw/s320/giant%2Bfrench%2Bmacaron%2Bunit%2Bcircle.jpeg" width="320" /></a><br />
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<tr><td class="tr-caption" style="text-align: center;">This student made the pizza from scratch!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">The Unit Volcano "China Quarantine Edition" (my student is back in China.)</td></tr>
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<a href="http://1.bp.blogspot.com/-SRKxfrC2Ypw/XqjGdMRi8aI/AAAAAAAAGmI/xaq6gaZs4TAe6el2Rx6BXsmEQcho2DvrQCK4BGAYYCw/s1600/IMG_3616.JPG" imageanchor="1"><img border="0" height="240" src="https://1.bp.blogspot.com/-SRKxfrC2Ypw/XqjGdMRi8aI/AAAAAAAAGmI/xaq6gaZs4TAe6el2Rx6BXsmEQcho2DvrQCK4BGAYYCw/s320/IMG_3616.JPG" width="320" /></a><br />
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<a href="https://drive.google.com/drive/folders/1wgbqe5AhbPj0YParUI2ohlbhMuH4Dztj?usp=sharing">Student made unit circle through Mine Craft</a></div>
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<a href="https://www.khanacademy.org/computer-programming/mrs-winer-math-circle/6080579533946880">Student programmed unit circle app through Khan Academy</a></div>
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Disclaimer: The projects below were from first semester and were NOT done during Quarantine...but I was saving these pictures to post all at the same time: </h3>
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<a href="http://3.bp.blogspot.com/-eh6USr6pAlI/Xql2TuwtPcI/AAAAAAAAGn4/p7WA7ugbaOYFmWYPYK2TLKYmAXWCwzvKACK4BGAYYCw/s1600/IMG_5540.jpg" imageanchor="1"><img border="0" height="320" src="https://3.bp.blogspot.com/-eh6USr6pAlI/Xql2TuwtPcI/AAAAAAAAGn4/p7WA7ugbaOYFmWYPYK2TLKYmAXWCwzvKACK4BGAYYCw/s320/IMG_5540.jpg" width="240" /></a><a href="http://1.bp.blogspot.com/-OykEUPZ_tXg/Xql2OfQceaI/AAAAAAAAGnw/4acVljwNoiQWr4tDX-9T6EJu1U6H0Z9JQCK4BGAYYCw/s1600/IMG_5542.jpg" imageanchor="1"><img border="0" height="240" src="https://1.bp.blogspot.com/-OykEUPZ_tXg/Xql2OfQceaI/AAAAAAAAGnw/4acVljwNoiQWr4tDX-9T6EJu1U6H0Z9JQCK4BGAYYCw/s320/IMG_5542.jpg" width="320" /></a><a href="http://2.bp.blogspot.com/-eK5B8hGxJ_U/Xql1_tKk01I/AAAAAAAAGno/e9fbB3qEWjYQzUpFhbbFfzhD0J8RZzjUACK4BGAYYCw/s1600/IMG_5541.jpg" imageanchor="1"><img border="0" height="240" src="https://2.bp.blogspot.com/-eK5B8hGxJ_U/Xql1_tKk01I/AAAAAAAAGno/e9fbB3qEWjYQzUpFhbbFfzhD0J8RZzjUACK4BGAYYCw/s320/IMG_5541.jpg" width="320" />\</a><a href="http://3.bp.blogspot.com/-tLnzzJLbROI/Xql2wzzQOfI/AAAAAAAAGow/qG1RXpuBgtYj1WMrpNjq386Q2P2aIwlVQCK4BGAYYCw/s1600/IMG_5538.jpg" imageanchor="1"><img border="0" height="240" src="https://3.bp.blogspot.com/-tLnzzJLbROI/Xql2wzzQOfI/AAAAAAAAGow/qG1RXpuBgtYj1WMrpNjq386Q2P2aIwlVQCK4BGAYYCw/s320/IMG_5538.jpg" width="320" /></a><a href="http://2.bp.blogspot.com/-I-6G4Q5sxSE/Xql26PEGdQI/AAAAAAAAGo8/IvUwe4X9DzgkfG1mEnDG_VqDQIkVnpoHgCK4BGAYYCw/s1600/IMG_5537.jpg" imageanchor="1"><img border="0" height="320" src="https://2.bp.blogspot.com/-I-6G4Q5sxSE/Xql26PEGdQI/AAAAAAAAGo8/IvUwe4X9DzgkfG1mEnDG_VqDQIkVnpoHgCK4BGAYYCw/s320/IMG_5537.jpg" width="240" /></a><a href="http://1.bp.blogspot.com/-ROgyqnN22dQ/Xql2g4NOD0I/AAAAAAAAGoY/lLJq6mI09sUBXS0ZEHuvBdRl-pYgKC6CgCK4BGAYYCw/s1600/IMG_5535.jpg" imageanchor="1"><img border="0" height="240" src="https://1.bp.blogspot.com/-ROgyqnN22dQ/Xql2g4NOD0I/AAAAAAAAGoY/lLJq6mI09sUBXS0ZEHuvBdRl-pYgKC6CgCK4BGAYYCw/s320/IMG_5535.jpg" width="320" /></a><a href="http://4.bp.blogspot.com/-ZO6EfAq6Hpk/Xql2dzopS7I/AAAAAAAAGoQ/e0LdUMGrlh4WaYk37XODt-aq_2QNldxzQCK4BGAYYCw/s1600/IMG_5544.jpg" imageanchor="1"><img border="0" height="320" src="https://4.bp.blogspot.com/-ZO6EfAq6Hpk/Xql2dzopS7I/AAAAAAAAGoQ/e0LdUMGrlh4WaYk37XODt-aq_2QNldxzQCK4BGAYYCw/s320/IMG_5544.jpg" width="240" /></a><a href="http://3.bp.blogspot.com/-gGR82KTWEos/Xql2ay8cl3I/AAAAAAAAGoI/vtA8MfNOhnoLgF-XEnon4-Y_cyqKXlBtQCK4BGAYYCw/s1600/IMG_5543.jpg" imageanchor="1"><img border="0" height="320" src="https://3.bp.blogspot.com/-gGR82KTWEos/Xql2ay8cl3I/AAAAAAAAGoI/vtA8MfNOhnoLgF-XEnon4-Y_cyqKXlBtQCK4BGAYYCw/s320/IMG_5543.jpg" width="240" /></a><a href="http://1.bp.blogspot.com/-z9Ddlpqkpqs/Xql2VxV2-NI/AAAAAAAAGoA/fzaGTg5tNA4HrIbjA-h7xHoLzOp091PuACK4BGAYYCw/s1600/IMG_5545.jpg" imageanchor="1"><img border="0" height="240" src="https://1.bp.blogspot.com/-z9Ddlpqkpqs/Xql2VxV2-NI/AAAAAAAAGoA/fzaGTg5tNA4HrIbjA-h7xHoLzOp091PuACK4BGAYYCw/s320/IMG_5545.jpg" width="320" /></a></div>
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Which one(s) are your favorite? </div>
Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com6tag:blogger.com,1999:blog-3454490001772574770.post-184003010810206042019-12-17T14:44:00.000-05:002019-12-17T19:37:59.204-05:00Conic Sections Projects using Desmos 2019 for Algebra 2 Honors or Pre-CalculusThis is only the second year that I have done Conics Projects on Desmos. (Click <a href="http://eatplaymath.blogspot.com/2017/03/a-great-conics-project-using-desmos.html">here</a> for previous Conics Desmos Project post). This year, I taught conic sections in the first semester, and so I assigned this before Thanksgiving break in case students wanted to work on it. They did a fantastic job!<br />
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I think this project is great for several reasons, but mainly:<br />
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<li>It's open-ended</li>
<li>They really learn about domain restrictions and intersections</li>
<li>They can use conic sections as well as parent functions, so it ties concepts together</li>
<li>They can relate math to something they enjoy</li>
<li>It's creative</li>
<li>They researched things I haven't taught them yet: inequalities, trig graphs, and lemniscates, for example</li>
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This year I added a peer review. I got the idea from my graduate class in Applied Learning. Each student was assigned a peer, and they had to say something that they liked about the project and something that they thought could be improved. They had to send this to me, and then I sent it to the peer, which ensured good quality and no negative comments. Then, the students had to make a change based on their peer's recommendation. Honestly, they gave better critical feedback than I ever could have! (See below for more info on the peer review).</div>
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Here are some of their projects.</h3>
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<a href="http://3.bp.blogspot.com/-Im_TBOz3IVw/XffVjt_3e5I/AAAAAAAAF80/T2XWsFJcoA0RKZhie76Hnh12xf4gtE2zACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B2.04.48%2BPM.png"><img border="0" src="https://3.bp.blogspot.com/-Im_TBOz3IVw/XffVjt_3e5I/AAAAAAAAF80/T2XWsFJcoA0RKZhie76Hnh12xf4gtE2zACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B2.04.48%2BPM.png" /></a></div>
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<a href="http://4.bp.blogspot.com/-mQ4p3u8mBDw/XfepgfstKHI/AAAAAAAAF7U/4hGSgrF_av8nhlfK-pCHLfXq65Je7RkSwCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B10.57.34%2BAM.png"><img border="0" src="https://4.bp.blogspot.com/-mQ4p3u8mBDw/XfepgfstKHI/AAAAAAAAF7U/4hGSgrF_av8nhlfK-pCHLfXq65Je7RkSwCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B10.57.34%2BAM.png" /></a></div>
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<a href="http://3.bp.blogspot.com/-aO8HsCJQQsE/Xfjn9FygfkI/AAAAAAAAF9M/yZpCGjNiu1I3olmQPN7FBwQePndVYklEACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-17%2Bat%2B9.36.14%2BAM.png"><img border="0" height="347" src="https://3.bp.blogspot.com/-aO8HsCJQQsE/Xfjn9FygfkI/AAAAAAAAF9M/yZpCGjNiu1I3olmQPN7FBwQePndVYklEACK4BGAYYCw/s640/Screen%2BShot%2B2019-12-17%2Bat%2B9.36.14%2BAM.png" width="640" /></a></div>
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<a href="http://3.bp.blogspot.com/-AbADvKwJjco/XfezQUUwwdI/AAAAAAAAF7g/s44V9ShzhIQqsGqDkvvYk8AGTZu9-bdwQCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B11.39.12%2BAM.png"><img border="0" src="https://3.bp.blogspot.com/-AbADvKwJjco/XfezQUUwwdI/AAAAAAAAF7g/s44V9ShzhIQqsGqDkvvYk8AGTZu9-bdwQCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B11.39.12%2BAM.png" /></a></div>
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<a href="http://4.bp.blogspot.com/-aCeCMOpmR8s/Xfe0Ey47hWI/AAAAAAAAF74/yvMltu5EVEAP6ly6qyYe_LJFG_VyZoZdgCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B11.42.43%2BAM.png"><img border="0" src="https://4.bp.blogspot.com/-aCeCMOpmR8s/Xfe0Ey47hWI/AAAAAAAAF74/yvMltu5EVEAP6ly6qyYe_LJFG_VyZoZdgCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B11.42.43%2BAM.png" /></a></div>
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<a href="http://1.bp.blogspot.com/-0DixCQzhxUc/XfezsmptrbI/AAAAAAAAF7s/xY32cAe5GpY1SU1vCUoxIZO7KQNIdeKAACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B11.40.53%2BAM.png"><img border="0" src="https://1.bp.blogspot.com/-0DixCQzhxUc/XfezsmptrbI/AAAAAAAAF7s/xY32cAe5GpY1SU1vCUoxIZO7KQNIdeKAACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B11.40.53%2BAM.png" /></a></div>
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<a href="http://4.bp.blogspot.com/-8qs9gupE8rI/Xfe1ABz2f6I/AAAAAAAAF8E/NCI15ZKqs4IZGazjOR4DAn0IfVWi7RgrwCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B11.46.44%2BAM.png"><img border="0" src="https://4.bp.blogspot.com/-8qs9gupE8rI/Xfe1ABz2f6I/AAAAAAAAF8E/NCI15ZKqs4IZGazjOR4DAn0IfVWi7RgrwCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B11.46.44%2BAM.png" /></a></div>
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<a href="http://3.bp.blogspot.com/-mkdzPddxb8s/XffVFIQZugI/AAAAAAAAF8c/Emiumk0cjVcphFEA74wHXN1aVOn0fA4aACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B1.53.56%2BPM.png"><img border="0" src="https://3.bp.blogspot.com/-mkdzPddxb8s/XffVFIQZugI/AAAAAAAAF8c/Emiumk0cjVcphFEA74wHXN1aVOn0fA4aACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B1.53.56%2BPM.png" /></a></div>
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<a href="http://3.bp.blogspot.com/-DSoPUX0cZNw/XffSOyE6f2I/AAAAAAAAF8Q/7ulVTZGVBZESlMJGMYly7CsUOQnEgaSZQCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B1.51.08%2BPM.png"></a><a href="http://2.bp.blogspot.com/-Nysfx3bAiFU/XffVIpgmWXI/AAAAAAAAF8k/G6olUMxEM-szFJNFnp7ivcWKjJIYqHoIACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-16%2Bat%2B1.53.36%2BPM.png"><img border="0" height="330" src="https://2.bp.blogspot.com/-Nysfx3bAiFU/XffVIpgmWXI/AAAAAAAAF8k/G6olUMxEM-szFJNFnp7ivcWKjJIYqHoIACK4BGAYYCw/s640/Screen%2BShot%2B2019-12-16%2Bat%2B1.53.36%2BPM.png" width="640" /></a></div>
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<a href="http://4.bp.blogspot.com/-d5yALiwvU9E/XfjvpRQY-_I/AAAAAAAAF-E/8z6REdlphegyQf6azgT1iny0rTxDnjTvwCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-17%2Bat%2B10.09.09%2BAM.png"><img border="0" src="https://4.bp.blogspot.com/-d5yALiwvU9E/XfjvpRQY-_I/AAAAAAAAF-E/8z6REdlphegyQf6azgT1iny0rTxDnjTvwCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-17%2Bat%2B10.09.09%2BAM.png" /></a></div>
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Examples of how the Final Project was turned in:</h3>
<a href="http://3.bp.blogspot.com/-eOrjFPdaR8I/XfjsaU7rkBI/AAAAAAAAF9k/zeBYK6pCso4oAWgbUVmpERBLpg_uFfyAgCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-17%2Bat%2B9.54.57%2BAM.png"><img border="0" src="https://3.bp.blogspot.com/-eOrjFPdaR8I/XfjsaU7rkBI/AAAAAAAAF9k/zeBYK6pCso4oAWgbUVmpERBLpg_uFfyAgCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-17%2Bat%2B9.54.57%2BAM.png" /></a></div>
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<a href="http://3.bp.blogspot.com/-tGZjECG6dbU/Xfjsg1lZ2EI/AAAAAAAAF90/B3fvdou4kusbmLYKWdXMKIMb3dvXABYoACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-17%2Bat%2B9.55.21%2BAM.png"><img border="0" src="https://3.bp.blogspot.com/-tGZjECG6dbU/Xfjsg1lZ2EI/AAAAAAAAF90/B3fvdou4kusbmLYKWdXMKIMb3dvXABYoACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-17%2Bat%2B9.55.21%2BAM.png" /></a></div>
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<h3>
Peer Review:</h3>
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How I set up the peer review. Each student sent their project to the person after the arrow. The person after the arrow then sent their response to me, which I read and then forwarded to the student. </div>
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<span style="color: black; font-family: "century gothic"; font-size: 18.0pt; font-weight: bold;"> </span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">Cristi</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">
->Will -> James->Manci-> He ->Lucas ->Bobby
->Grace ->Irina-> Leo-></span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">dylan</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">
-></span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">zach</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;"> -></span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">andres</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;"> -></span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">anthony</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">
-> </span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">niamh</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;"> -></span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">ella</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;"> -></span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">ashley</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;"> -></span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;">zhongxuan</span><span style="color: black; font-family: "century gothic"; font-size: 18.0pt;"> -></span></div>
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<span style="font-family: "century gothic"; font-size: 18pt;">blake</span><span style="font-family: "century gothic"; font-size: 18pt;">
->jack -></span><span style="font-family: "century gothic"; font-size: 18pt;">cristi</span>
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A Great Peer Review</div>
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<a href="http://1.bp.blogspot.com/-2L4_Ah8hYbI/Xfjq_RctIpI/AAAAAAAAF9Y/LoAvUOYy8qs2Qo2cBWZ7cPd2DfNo-U35wCK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-17%2Bat%2B9.49.01%2BAM.png"><img border="0" height="548" src="https://1.bp.blogspot.com/-2L4_Ah8hYbI/Xfjq_RctIpI/AAAAAAAAF9Y/LoAvUOYy8qs2Qo2cBWZ7cPd2DfNo-U35wCK4BGAYYCw/s640/Screen%2BShot%2B2019-12-17%2Bat%2B9.49.01%2BAM.png" width="640" /></a></div>
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Here is my Rubric.</h3>
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<b style="mso-bidi-font-weight: normal;">RUBRIC 30 POINTS
TOTAL</b></div>
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_____ 4 points Creativity</div>
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_____ 3 points Colorful</div>
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_____ 5 points Sophistication of conics</div>
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_____ 4 points Use of domain restrictions</div>
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_____ 5 points Final project with all conics shown
prominently is printed <b>in color do not
wait till the last minute to do this, nor have poor printer quality</b> and
pasted on construction paper<b></b></div>
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_____ 4 points Equations printed out and pasted next to
picture on construction paper (can go off the </div>
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page if
necessary.) </div>
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______5 peer review turned in on time (-2 if late per day)
(graded separately – not part of 30 points)</div>
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______5 peer review emailed to me (graded separately - not
part of 30 points)</div>
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______5 corrections based on peer review </div>
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How this project related to my Doctoral study in the Applied Learning Sciences</h3>
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(Excerpt from my paper)</div>
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<span style="mso-bidi-font-weight: bold;">I believe that the way I teach is an amalgamation of several learning
theories: Piaget’s constructivism, Papert’s constructionism, Vygotsky’s social
constructivism, and even Behaviorialist theory, when I need to get facts across
quickly. However, with my learning project, I am going to focus on Papert’s
Constructionism, where </span><span style="color: #333333;">“learners make
knowledge their own,” (Kafai, 2006 p. 39) and physical objects are important.
Using ideas gleaned from Piaget when he worked with him in Geneva, Seymour Papert
found it was possible to learn abstract concepts concretely through
objects-to-think-with. The objects my students will think with are graphs of
conic sections. As of this writing, my students are learning how to graph and
find equations of conics, yet I believe that they do not quite have ownership
of the concept. It is something they know they need to study to pass the
course, but I think that the topic is abstract and separate from them. Through
the creative drawing activity, students will be transforming the ideas taught
in the classroom and will express them through the website Desmos.com. Similar
to LOGO, students will create designs of their choosing by “telling” the
computer what to do; in this case, entering equations and playing with them
until they are in the “correct spot,” that is, getting it out of their heads
and onto paper. Every student can (and is encouraged to) relate conics to
something that they enjoy, for example: create a beach scene, a zoo, a hockey
arena, or a videogame scene, for example. The hope is that they will appropriate
their knowledge to make it their own (Kafia, 2006).</span></div>
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<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in; margin-left: .5in; margin-right: 4.5pt; margin-top: 0in; text-indent: -.5in;">
Kafai, Y. B. (2006).
Constructionism. In R. K. Sawyer (Ed.), The Cambridge handbook of the
learning sciences (1st ed.) (pp. 35–46). Cambridge, England: Cambridge
University Press.</div>
<br />Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com7tag:blogger.com,1999:blog-3454490001772574770.post-41467794340154655452019-12-17T11:31:00.000-05:002019-12-17T11:31:01.752-05:00Math Poetry Project!My school has a Literary Magazine that gets published once a year. They ask for submissions from all students, and this year, I decided to offer an optional 20 point project where students had to write a poem about math. It was very open-ended, but it had to be worthy, in my mind, of submission. In other words, no, a Haiku did not count (yes, that was asked!) The only requirement was that students had to get a writing conference beforehand (and submit rough drafts to me, where I helped them as well.)<br />
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The results were fantastic! I strongly suggest this project because it gives students a way to discuss math and reflect on math that they so rarely get to do. So many were about anxiety. I hope writing about it made them feel better! Some are also written by students for whom English is a second language, which definitely was out of their comfort zone. I am really proud of all of my students who submitted a poem. Here are some of them, my favorite being the first one on Fixed vs. Growth mindset.<br />
<a href="http://2.bp.blogspot.com/-3jPF5ET4Wk8/XfjzAAH79LI/AAAAAAAAF-Q/FWbAvFqaOoYK3E77a8TCrMEFMudJDl20ACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-10%2Bat%2B2.01.27%2BPM.png" imageanchor="1"><img border="0" src="https://2.bp.blogspot.com/-3jPF5ET4Wk8/XfjzAAH79LI/AAAAAAAAF-Q/FWbAvFqaOoYK3E77a8TCrMEFMudJDl20ACK4BGAYYCw/s1600/Screen%2BShot%2B2019-12-10%2Bat%2B2.01.27%2BPM.png" /></a><br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Test Day</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Today is the day of the big math test </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Last night I studied so much I got no rest </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">As the day continues I know what’s coming </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I get all nervous and my brain starts humming </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I used to arrive and take out my pencils </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But now I unpack all the utensils </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Add calculators and compasses to the list</span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Once the bell rings, I clench the pencil in my fist </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">As the teacher begins the short review </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I start to feel like I might have the flu</span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I try to listen and pay attention</span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But I simply can’t with all this tension </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I need every fraction of a second I can get </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And as the time runs down I begin to sweat</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I look up at the clock, watching the hands tick </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And stare at my paper. Which answer to pick?</span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">As I see everyone starting to finish </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">My hope of scoring well is beginning to diminish </span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I must finish this page quick </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">With all this stress, I might get sick</span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Just as I’m about to turn it in </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">My entire head begins to spin </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I check through the test just once more </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Searching for any mistakes that would lower my score</span></div>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">The test is finally over now </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And the only thought in my mind is “wow”</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">After a few days of anxiously waiting </span></div>
<br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 11.5pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">It turns out I got a pretty good rating!</span></div>
<div>
<br /></div>
<div>
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951"></span><br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951"><span style="font-family: "habibi" , serif; font-size: 18pt; vertical-align: baseline; white-space: pre-wrap;">Infinity</span></span></div>
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951">
</span>
<br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951"><span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">Shall I compare it to a school’s day?</span></span></div>
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951">
</span>
<br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951"><span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">It is greater than all the galaxies,</span></span></div>
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951">
</span>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951"><span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">A buffet of values that can’t be weighed.</span></span></div>
<span id="docs-internal-guid-09ab5bf3-7fff-c077-613a-b117fe8cf951">
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">Earth cannot contain its immensity</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">So grand, so fine, in its complexity,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">When others try to count it, it’s in vain,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">As abundant as the Aegean sea.</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">If others try to grasp it, it’s their bane;</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">Its eternalness will never once fade.</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">As many digits as there are in pi</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">Its size is comparable to a parade.</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">It is impossible to specify;</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">It is always a magnificency;</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "habibi" , serif; font-size: 14pt; vertical-align: baseline; white-space: pre-wrap;">It stays the largest, as infinity.</span></div>
<span id="docs-internal-guid-e24a4b47-7fff-054a-8745-a3adf64bcc01"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
<span id="docs-internal-guid-f3378a80-7fff-7fa9-1ab3-d5b7b452902d"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">He met math</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">With a glance</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Through his lens</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">And loved it twice.</span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Once in China</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">In Winter with ice</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Once in English</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">In one long always warm season</span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">In different schools,</span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Low low scores,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">On math tests,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Vanished his smiling face.</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Every night, he studied and suffered. </span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Many, many times</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">A barrier of languages tricked him. </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Time, and the sand flowing in the hourglass</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Hid his broken heart.</span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Math made him hurt.</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Math made him love.</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">He was and is hurt by the scores </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">But among all subjects,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">Math affects him the most</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "courier new"; font-size: 14pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;">His love since he was small.</span></div>
<div>
<br /></div>
<span id="docs-internal-guid-8cae5f4d-7fff-c646-cdee-4e592eba4d72"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Today is the day of the big math test </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Last night I studied so much I got no rest </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">As the day continues I know what’s coming </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I get all nervous and my brain starts humming </span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I used to arrive and take out my pencils </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">But now I take out all the utensils </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Add calculators, compasses, and graph paper to the list</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Once the bell rings, I clench the pencil in my fist </span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">As the teacher begins the short review </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I feel like I might have the flu</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I try to listen and pay attention</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">But I simply can’t with all this tension </span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I need every fraction of a second I can get </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">And as the time runs down I begin to sweat</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I look up at the clock, watching the hands tick </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">And stare at my paper. Which answer to pick?</span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">As I see everyone starting to finish </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">My hope of scoring well is beginning to diminish </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I must finish this page quick </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">With all this stress, I might get sick</span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Just as I’m about to turn it in </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">My entire head begins to spin </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I check through it once more </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Searching for any mistakes that would lower my score</span></div>
<br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">The test is finally over now </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">And the only thought in my mind is “wow”</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">After a few days of anxiously waiting </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "times new roman"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">It turns out I got a pretty good rating.</span></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<br /></div>
<div style="text-align: center;">
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">In eighth
grade, I was so good at math,<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Now that
thought just makes me laugh.<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Nine more
hours till the test,<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Just keep
studying and hope for the best.<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<br /></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Slope, range,
and domain<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">All floating
through my brain.<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Seven more
hours I have to study<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">To try to make
Algebra II my buddy.<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<br /></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">So many
formulas in my head,<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Don’t think I
will ever get to bed.<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Five more
hours till the test,<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Now is not the
time to rest.<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<br /></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">The long word
problems cause me pain,<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">There’s my
grade down the drain.<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Three more
hours to gain knowledge,<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">With a C in
math, will I get into college?<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<br /></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">As graphs of
equations circle my brain<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">I wonder, will
conics drive me insane?<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">One more hour
until I’m done.<o:p></o:p></span></div>
<div align="center" style="margin-bottom: .0001pt; margin: 0in; text-align: center;">
<span style="color: black; font-family: "Times","serif"; font-size: 13.5pt;">Maybe studying
functions will be more fun.<o:p></o:p></span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"><b><br /></b></span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"><b>In-Test Stress</b></span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Equations flowing through my veins</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Transformations filling up my brains</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Numbers racing through my head</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">“You don’t need to study more!” is what my mom said</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Little did I know that she was very incorrect</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">It seems that this test has surpassed my natural intellect</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">As I search my memory for previous knowledge</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">I question if I will ever be accepted into my dream college</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">I know, I know, I’m being melodramatic</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">But how in the world does one graph a quadratic?</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Parabolas, hyperbolas, curves, and more</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">It’s looking like I won’t get a good score</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">But then it comes to me, parent functions and all!</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Maybe this test won’t be my downfall</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">My pencil starts to write very fast</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">I begin to put my confusion into the past</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Domain and range? Easy, I know this</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">There is not one question that I will miss!</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Seven minutes remaining on the clock</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">I’m reviewing my answers, my focus in lock</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Two minutes to go and I turn in my test.</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">A huge weight has been lifted off my chest.</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Next time, I will make sure not to get so upset</span></div>
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<span style="font-family: "arial"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Because if I try my best, it’s a deserving grade I will get.</span></div>
</span></span></div>
<div>
<span id="docs-internal-guid-562af8b6-7fff-3bd9-411e-b00720408701"></span><br />
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<span id="docs-internal-guid-562af8b6-7fff-3bd9-411e-b00720408701"><span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><b>Life is Mathematic</b></span></span></div>
<span id="docs-internal-guid-562af8b6-7fff-3bd9-411e-b00720408701">
</span>
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<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span id="docs-internal-guid-562af8b6-7fff-3bd9-411e-b00720408701"><span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Life can be like a linear function</span></span></div>
<span id="docs-internal-guid-562af8b6-7fff-3bd9-411e-b00720408701">
</span>
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<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span id="docs-internal-guid-562af8b6-7fff-3bd9-411e-b00720408701"><span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">But when challenges arise, it’s like the sine</span></span></div>
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</span>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span id="docs-internal-guid-562af8b6-7fff-3bd9-411e-b00720408701"><span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Challenges can give life vibration</span></span></div>
<span id="docs-internal-guid-562af8b6-7fff-3bd9-411e-b00720408701">
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">While without them life is a straight line</span></div>
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<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Life can be like a linear function</span></div>
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<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">While troubles can be like holes</span></div>
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<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Holes may halt the function</span></div>
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<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">But the function always continues</span></div>
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<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Life can be like a linear function</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">And your attitude can be the slope</span></div>
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<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">A positive attitude gives life ascension</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">While a negative attitude can only cause a drop</span></div>
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<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Life can be like a linear function</span></div>
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<span style="font-family: "arial"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">And I hope you perceive your life with satisfaction</span></div>
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<br /></div>
</span></div>
<div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are like karma, </span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">you give something you get something.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are unique,</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">different parent functions and different graphs.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions must pass a test, </span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">a vertical line on a graph to prove one input goes to exactly one output.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions can be treated like numbers, </span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">you can subtract, multiply, divide, and add them together.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions can be like mountains,</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">intervals of increases and decreases, and peaks and troughs.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are like long movies,</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">sometimes they just never seem to end.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are also like toddlers,</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">they can’t always go very far before stopping.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are like elevators, </span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">they go up and down but not always forever.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions can be expressed in many forms, </span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">equations, graphs, maps, or tables.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are like rollercoasters,</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">up and down, and steep and not.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are patterns, </span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">easy to predict and always following a rule.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are like a crystal ball,</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">they help us to predict the future.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are like glasses, </span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">they enable us to see and visualize real-world things.</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Functions are like blueprints,</span></div>
<span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span id="docs-internal-guid-038d3885-7fff-6fed-ab72-de4d01bcf870"></span></span><br />
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">they enable us to easily understand how the world works the way it does.</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><br /></span></div>
<span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">
</span>
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<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">It winds you through its paths</span></span></div>
<span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">
</span>
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<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Gives you calculations on top of calculations</span></span></div>
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</span>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">All in pursuit of the satisfying solution</span></span></div>
<span style="font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But, make one mistake</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And that answer is gone</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">So very treacherous</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">These twists and turns</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Of mathematics can be</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Equations on top of equations</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Operations, for example</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Can put you on a rollercoaster of math </span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Like the graph of sine</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And then, after so much calculation</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">The work results in one painfully simple solution</span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Like one</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">(5xy + 6x^7+9y^18)^0</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">If one does not notice</span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">In a brief moment of not paying attention</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">That there is an exponent 0</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">They might puzzle themselves with the problem for hours</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Mathematics</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">The solving of every problem is a journey</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Filled with highs and lows </span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Like the maxes and mins of a parabola</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">At some points, the min is hit</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">One might consider giving up </span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But when they decide to continue</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And then finally scramble through the last calculations</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And box in the set of numbers that answers their questions</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">How satisfyingly simple it is</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">What a numerical miracle</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">What a feeling of giddiness fills the person at that very moment</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Because of mathematics</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Mathematics, which is really just</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">One long, arduous journey </span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Made up brick by brick </span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Problem by problem</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Number by number</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><br /></span></div>
<br /><br /><span id="docs-internal-guid-35066796-7fff-daab-a006-5d32aa5d26b5"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">focusing, scribbling, erasing, and rewriting</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">these are parts of the thrill of math.</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">graphing, translating, reflecting, and shifting </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">even if it involves making mistakes</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">when you’re passionate about something</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">just doing it sparks joy</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">sitting, plotting, computing, and </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">graphing, translating, reflecting, and shifting</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">can bring such satisfaction.</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">formulating, equating, expressing, and understanding,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">it requires hard work,</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">time</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">dedication</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">and passion</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">but in the end, it is worth it.</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">working, thinking, calculating, and stretching your brain</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">when the difficulty rises,</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">there are challenging problems,</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">that are not so easy.</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">but a part of the joy of solving</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">is doing these things</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">in ways you might not have th</span><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: center; vertical-align: baseline; white-space: pre-wrap;">The Missing Variable: x</span><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: center; vertical-align: baseline; white-space: pre-wrap;"><span style="font-size: 0.6em; vertical-align: super;">2</span></span><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; text-align: center; vertical-align: baseline; white-space: pre-wrap;"> + 9x + 20 = 0 </span></div>
</span><span id="docs-internal-guid-506ccf45-7fff-a4b2-3fd5-ea6dc3c1baa0"><br /><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Something is missing</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">An incomplete whole</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">For x I can’t find</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Its answer, my goal</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The problem seems hard</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">We do not comprehend</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Try and we try</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">But we hit a dead-end</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">We cannot give up</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Commitment is key</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">We must solve for x</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Then we’ll be free</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Digits on the right</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Then zero we said</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Quadratic formula?</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Factoring instead</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Put parenthesis</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">X has been squared</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">For two solutions</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Do not be scared</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Nine’s the coefficient</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">But it’s not lonely</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">There is a constant</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Of twenty only</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Multiplies as twenty</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Adds to be just nine</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I will guess and check</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Till these numbers fit fine</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Could it be two and ten?</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">When added, twelve is seen</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">What about six and three?</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Multiplied it’s eighteen</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Factoring is hard</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Too many numbers</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Forever my mind</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Will be full of wonders</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Wait! I got it?</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The answer is mine</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Added it’s twenty </span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Together it’s nine</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">After many efforts</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Four and five will work</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The problem’s nearly done</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Soon I can smirk</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">X plus five is zero</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">also works with four</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Just two solutions</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">There are not any more</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Now subtract the numbers</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Onto the other side</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Negative four, negative five</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I am filled with pride</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">X was hard to find</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">There was a struggle</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">With math you must grind</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">But after the trouble</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">There has been a breakthrough</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Something is clear</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">You have reached success</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The end, you are here</span></div>
</span><div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 2.4; margin-bottom: 0pt; margin-top: 0pt; text-align: center; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 24pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Night-gebra</span></div>
<span id="docs-internal-guid-9b877eec-7fff-bee7-6c90-26de0cdaeea7"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">By my nightlight, I study my book</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I’ll learn these equations</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">By hook or by crook</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Hours are spent finding eccentricities</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Staring at these complex ellipticities</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I scramble to simplify</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">As I kiss my sleep goodbye</span></div>
<br /><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">I put in my airpods</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Thinking about the odds</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The rhythm makes me tap</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Feeling it’s a trap</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Wishing I could figure it out </span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">But all I do is doubt</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">My abilities?</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">All liabilities!</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">The crescent moon shines into my window</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Oh how I wish to lay on my pillow</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">But the problems go round and round with no near end</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">As I search every corner for a dividend</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">My morning alarm starts to blare</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Algebra hates me, I swear</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">Should I give up and just stay at home?</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;">It’s easier to write a poem!</span></div>
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<span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;"><b>Sir Cull</b></span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">360 degrees </span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">and a shape that always puts you at ease,</span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I come in all different sizes, always aiming to please.</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I am defined by area, which can vary,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But fear not, my radius and pi are not very scary.</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">There is also an equation for my shape, which has many components</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">If you know these are the center and radius, then you are in the bonus!</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">The points defined as the center are k and h,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But be careful because in the equation, they are not so great!</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><br /></span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">They are not so great because they are opposites of their true value</span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Which trips people up and makes them blue.</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">H is subtracted from X while Y subtracts K,</span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Don’t forget to put each in parentheses and square, or Mrs. Winer will not let you stay!</span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Do not get excited as there are a couple more steps,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But do not be scared because these are easier than the rest!</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Add an addition sign between the two terms, which will almost wrap it up,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Then do not forget to add an equal sign, and the last term is abrupt!</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><br /></span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">The most important part as we see it in every circle equation,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">It is the radius, and will never go under the process of evasion!</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Don’t forget to square the radius at the end though,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Because if you do not, the problem will not flow!</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Last but not least, there is another term that you can not forget,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">It is defined by 2𝛑r, so don’t you fret!</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">It defines the perimeter of the circle, which is essential,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But do not overhype the circumference, as it is not always frequential.</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">As you can see, circles like me are fun,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Just because they are complicated does not mean they cannot be a pun.</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">After all, everyone is complicated and that is a fact,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Without complications no one would be in tact.</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And most importantly, without problems, there would not be math,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">And without math, the idea of me, as a circle, would never be in your path!</span></div>
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<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Maybe you guessed, maybe you could not</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">But I am the greatest, being the only alive shape that you got.</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">I am the one,</span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">The only,</span></div>
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<span style="background-color: transparent; color: black; font-family: "times new roman"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"></span></div>
<div dir="ltr" style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;">Mr. Sir Cull</span></div>
<div style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"><br /></span></div>
<div style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"></span><br />
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Clarity in the Storm</span></div>
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<b id="docs-internal-guid-ef5e0b23-7fff-50d3-51ac-ac84dce31e76" style="font-weight: normal;"><br /></b></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Swirls of numbers,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">No order to be found</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">They run rapidly through my mind</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">The pieces don’t fit,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I see no respite from the chaos</span></div>
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<b style="font-weight: normal;"><br /></b></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Then slowly the storm starts to calm,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">With time I see clearly,</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I’m no longer overwhelmed</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Every breath calms me </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">The world stops spinning </span></div>
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<b style="font-weight: normal;"><br /></b></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Deep breath,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Step one,</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Deep breath,</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Step two,</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">The clouds are fading away </span></div>
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<b style="font-weight: normal;"><br /></b></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Finally, I’ve opened a gap in the clouds</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Patterns,</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Everywhere, they repeat </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">They guide me forwards</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Clarity like never before</span></div>
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<b style="font-weight: normal;"><br /></b></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Before, the storm swept me up,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">But now, I’m carried high above the chaos below</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Winds swirl like cube root functions</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I’m lifted through inequalities and decimals</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I feel a weight lifted from my shoulders</span></div>
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<b style="font-weight: normal;"><br /></b></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">The equations start to fit,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Pieces connect in new ways,,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">The chaos of the storm is gone</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">What I need is right here,</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I’ve made sense of what’s in front of me</span></div>
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<b style="font-weight: normal;"><br /></b></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Something shimmers in the distance</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">The concept floats closer and closer</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Through the mist I see it faintly, </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Warm rays meet me with satisfaction</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">The answer to my confusion is here</span></div>
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<br /></div>
</div>
</div>
<div style="background-color: transparent; color: black; font-family: "Times New Roman"; font-size: 11.5pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; text-decoration-line: none; white-space: pre-wrap;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre;"></span><br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Today has been a long day</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I have had so much to do</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I can’t even find the right words to say </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">But I have to see the day through.</span></div>
<b id="docs-internal-guid-866d4ee0-7fff-7f9f-9de9-3fc7a8e14591" style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I may have drifted off in class</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I probably should have paid more attention</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">But I didn’t realize we were going so fast </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">And I know you have the best intention</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I started to focus again </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">And looked at the board</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">But all I saw were marks of pen</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">And my brain just spiraled downward</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">So I find it a bit of a challenge</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">To be the best, to know the most</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">When the lack of sleep has done so much damage</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">All day during school I feel like a ghost. </span></div>
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<br /></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I can’t seem to grasp the concepts like everyone else</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I take a bit more time</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">But when I do, the feeling is like nothing else </span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">And the world feels like it’s mine</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">There come the days I want to give up</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">Because I get the problem wrong every time</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">My world is not going to blow up </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">So I need to finish the climb</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I wake up I study </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I study all day</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I always feel so cruddy</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">And I never have time to play </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">But when I get the problem right</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">I feel like I can touch the sky</span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">My face lights up so bright</span></div>
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<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap; white-space: pre;">And you can see teardrops in my eye</span></div>
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Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com2tag:blogger.com,1999:blog-3454490001772574770.post-54737617429700699322019-06-18T16:43:00.002-04:002021-03-25T13:46:35.999-04:00Taking Students on an Immersion Trip to Peru! Climbing to New Heights.<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
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I am so fortunate to work at a school that has an immersion program. Previously, I have taken students to Quebec, Greece, and Ireland. This year, my department chair, Carlton and I took a group of 11 students to Peru. Carlton and I spent a good amount of time Skyping with Dustin from <a href="https://rusticpathways.com/">Rustic Pathways</a> months before to create the perfect Peru immersion. When I bring students on immersions, my goal is to incorporate adventure for students and that are "once in a lifetime" events. Carlton's goal is to incorporate community service. Dustin helped us create a terrific combination of both that definitely did not disappoint. My son had done several Rustic Pathway trips, including Peru, so I knew we were in good hands.<br />
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The day after graduation, we all boarded a non-stop flight from Fort Lauderdale to Lima, Peru. Non-stop was definitely the way to go, and it was only about a six or seven-hour trip. The only surprise was that we did not get meal service on Jet Blue during this lengthy evening trip, so we had to purchase our own meals, which consisted of a decent turkey sandwich. Carlton and I discovered that we are similar in that we always like to "feel full" when we travel - so we were constantly eating. We were abundant with snacks and great kids in tow: six upcoming seniors and five upcoming juniors...interesting dynamics for sure, especially since this included 10 girls and only one boy!<br />
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I should mention that we like to meet the kids out before we leave for immersion. We met them for lunch at a <a href="https://www.warikeboca.com/">Warike</a>, a Peruvian restaurant in Boca about a month before leaving. It was a great way to get to know the kids and to begin to think about the culture we were about to dive into. Of the 11 students, I taught five of them previously and did not know the other six yet at all. What started off with awkward conversations in a restaurant in Boca soon became close-knit group discussions by the end of the trip. It was fun to see it unfold.<br />
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<br />Days 1 and 2</h3>
We landed in Lima and were greeted by our Rustic Pathways leader for the week, Sofia. We were surprised to find out that she was from Boca, too! She made us feel right at home. She was funny, fully animated, and always excited. We loved her jokes and found her "resting concern face" endearing. We boarded the bus quite easily and made our way to a vegan restaurant for dinner. We stayed overnight in Lima, had breakfast at the hotel the next morning, and headed to the airport for a quick flight to Cusco in the morning.<br />
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This day was a bit of a blur. Flying again and adjusting to the altitude really took on the bulk of the day, and I don't remember much! But we did walk around Cusco City and checked into our hotel for the night, which would be the only hotel we would stay in for more than one day in a row (three days.) We also met our other trip leader, a Peruvian named Raul who worked with National Geographic in the past. He was a HUGE wealth of knowledge! Between him and Sofia, we immediately felt at ease and knew we were in excellent hands for the entirety of this trip. Most importantly, we needed to: 1) Drink copious amounts of the water that Rustic Pathways always had on-hand for us, and 2) Not pet any of the dogs or other animals that were so cute and were always following us around (this was hard!) 3) Realize that Carlton was now forever known as Carlos.<br />
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<a href="https://1.bp.blogspot.com/-Nubo2X-Ja6Y/XQjrCRarltI/AAAAAAAAFSQ/arda1uPCUwwkkZN-T_TA0tq1UHJTHpwZgCLcBGAs/s1600/IMG_3143.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-Nubo2X-Ja6Y/XQjrCRarltI/AAAAAAAAFSQ/arda1uPCUwwkkZN-T_TA0tq1UHJTHpwZgCLcBGAs/s320/IMG_3143.JPG" width="240" /></a></div>
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Gorgeous views landing in Cusco</div>
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An alpaca and a woman in Sacsaywaman </div>
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Cusco</div>
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The Sacred Valley</div>
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Famous Inca wall in the narrow alley of Loreto, Cusco</div>
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Another vegan meal - nothing too heavy so we could adjust to the altitude.</div>
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Back at the hotel in Calca, Sofia got the group together and did some get-to-know-you activities. She also promised to tell each of us what our individual "personality pasta" was by the end of the trip. We went to bed early to get ready for a full day of community service the next day.</div>
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<h3>
Days 3 - 5</h3>
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We had breakfast at the hotel, which usually consisted of amazing bread, eggs, and coffee. The coffee was served cold, and you were supposed to pour hot water in it to heat it up and to make it very watered down. It took a lot of broken Spanish on my part and broken English on the owner's part, but I got full-blast delicious coffee without the hot water - I just had to heat it in the microwave. I think the owner was floored that I would dare to drink my coffee this way - so strong and so delicious!</div>
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<tr><td class="tr-caption" style="text-align: center;">The traditional and amazing bread had with butter and jam or eggs and avocado along with fresh pineapple or papaya juice.</td></tr>
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We had no idea what our community service activity would be. We wondered if it would be painting, building guinea pig (<i>cuy</i>) hutches...what could it be? All we knew was that we would be working to beautify a girls' dorm for girls who otherwise would have had to walk maybe 5+ hours a day to be able to attend school. These girls spoke the native language of Quechan but also were learning Spanish and English in addition to all of their other studies!</div>
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We walked to the school from our hotel and were given our task: to dig a garden on the side of the school. At our site were a number of shovels, pickaxes, a wheelbarrow, a big filter to filter out large rocks from dirt that was to be scooped, and lots of buckets. We slathered on our sunscreen, donned our hats, chose our gloves, and went to work. </div>
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This work was not for the weary. After about 30 minutes, I truthfully could not believe we signed up for this! While several students were working <b>very</b> hard, a few felt the same way as me - this was difficult manual labor...and we had 3 full days ahead of us! The work entailed pickaxing at dirt and rocks and then scooping the dirt to be thrown through the filter. The large rocks that didn't make it to the filter were then shoveled into a wheelbarrow and taken to be dumped in the front. </div>
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The filtered dirt had to go to the back of the house through a very narrow corner that we had to cross individually and very carefully. Then we made an assembly line to get the buckets of dirt from the soon-to-be garden out to the back of the house, where we learned how to make mud bricks! </div>
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Everything was used from the filtered to the non-filtered dirt - nothing went to waste...except all of the dirt that was in our socks, eyes, and in some funny cases, even on our teeth! Students and Carlton volunteered to stomp in the mud combined with hay to mix it...I heard it was very cold and wasn't the most comfortable of things to do! </div>
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<tr><td class="tr-caption" style="text-align: center;">Assembly line</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">We made 300 mud bricks in total!</td></tr>
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The first day was definitely the hardest. I had dirt so ground into my toes that when I got a pedicure <i>a whole week later</i>, there was still dirt to be found!! This was also because many of our showers were FREEZING so we couldn't stay in them too long! But it all added to the experience. Daily, we were rewarded with homemade lunches and dinners made with love from cooks through Rustic Pathways. We loved the soup and cheese on bread, and could not believe that there was another course after that! We heartily ate whatever they made. A favorite was a chicken stirfry with potatoes. We learned that Peru has over 4000 potato varieties! We ate potatoes every meal and in every way. Everything was delicious and they even made vegetarian food for our one vegetarian student. We stopped <b>a lot </b>for breaks that included local cookies and hot chocolate!</div>
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Our biggest reward was meeting the girls, who were at school while we worked. We had dinners with them each night. After dinner, they braided our hair. They giggled and loved when we called their friends by the name of the boy they thought their friends liked. We played a game called "pasa la voz," which was kind of like the game Telephone, but with gestures like touching the person's head next to you and passing it on. This had us laughing very hard! The language barrier was at times difficult, but I was impressed with how well our non-native speaking students did to translate. Kudos to our Spanish department! </div>
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On our walk home from the school at night, the stars were so bright. We marveled at our view of the Southern Cross!</div>
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<tr><td class="tr-caption" style="text-align: center;">The Southern Cross</td></tr>
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While we did work hard for three days, we took a trip one morning to go to a <a href="http://www.museoinkariy.com/en/">local museum</a> to learn a lot about the Incas and the people before with the brilliant Raul as our guide!</div>
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<tr><td class="tr-caption" style="text-align: center;">A picture from the local museum</td></tr>
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Here is more information about the girls' dorm and the Sacred Valley Project. Please watch! It's amazing where these girls come from and what this project provides for them. <iframe allowfullscreen="" class="YOUTUBE-iframe-video" data-thumbnail-src="https://i.ytimg.com/vi/vRqrTjQMQuo/0.jpg" frameborder="0" height="266" src="https://www.youtube.com/embed/vRqrTjQMQuo?feature=player_embedded" width="320"></iframe></div>
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<tr><td class="tr-caption" style="text-align: center;">Feeling very productive after three hard days of work!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">¡Adios, amigas! </td></tr>
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<br />We had a great meeting led by Sofia on the last night of our community service in a common area at the hotel. We found that what started out to be probably the hardest work we had ever done ended up to be the most rewarding. Funny how that works! Carlton and I were profoundly touched by how hard the kids worked and how readily they played with the girls. We did find that the students were really worried about the upcoming hike the next day. I told them the story of my best friend Debbie, who died of ALS in 2018, and how we needed to do this hike for someone who can't. Carlton spoke about how he was touched by the students' teamwork. It really was a moving meeting for us both.</div>
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We were also surprised that we could move the next morning - this was the most taxing thing I had ever done in my life...SO FAR...</div>
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Day 6</h3>
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After our three days of service, we were ready to see Peru. It was smart to do the community service first - we got a taste of the realities of the girls' lives and also had our hearts and souls full. So we left our beautiful hotel and headed to the cute town of <a href="https://en.wikipedia.org/wiki/Ollantaytambo">Ollantaytambo</a> to hike to some Incan ruins.</div>
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I need to really point out here that when Carlton and I agreed to Dustin's suggestions in planning for the trip, we really had no idea what it entailed...which was good....all I really heard was blah blah blah Machu Picchu blah blah blah. I had no idea that we would be taking on such a tolling hike after three hard days of work. I'm not sure I would have agreed! Having said that, I am SO glad I did! We trusted Dustin's team to create the absolute best itinerary, and I am so thankful to him!</div>
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The hike was beautiful, but we found ourselves wondering when we would get to our destination. We hiked a lot and rested a lot, but couldn't see the ruins despite walking for what seemed like a few hours. Along the way, we were accompanied by a local who would do a tribute to Pachamama, a goddess of the Andes, once we reached our destination. Everywhere we hiked, we seemed to have dogs around us that easily navigated the rough terrain...which was more than could be said for me, as I fell on the way down! The rocks were very slippery to navigate; some students intentionally slid down on their bottoms ("No shame in that!" Sofia would call out!) </div>
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<tr><td class="tr-caption" style="text-align: center;">The terrain was not easy to climb up - and harder to climb down!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Awwww</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">We made it!</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-umW8ifsM74g/XQlG1wLmM0I/AAAAAAAAFpI/NkUkJ58Y73kFIEpZIIiRr1zcAEbIRL7mACLcBGAs/s1600/PHOTO-2019-05-31-15-00-49.jpg" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" data-original-height="768" data-original-width="1024" height="240" src="https://1.bp.blogspot.com/-umW8ifsM74g/XQlG1wLmM0I/AAAAAAAAFpI/NkUkJ58Y73kFIEpZIIiRr1zcAEbIRL7mACLcBGAs/s320/PHOTO-2019-05-31-15-00-49.jpg" width="320" /></a></td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-YkemXP7OMOM/XQj5hszeFlI/AAAAAAAAFWI/leKPnUjIchEhfKhkEvb3xW1iSfz2aOP4gCLcBGAs/s1600/IMG_3757.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://1.bp.blogspot.com/-YkemXP7OMOM/XQj5hszeFlI/AAAAAAAAFWI/leKPnUjIchEhfKhkEvb3xW1iSfz2aOP4gCLcBGAs/s320/IMG_3757.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Spectacular views!</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-URdZaWs3J8s/XQj5i2Tt5RI/AAAAAAAAFWM/yA_Ru_VOwncz6EGQrzNjgO-8Wc7LiNbpACLcBGAs/s1600/IMG_4210.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-URdZaWs3J8s/XQj5i2Tt5RI/AAAAAAAAFWM/yA_Ru_VOwncz6EGQrzNjgO-8Wc7LiNbpACLcBGAs/s320/IMG_4210.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Perfect spot for a nap.</td></tr>
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<a href="https://1.bp.blogspot.com/-BZc1UArRUdU/XQj5l7dceaI/AAAAAAAAFWU/g1ae6UKz5w46ULQoqT2dOe5ffivtxQfJACLcBGAs/s1600/IMG_4754.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://1.bp.blogspot.com/-BZc1UArRUdU/XQj5l7dceaI/AAAAAAAAFWU/g1ae6UKz5w46ULQoqT2dOe5ffivtxQfJACLcBGAs/s320/IMG_4754.JPG" width="320" /></a></div>
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<a href="https://1.bp.blogspot.com/-RTC-5eMOULU/XQj5ncn4_YI/AAAAAAAAFWc/Lk3kPmGJUxUfSpmFN-Uvih-ntUIlslqfwCLcBGAs/s1600/IMG_5986.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://1.bp.blogspot.com/-RTC-5eMOULU/XQj5ncn4_YI/AAAAAAAAFWc/Lk3kPmGJUxUfSpmFN-Uvih-ntUIlslqfwCLcBGAs/s320/IMG_5986.JPG" width="320" /></a></div>
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<tr><td class="tr-caption" style="font-size: 12.8px;">Pachamama Offering</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-SeSEzTAXj3s/XQj53GvAHEI/AAAAAAAAFXU/2Wpg9hUXazIWigi1mJxEfR94vEJwrFUpACEwYBhgL/s1600/IMG_2418.MOV" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="854" data-original-width="480" height="320" src="https://1.bp.blogspot.com/-SeSEzTAXj3s/XQj53GvAHEI/AAAAAAAAFXU/2Wpg9hUXazIWigi1mJxEfR94vEJwrFUpACEwYBhgL/s320/IMG_2418.MOV" width="179" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">The actual offering<br />
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-LZ4id-ftOaE/XQj5pZaln5I/AAAAAAAAFWk/dg0lJjD-S2g-FgJJf2IidrghwNiHSjXeQCLcBGAs/s1600/IMG_6068.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-LZ4id-ftOaE/XQj5pZaln5I/AAAAAAAAFWk/dg0lJjD-S2g-FgJJf2IidrghwNiHSjXeQCLcBGAs/s320/IMG_6068.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">A beautiful waterfall underneath the ruins</td></tr>
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<a href="https://1.bp.blogspot.com/-OVIydhgVBZo/XQj5uDpeB9I/AAAAAAAAFW4/lDOIUrRe028g9HKoy1Q7CJPhuBe8ARo2gCLcBGAs/s1600/IMG_8265.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-OVIydhgVBZo/XQj5uDpeB9I/AAAAAAAAFW4/lDOIUrRe028g9HKoy1Q7CJPhuBe8ARo2gCLcBGAs/s320/IMG_8265.JPG" width="240" /></a><a href="https://1.bp.blogspot.com/-kVQunsKjOlg/XQj5oDnJgeI/AAAAAAAAFWg/5tHvaVTaT9cjn140LrS2wS4T66Ow6BfbwCLcBGAs/s1600/IMG_7347.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-kVQunsKjOlg/XQj5oDnJgeI/AAAAAAAAFWg/5tHvaVTaT9cjn140LrS2wS4T66Ow6BfbwCLcBGAs/s320/IMG_7347.JPG" width="240" /></a></div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-KCgtz3Bc44g/XQj5qVp2ILI/AAAAAAAAFWo/t9OgJXFCHmg52rvB_cxdrd0sZ-FDI1wuQCLcBGAs/s1600/IMG_7510.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-KCgtz3Bc44g/XQj5qVp2ILI/AAAAAAAAFWo/t9OgJXFCHmg52rvB_cxdrd0sZ-FDI1wuQCLcBGAs/s320/IMG_7510.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Meeting some travelers on our way down</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Families gathering corn</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-z32eAxw98uc/XQj5uNT9D_I/AAAAAAAAFW0/uXESIUiGvhQh8za4JsT-3HuZPn-sRHBqQCLcBGAs/s1600/IMG_9110.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://1.bp.blogspot.com/-z32eAxw98uc/XQj5uNT9D_I/AAAAAAAAFW0/uXESIUiGvhQh8za4JsT-3HuZPn-sRHBqQCLcBGAs/s320/IMG_9110.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The ruins we walked to<br />
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<span style="font-family: inherit;">That night, we walked in Ollantaytambo to an amazing restaurant where we ate a TON of food family style. There were so many courses! One of the things we tried was alpaca! It tasted like very good steak! </span><br />
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-Wm4fbYH_QO8/XQj_r9nTs4I/AAAAAAAAFY0/8K7nvh-DnaAUogJQ5aY-SJph0JJR0RQpwCEwYBhgL/s1600/IMG_9896.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-Wm4fbYH_QO8/XQj_r9nTs4I/AAAAAAAAFY0/8K7nvh-DnaAUogJQ5aY-SJph0JJR0RQpwCEwYBhgL/s320/IMG_9896.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">So not to be left out, the girls did his hair, too!</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-ZwLRQ_8y7Z4/XQj_rTZt7eI/AAAAAAAAFYs/TE9QmRq5AasSio7aiH-LcTiUoOc95dJxQCEwYBhgL/s1600/IMG_9564.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-ZwLRQ_8y7Z4/XQj_rTZt7eI/AAAAAAAAFYs/TE9QmRq5AasSio7aiH-LcTiUoOc95dJxQCEwYBhgL/s320/IMG_9564.JPG" style="cursor: move;" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">alpaca</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-B0j9u_zHBmk/XQj_lRuTfZI/AAAAAAAAFYw/XPr8m5tZsL8K-Ls5it26sM4I23mxsf6FACEwYBhgL/s1600/IMG_2114.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-B0j9u_zHBmk/XQj_lRuTfZI/AAAAAAAAFYw/XPr8m5tZsL8K-Ls5it26sM4I23mxsf6FACEwYBhgL/s320/IMG_2114.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">tres leches</td></tr>
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The next day, we also did a little touring of Ollantaytambo, which included visiting an adorable shop with even more adorable animals!<br />
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<tr><td class="tr-caption" style="text-align: center;"><i>cuy</i></td></tr>
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<a href="https://1.bp.blogspot.com/-FiBBNJNrB6A/XQj_pAD7QiI/AAAAAAAAFYw/3QMwGnOxgB4T44llMWpZRMj4U2TML0bHACEwYBhgL/s1600/IMG_7022.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-FiBBNJNrB6A/XQj_pAD7QiI/AAAAAAAAFYw/3QMwGnOxgB4T44llMWpZRMj4U2TML0bHACEwYBhgL/s320/IMG_7022.JPG" width="239" /></a></div>
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We went back to our very cute hotel early, which was nice because I was able to read my book <a href="https://www.amazon.com/Overstory-Novel-Richard-Powers/dp/039363552X">Overstory by Richard Powers</a>. It's a very long but interesting book, and I'm still not done with it! I do recommend it if you have the time to put into reading it. I appreciated our rests after very hard (and fun!) days of exercise and altitude!</div>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-ynPNNfZQZos/XQj_lt5Yl7I/AAAAAAAAFYs/0anZl2X8TCU5MtrM8vMojgtxbQYTlmbHQCEwYBhgL/s1600/IMG_1981.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-ynPNNfZQZos/XQj_lt5Yl7I/AAAAAAAAFYs/0anZl2X8TCU5MtrM8vMojgtxbQYTlmbHQCEwYBhgL/s320/IMG_1981.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">Our hotel</td></tr>
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<tr><td class="tr-caption" style="font-size: 12.8px;">View from the rooftop of the hotel</td></tr>
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<h3 style="clear: both; text-align: left;">
Day 7</h3>
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The next morning, we boarded a train to Aguas Calientes, the town at the base of Machu Picchu. This was a very enjoyable, relaxing, and picturesque train ride. Kids completed some summer homework, played Uno, listened to music on shared airpods, and just enjoyed doing nothing for a few hours. When we got to Aguas Calientes, we did a little shopping in a great shopping area right outside of the train station, ate more delicious food, and went to bed early to get ready for our Machu Picchu hike in the morning.</div>
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<tr><td class="tr-caption" style="text-align: center;">on the train</td></tr>
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<h3>
Day 8</h3>
We did not do the<i> early early</i> hike, though we were woken up by several travelers who were out the door at 4am. A few students opted to take the bus up to the top of Machu Picchu, but most did the hour and 45-minute hike. We asked Raul, who does this trek about 110 times a year, how long it would take him without all of the breaks we took, and he said 45 minutes! It was a truly glorious climb. Once again, we were accompanied by a dog which we either nicknamed Scrappy or Scruffy - I can't remember, but he stayed with us for the entire hike. The views were spectacular. If you can climb it, I definitely recommend doing so. It was such a sweet reward to get to the top! This was much easier than the hike from yesterday as there were steps for us to take - albeit A LOT of steps! But everyone who did it felt such a feeling of accomplishment!</div>
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<tr><td class="tr-caption" style="text-align: center;">Our fearless leaders Sofia and Raul!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">A lovely lunch break after the hike up</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Delicious boxed lunches!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Scruffy/Scrappy</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">The Southern Cross rock!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">A sweet reward after a long day!</td></tr>
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<h3>
Day 9</h3>
If this wasn't enough, the next day we had another exciting adventure ahead: Via Ferrata! I had absolutely no idea what this was until we got there! I thought we were just hiking another mountain...boy was I wrong! <a href="https://en.wikipedia.org/wiki/Via_ferrata">Via Ferrata</a> stands for Italian path, and there are only a few in the world. First, we got into climbing gear and learned how safety rules. Once we got our training, we headed out by stepping on iron bars and climbing up, transferring two carabiners every few steps to the next wire ahead. Of all of the things we did, I think this was one of the most significant in adventure and rewardIt was hard, the air was thin, and we were hundreds of feet in the air. Our safety depended on our closing our carabiners properly. I always felt safe, but truly most impressive was our 10 students who climbed without complaint. They may have been scared, but they didn't show it. They saw the person above them climbing, and they saw their teachers below them climbing. They really couldn't stop once they started, and thankfully no one wanted to (we did discover a student had a strong fear of heights on our first hike, and she opted to not join us for Via Ferrata.) The reward? Zip lining all the way down (6 zip lines - one tandem) after the climb!</div>
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After this absolutely amazing day, we headed back to Cusco and stopped at a weaving place where students were taught about the Peruvian art of weaving, tasted <i>cuy</i>, and did some shopping. </div>
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That night, Sofia had us gather as a group again in the common room of the hotel and reflect on our trip. She asked us to each talk about "<a href="https://medium.com/philosophy-logic/rose-thorn-bud-rtb-a-5-minute-game-to-kickstart-your-mindfulness-habit-5ca54dee0e21">a rose, a bud, and a thorn</a>" or, in other words, what was a highlight of the trip, something that you want to take with you and something that did not go so well. It was a really meaningful conversation for all that once again brought us all together. Many were so proud of themselves for coming so far with the climb that day.</div>
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<h3 style="clear: both; text-align: left;">
Day 10</h3>
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Our final day in Peru, we were surprised with a visit to a chocolate factory! WHAT FUN! We got our hands dirty again, but this time in edible "dirt!" We loved it and were able to make and take a lot of goodies home for our family. The chocolate was delicious! I was impressed with Carlton's and my chocolate making skills as we used a pestle and mortar to win a contest...we probably should have let the kids win, but not when chocolate prizes are involved!</div>
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We had one final lunch together before heading to the Cusco airport for our flight to Lima. </div>
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Back at the hotel, after we situated our luggage, Sofia asked us all to sit again. As is the tradition with Rustic Pathways, she gave each of us a woven bracelet and asked the person on our left to put it on the person on the right. The person putting on the bracelet would then say something nice about the person on the right, and then all were invited to chime in to say something special about that person. My favorite was when a student called me a "mom," but then another said, "No, you're more like the favorite aunt." I liked that sentiment! We all came away feeling lifted by one another. </div>
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On the bus ride to the airport, as promised, we all got our personality pasta from Sofia. I wish I could remember mine?? Maybe lasagna because it was warm and comfy? Haha, I can't remember. But our "gnocchi master" Sofia came through :) When we got to the airport, we said a very sad goodbye to Raul. </div>
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It was great that Sofia flew back to Lima with us, so we all had our bearings. She even came into the terminal with us and we had our last meal together of Papa John's pizza. (There is a Papa John dance that goes with this, but only a few have seen it.) Students were very sad to say goodbye to Sofia, as you can tell from the photo. But we are hoping to do a Peruvian cooking class in Boca once she comes back to the States!</div>
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Our flight from Lima to Fort Lauderdale left at 11pm, which was a perfect red eye. We slept on the plane and arrived at about 6am the next morning, tired but filled to the brim in our hearts, immersed in the culture of this beautiful country and its people. We came home to our families telling amazing stories and sharing moments that we will all remember for a lifetime. </div>
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Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com0tag:blogger.com,1999:blog-3454490001772574770.post-77276642287042496802018-12-22T15:46:00.000-05:002018-12-22T15:46:14.166-05:00Student Guest Blog Post: Sweet Treats in Deceit - Problem Solving Project<h2 style="clear: both;">
Here is second post by a different student in my Honors Problem-Solving Seminar; not every student had to do something that involved pure math. This student chose to use problem solving to figure out how to make cookies that she could eat...and the results were delicious!!</h2>
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<br />For the remaining blog posts, go to <a href="http://sasproblemsolving.blogspot.com/">sasproblemsolving.blogspot.com</a></h2>
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My name is Jamie and I wanted to solve the problem of substituting healthy options for unhealthy ingredients in a variety of desserts. Solving these problems are interesting to me because I love to bake, but I am gluten-free and mostly sugar-free, so I am unable to bake as much as I used to. Due to this, I am now able to bake, but with ingredients that stick to my diet. Although there are many recipes that were made to be healthy that I have tried in the past, I have never enjoyed them. Because of this project, I have created new recipes that hopefully I, as well as other people in the same situation, will always be able to enjoy in the future.</div>
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<a href="http://3.bp.blogspot.com/-lpIrzkWX9Uw/XB5RisNkwdI/AAAAAAAAAKg/aBzD3s9vu_QOiL6yqvtCOaPxRFG7bhtsQCK4BGAYYCw/s1600/banana.JPG" imageanchor="1"><img border="0" height="400" src="https://3.bp.blogspot.com/-lpIrzkWX9Uw/XB5RisNkwdI/AAAAAAAAAKg/aBzD3s9vu_QOiL6yqvtCOaPxRFG7bhtsQCK4BGAYYCw/s400/banana.JPG" width="300" /></a><br />
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First, in order to correctly replace traditional dessert ingredients with healthy ones, I had to study the chemical reactions in baking to reproduce the same reactions, but with healthier ingredients. For example, the melting of butter in the oven causes cookies to spread out and flatten. It creates smaller air pockets, resulting in the product becoming much chewier. Coconut oil can be substituted for butter, but be careful not to use too much because then the cookies will taste like coconut.</div>
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<a href="https://1.bp.blogspot.com/-C3MHtc37IHw/XB5TWztkDtI/AAAAAAAAAL4/9T1dK7x93iMh-J5hLNHibagX7lxRfqiWQCLcBGAs/s1600/IMG_3870.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-C3MHtc37IHw/XB5TWztkDtI/AAAAAAAAAL4/9T1dK7x93iMh-J5hLNHibagX7lxRfqiWQCLcBGAs/s400/IMG_3870.JPG" width="300" /></a><br />
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Sugars contribute to the taste of your product, as well as caramelization and the Maillard reaction. The <a href="https://www.jessicagavin.com/maillard-reaction/">Maillard reaction</a> is the combination of proteins and sugars, at 310˚, which creates rings and the brown color seen in most cookies. Also, as the sugars continue to break down, at 356˚, they turn into a brown, flavorful liquid, which is a process called caramelization. White sugar is mostly sucrose, so only dark sugars such as brown sugar are used for to create the Maillard reaction. This is why most cookie recipes call for both granulated and brown sugars because the white sugar is used for one process, while the brown is used for the other. To make up for sugar’s major part in the taste of the cookie, honey, dates, and banana can be used, or other natural sugars.</div>
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<a href="https://2.bp.blogspot.com/-ZFs59fJI218/XB5TyE3eNbI/AAAAAAAAAME/W0VkUDrD0bglGfiHqjuUlflmOntdnl-DACLcBGAs/s1600/IMG_2849.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://2.bp.blogspot.com/-ZFs59fJI218/XB5TyE3eNbI/AAAAAAAAAME/W0VkUDrD0bglGfiHqjuUlflmOntdnl-DACLcBGAs/s400/IMG_2849.JPG" width="300" /></a><br />
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Additionally, the thickness of a cookie depends on the amount of flour used. If a thicker cookie is wanted, additional flour should be added to your product. Some substitutions for all-purpose flour consist of either almond, oat, potato, or gluten-free flour. For my project, I used almond and oat flour, but it depends on personal preference.<br />
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<a href="https://3.bp.blogspot.com/-uUWZzOGDs8g/XB5TRb3c8tI/AAAAAAAAAL0/4fqe-_hyr4UJhtDjzkDD-kLrUbkikWXawCLcBGAs/s1600/IMG_4166.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://3.bp.blogspot.com/-uUWZzOGDs8g/XB5TRb3c8tI/AAAAAAAAAL0/4fqe-_hyr4UJhtDjzkDD-kLrUbkikWXawCLcBGAs/s320/IMG_4166.JPG" width="320" /></a><br />
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The final ingredient I will eliminate from dessert recipes is chocolate, which for most people, is the most important part. A couple of months ago, I substituted milk chocolate for dark chocolate, precisely 86% cacao. Most people would call it disgusting because it is extremely bitter, but to me, it is my favorite type of chocolate. Because I have become accustomed to eating it, I no longer enjoy eating milk chocolate. Due to this, in my recipes, I have use <a href="https://www.livestrong.com/article/471858-benefits-and-risks-of-72-dark-chocolate/">86% cacao</a>, which is actually extremely beneficial because of all the antioxidants, as well as lowering risks of diseases. Here are my two cookie recipes. I hope you enjoy them as much as I do!<br />
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Zucchini Chocolate Chip Cookies:</div>
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<a href="https://3.bp.blogspot.com/-TW7p7mbc-VM/XB5SsBf19FI/AAAAAAAAALY/xLn8t5cXQQMlpYixJY48hoZsc0GKhPdIwCLcBGAs/s1600/IMG_1804.JPG" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://3.bp.blogspot.com/-TW7p7mbc-VM/XB5SsBf19FI/AAAAAAAAALY/xLn8t5cXQQMlpYixJY48hoZsc0GKhPdIwCLcBGAs/s400/IMG_1804.JPG" width="300" /></a></div>
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3/4 cup oat flour<br />
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3/4 cups shredded zucchini<br />
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1 teaspoon baking soda<br />
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1 tablespoon almond butter<br />
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1/2 cup almond flour<br />
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1 teaspoon cinnamon<br />
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1/2 teaspoon salt<br />
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1 teaspoon coconut oil<br />
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1 tablespoon honey<br />
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1 1/2 teaspoon vanilla<br />
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2 eggs<br />
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1/4 banana<br />
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Preheat oven to 325˚. Whisk eggs and combine with almond butter, banana, zucchini, honey, vanilla, and coconut oil. Add in salt, cinnamon, baking soda, almond flour, and oat flour. Bake for 25-30 minutes.<br />
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<a href="https://1.bp.blogspot.com/-BFyG1-G7mTY/XB5SD-jKsbI/AAAAAAAAALE/iOSUWnLp4aox9i7p4M0gj3ADZvs_dc5OwCLcBGAs/s1600/IMG_4160.JPG" imageanchor="1" style="clear: right; margin-bottom: 1em; margin-left: 1em; text-align: center;"><img border="0" data-original-height="1600" data-original-width="1200" height="400" src="https://1.bp.blogspot.com/-BFyG1-G7mTY/XB5SD-jKsbI/AAAAAAAAALE/iOSUWnLp4aox9i7p4M0gj3ADZvs_dc5OwCLcBGAs/s400/IMG_4160.JPG" width="300" /></a><br />
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Banana Chocolate Chip Cookies<br />
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1 banana<br />
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2 eggs<br />
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1 teaspoon baking soda<br />
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8 dates<br />
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2 1/2 teaspoon vanilla<br />
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1 ½ cup oat flour<br />
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2 tablespoon honey<br />
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1/2 teaspoon coconut oil<br />
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1/4 teaspoon salt<br />
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86% cacao chocolate</div>
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Preheat oven to 325˚. Remove the seeds from the dates and blend them until they are no longer solid. Add in the eggs, honey, coconut oil, vanilla, and a mashed banana. Mix thoroughly. Combine the remaining dry ingredients with the wet mixture. Place tablespoons of the cookie dough onto a pan with parchment paper and flatten each of them. Bake for 25-30 minutes.<br />
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Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com0tag:blogger.com,1999:blog-3454490001772574770.post-48218663614224704352018-12-21T10:21:00.001-05:002018-12-21T18:04:13.797-05:00Student Guest Blog Post: Drawing Mandalas with Compasses and Protractors! Geometry Art!<h3>
Here is the first guest post from my student Morgan! Morgan was in my Honors Problem-Solving Seminar class, and her final project was to learn how to draw a mandala using math! Enjoy! For the rest of the posts, visit: <a href="http://sasproblemsolving.blogspot.com/">sasproblemsolving.blogspot.com</a></h3>
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Hi! My name is Morgan, and because of my love for yoga, I decided<span style="color: red;"> </span>to learn how to draw a mandala!<br />
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<span style="color: black;"><a href="http://spiritualawakening.weebly.com/mandalas-what-are-they.html" target="_blank">Mandalas</a> </span>represent an imaginary place that one's mind travels too when he or she meditates. Each object one observes in that place has significance, embodying an aspect of wisdom or reminding the meditator of a guiding principle. The mandala's purpose is to help transform ordinary minds into enlightened ones and to assist with healing just as yoga has for me with anxiety. The different movements and yoga positions leave me feeling relaxed and allow me to clear my mind. I felt a similar feeling of relaxation when I drew my mandala.<br />
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Having never drawn a mandala before, I had predicted it to be a long, complicated process that would be draining. However, I felt calm and stress-free as I allowed my mind to unravel and draw my mandala. At first, it was a little challenging to know what shapes and lines to draw after I had created the skeleton of the mandala, but by the end, I didn't even have to think much. I went with my intuition and let my mind do what it felt in the moment.<br />
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Here is a video of my first mandala drawing, showing the whole process and what goes into creating a mandala.<br />
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My first mandala completed</div>
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A close up shot of my mandala</div>
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Materials needed to draw a mandala:</div>
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<li>Compass</li>
<li>Protractor </li>
<li>Ruler </li>
<li>Pencil</li>
<li>Black pen with felt tip (thin<span style="color: red;"> </span>sharpies will do)</li>
<li>Blank notebook or 8.5 by 11 sheet paper</li>
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Procedure:</div>
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<li>Draw “skeleton” in pencil.</li>
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<li>As I showed in my video, use your compass to draw a small circle in the center of the paper then continue outward drawing circles until you reach near the end of the piece of paper. </li>
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TIP: rotate the paper while using the compass as shown in this video. </div>
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<li>Once your circles are complete, use your ruler to draw straight lines to divide the circle up into several different sections. </li>
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<a href="https://1.bp.blogspot.com/-iSMtrEt-WUA/XBmh9-ZariI/AAAAAAAAAQ4/3xwss9Vq47AKZAoVK85a1Krz2zUDzwnhwCLcBGAs/s1600/IMG_3780.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="773" data-original-width="1450" height="212" src="https://1.bp.blogspot.com/-iSMtrEt-WUA/XBmh9-ZariI/AAAAAAAAAQ4/3xwss9Vq47AKZAoVK85a1Krz2zUDzwnhwCLcBGAs/s400/IMG_3780.jpg" width="400" /></a></div>
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22.5 cm trick shown above</div>
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<li>In addition, although I didn't show it in my video, you can use a protractor and make markings at every 22.5 cm then use a ruler to draw lines so that your mandala is more precise.</li>
<li>Also, the circles do not need to be exactly the same amount apart from each other. It actually comes out better if you organically draw some circles close together and and some further apart. </li>
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<li>Then begin using your black felt tip pen (or Sharpie) to draw the mandala. </li>
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<li>Some commons designs and shapes include:</li>
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<li>Petals </li>
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<li>Longer and thinner</li>
<li>Shorter and rounder</li>
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<li>Triangles</li>
<li>Various line lengths </li>
<li>Circles with dots </li>
<li>Squares </li>
<li>Symbols such as: </li>
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<li>Flowers</li>
<li>Suns</li>
<li>Moons</li>
<li>Trees<div class="separator" style="clear: both; text-align: center;">
<img border="0" data-original-height="828" data-original-width="1050" height="251" src="https://4.bp.blogspot.com/-lnIFsJWH1MY/XBwcDoaz2qI/AAAAAAAAARE/Ue4Uceg2KP47UcGcmPSykNyGKQ4hp9-IQCLcBGAs/s320/Screen%2BShot%2B2018-12-20%2Bat%2B5.46.46%2BPM.png" width="320" /></div>
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<a href="https://www.youtube.com/watch?v=OiSzGBguPm0" target="_blank">Basic designs</a></div>
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<li>Tip: Begin with drawing simpler shapes then use dots and smaller designs to fill in shapes and the areas surrounding them!</li>
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<li>After you finish drawing and designing with the black felt tip pen, erase the pencil marks underneath and admire your mandala! </li>
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<li>You can also add color to your mandala to brighten it up if you want!</li>
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After learning how to draw a mandala, I shared the process with some students who are part of <a href="https://www.instagram.com/sa.mao/" target="_blank">Saint Andrew's Mu Alpha Theta</a>, which is a math club at my high school. Here below are some photos of them and their mandalas.<br />
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<a href="https://2.bp.blogspot.com/--SMRPm8i7pE/XBme-mUGG3I/AAAAAAAAAQA/fUaCzBPgigkHgsgXQfGuz8NksSxjj1xxwCLcBGAs/s1600/IMG_3693.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://2.bp.blogspot.com/--SMRPm8i7pE/XBme-mUGG3I/AAAAAAAAAQA/fUaCzBPgigkHgsgXQfGuz8NksSxjj1xxwCLcBGAs/s320/IMG_3693.jpg" width="320" /></span></a></div>
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Designing the mandala</div>
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<a href="https://2.bp.blogspot.com/-Ux3r8xFO89g/XBmfMYW9umI/AAAAAAAAAQI/RvrSQgT1o947QeNAV8TV_QjyjmNwpwAdACLcBGAs/s1600/IMG_3674.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" data-original-height="1600" data-original-width="1541" height="320" src="https://2.bp.blogspot.com/-Ux3r8xFO89g/XBmfMYW9umI/AAAAAAAAAQI/RvrSQgT1o947QeNAV8TV_QjyjmNwpwAdACLcBGAs/s320/IMG_3674.jpg" width="308" /></span></a></div>
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Beginning the design after creating the skeleton</div>
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<a href="https://2.bp.blogspot.com/-0kIAggYY9k0/XB03yZ3g28I/AAAAAAAAE_M/CgnCPi40I3wjOUn235nsQW8LamDkQ000wCLcBGAs/s1600/IMG_3665%2Bcopy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="175" data-original-width="232" src="https://2.bp.blogspot.com/-0kIAggYY9k0/XB03yZ3g28I/AAAAAAAAE_M/CgnCPi40I3wjOUn235nsQW8LamDkQ000wCLcBGAs/s1600/IMG_3665%2Bcopy.jpg" /></a></div>
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Working on the first step with compasses</div>
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<a href="https://2.bp.blogspot.com/-PsWEq0Y9pD0/XBmf4Hi-v9I/AAAAAAAAAQY/B2w1WzbqnOMZKV8rLONymvkOjtScOP4gwCLcBGAs/s1600/IMG_3695.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-PsWEq0Y9pD0/XBmf4Hi-v9I/AAAAAAAAAQY/B2w1WzbqnOMZKV8rLONymvkOjtScOP4gwCLcBGAs/s320/IMG_3695.jpg" width="240" /></span></a></div>
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A colorful mandala!</div>
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<a href="https://2.bp.blogspot.com/-xdPGKEf05yE/XBmgNAKlO7I/AAAAAAAAAQk/m67tlMgzQlkujqx0g9fFvwiePwJsleEFACLcBGAs/s1600/IMG_3690.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-xdPGKEf05yE/XBmgNAKlO7I/AAAAAAAAAQk/m67tlMgzQlkujqx0g9fFvwiePwJsleEFACLcBGAs/s320/IMG_3690.jpg" width="240" /></span></a></div>
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A finished mandala with a unique design: a different design for each half</div>
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<a href="https://2.bp.blogspot.com/-byv5hjPmmNE/XB0357GztmI/AAAAAAAAE_Q/NKBD7PMuL5sXWetUY4oUZrXZzNsXDJz_gCLcBGAs/s1600/IMG_3699.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="222" data-original-width="266" src="https://2.bp.blogspot.com/-byv5hjPmmNE/XB0357GztmI/AAAAAAAAE_Q/NKBD7PMuL5sXWetUY4oUZrXZzNsXDJz_gCLcBGAs/s1600/IMG_3699.jpg" /></a></div>
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Another finished mandala</div>
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I hope my blog inspires you and teaches you about mandalas! I have linked some mandala designers and tutorials that I found helpful below as resources for you. :) </div>
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Here are some accounts that I found inspiring when creating my mandala!<br />
<span style="color: black;"><a href="https://www.instagram.com/courtneybetts/" target="_blank">@courtneybetts</a> was super helpful in getting me started with my mandala and giving me tips. She has a super cool art Instagram story on her page that features beautiful mandalas. I came across </span><span style="color: black;"><a href="https://www.instagram.com/mandalabybhagya/" target="_blank">@mandalabybhagya</a> 's Instagram page when looking for inspiration for designs for my mandala. She has lots of intricate colorful mandalas, too! </span><br />
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<a href="https://1.bp.blogspot.com/-vWy4dewzYCo/XBwgb03KZOI/AAAAAAAAARY/tGISi12Pf-g1FIPUFRAIdhwt_O1fQfkcgCEwYBhgL/s1600/Screen%2BShot%2B2018-12-20%2Bat%2B6.04.50%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1062" data-original-width="896" height="320" src="https://1.bp.blogspot.com/-vWy4dewzYCo/XBwgb03KZOI/AAAAAAAAARY/tGISi12Pf-g1FIPUFRAIdhwt_O1fQfkcgCEwYBhgL/s320/Screen%2BShot%2B2018-12-20%2Bat%2B6.04.50%2BPM.png" width="269" /></a></div>
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One of <a href="https://www.instagram.com/mandalabybhagya/" style="text-align: start;" target="_blank">@mandalabybhagya</a>'s colorful mandalas</div>
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Another one of <a href="https://www.instagram.com/mandalabybhagya/" target="_blank">@mandalabybhagya</a>'s beautiful creations</div>
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Lastly, here are some tutorials that I recommend to help you on your mandala journey!<br />
<span style="color: black;"><a href="https://www.youtube.com/watch?v=OiSzGBguPm0">https://www.youtube.com/watch?v=OiSzGBguPm0</a></span><br />
<span style="color: black;"><a href="https://www.youtube.com/watch?v=QcHDIK0E5KY&t=573s">https://www.youtube.com/watch?v=QcHDIK0E5KY&t=573s</a></span><br />
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Thanks for reading! :)<br />
<br />Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com3tag:blogger.com,1999:blog-3454490001772574770.post-53184135556029659392018-11-22T13:36:00.002-05:002018-11-23T18:14:35.925-05:002018 - A Year of Sorrow and Gratitude<h4>
<i><span style="font-family: "times" , "times new roman" , serif;">It was the best of times, it was the worst of times. </span></i></h4>
<span style="font-family: "times" , "times new roman" , serif;">Is it bad that I don't remember if I read that book? Charles Dickens, I believe. Pretty sure I didn't. It's how I'm feeling today, on this day of gratitude, Thanksgiving 2018. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">I am sitting in my living room while my cleanly shaven son (thank goodness!) sat down to do the ton of work he was assigned over Thanksgiving (not nice, professors!) and my husband makes us lunch...he's whipping together leftovers for a nice meal, as he is always prone to do. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">My son's cat, Arthur, a crazy, relentless Bengal, is trying to get a taste of everything on the counter. And I just took an awesome yoga class, showered, and feel cozy in my long sleeve "Trust Me, You're Lovely" t-shirt, jeans, and wrapped in a cushy blanket that was a birthday present from a great friend. I checked my Apple Watch and it's 79˚ outside...I guess I don't need the crackling of a fireplace, though Alexa would do that for me when she understands what I'm saying. Which is about half the time. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">I'm so grateful, as I glance over at AJ, working hard and seeing how it paid off. This year, he was accepted into the Medical Honors Program at UF, which means to say...HE'S IN MEDICAL SCHOOL! And what makes me so happy is that it's made HIM so happy. To see his relief, after a toiling sophomore year of applications and workload has brought me so much joy. I am so unbelievably proud of him. I'm blessed to call him my son. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">It's a good life. I cannot complain. I've been lucky in many ways. Even though life has had its ups and downs in my "short" 50 years, there's one thing that I have felt my whole life: <b>unconditional love</b>. Whether from my husband and son or my grandparents, sister, endless aunts and uncles and cousins, in-laws, and best friends, it's one thing that has held true in my life - and I think that's what has helped me get through tough times like when I was young and lost both parents and a grandparent within 18 months. Love can't fill the hole in my heart, but it can make it smaller. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">Maybe this is why I normally look at life as having my glass half full. My students often say I am "always happy." My friends, upon hearing the tragedy of my early life say, "How are you so 'normal'?" (Hah, do they really know me??) To me, it's from knowing I always had someone there who had my back. Even when life threw curveballs, there was always a multitude of people I could count on. And when I discovered that there were people I <i>couldn't</i> count on, which would crush me, I would eventually realize that I have others that I sometimes lost sight of--others that were there for me no matter what. And that's what has kept me going. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">2018 <b>Needs. To. Go</b>. I'm reminded of <a href="http://bon%20qui%20qui/">Bon Qui Qui</a> from Mad TV as I write that. It also reminds me of Jenna, my former student turned friend who always quotes this with me. Needs. To. Go. Three deaths and three cancer diagnoses - and there is still a month left in the year.</span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">The beginning of the year was brutal. I lost my best friend Debbie in April when ALS left her with only a mind and a laser attached to her glasses where she could point to letters on a board. And yet, she was still <i>so damn funny</i>. She just knew what to say. The woman was brilliant. And a mom to so many of us. I used to get upset when she wouldn't get back to me before she got sick, but I realize now how many people in this world depended on her...she couldn't give that much of herself to anyone beyond her family. And yet, she gave me so much. I'm confident I could now act in any play where I am a character that needs to cry on cue. Thinking of her brings me to tears in an instant. I still find it difficult to talk to anyone about her without choking up. A text from her mom can bring me to tears - the thought of her being without her daughter kills me. And the thought that I don't know what I can do for her kids, other than letting them know I'm thinking of them, is hard. Her mother texted me recently: "You two were inseparable from the moment you met." It's true. We always had each other. She had my back, and when people weren't treating me right, she stood up for me. When she died, I did feel like half of me died, too. I honestly can't even write about it anymore at this moment. It's just unbearable.</span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">2018 also brought the sudden death of an aunt. Although she had been divorced from my uncle for quite some time, we messaged each other occasionally and caught up on Facebook often. She was competitive, like me, and she laughed a lot, like me. Even though she was my aunt, we were only a few years apart and we got along very well. It was sad to know that days after I got my nails polished to look like hers (which I saw from a Facebook post), she was gone. Just like that. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">And a few weeks ago, my stepfather died. I was not close with him, but I did live with him for about six years, and he was the father of my sister. Going to his funeral conjured up a lot of memories that I shoved in the back of my mind. Memories like the loss of my mother. My sister keeps finding gems in the house, like a paper where my mother wrote that she was proud of me and that I was 18 years old and studying to be a teacher. I hadn't seen anything with her handwriting in 30 years. It has always been easier for me to not think about those who have died as the pain is too difficult for me to bear. So seeing a lot of things from my mother as well as seeing my sister, devastated at being an orphan, made this last month so sad.</span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">2018 was a year where three- yes three! people in my world were diagnosed with cancer. I helped one through chemo twice, which, while helping my friend, also allowed me to be the daughter I never was for my mother. Thankfully, hers was stage 1, and she seems to now be doing great. The second is all the way across the country, and I can't really help her with her stage 4 cancer, other than letting her know I'm thinking about her and her family. It was shocking to see this funny, vibrant friend who loves to wear clown noses and make others laugh, lay debilitated in bed. And the third is a new diagnosis...someone very close to me, and I don't want to say the relationship as it's not quite public. But I'm beyond crushed, defeated, and overwhelmed. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">These negatives outweigh the positives this year. I have my sad moments, and they tend to manifest themselves after a couple of glasses of wine. But what I have discovered is that finding a way to make my students shine has been the turnaround that I needed this year in my life. </span><span style="background-color: white; color: #222222; font-family: "times" , "times new roman" , serif;">I just got back from a taking 5 students to TED-Ed Weekend in NYC. I think for me, what was so exciting was to see students connecting with other students from around the world. In hearing their talks, they see that they are not that different from each other. In a world where there is <i>so much hate and divisiveness</i>, <b>I see hope in our future</b>. These students are realizing that although we are each uniquely different humans, we all have common threads that bind us to each other. And to give students this platform where they can spread their individual ideas worth sharing can be life-changing. Not just for them, but also for me. To witness the evolution of students having nothing on paper to delivering a rich and deep talk has been one of the most rewarding parts of my job - and perhaps my entire career. To watch them shine on the stage when many of them never thought they could do it - and to see their peers, parents, and teachers congratulate them on such an accomplishment - it gives me chills when I think about it. Each student has something that they created that is their very own - no one else has their unique story. And yet everyone can relate to their story in their own way. And this brings us all closer as humans - when we can relate to someone else's ideas and make it our own. </span><br />
<span style="background-color: white; color: #222222; font-family: "times" , "times new roman" , serif;"><br /></span> <span style="background-color: white; color: #222222; font-family: "times" , "times new roman" , serif;">To see the chain reaction of events: from my text to a former student's parent in Aruba, asking her if she wanted to speak at our event, to then seeing her knock it out of the park on the big stage in NYC - yes, that is almost unbearable as well - emotions-wise that is...but this time, in a good way. Here and now, my heart is full. </span><br />
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<span style="font-family: "times" , "times new roman" , serif;">None of us know how much time we have in this world. And I'm realizing that making someone else's life brighter is all that's all it takes to put me in a good mood. And thankfully, I get that through the job I love: teaching. I remember always wanting to be a teacher, and after my first five years of teaching in New Jersey, I remember thinking: I'm done. I'm not cut out for this. I suck. My principal told me otherwise. My vice-principal got down on one knee and sang to me at the last faculty meeting before I moved to Florida. They saw my potential when I did not. Who knew that answering one little newspaper ad in the Palm Beach Post would bring me to a school that I've worked at now for almost half my life. And who also knew that my background in curating and running shows as the President of a random club in high school called "Sights and Sounds" would have helped me develop this passion to get my students to do TED talks. Although I absolutely love teaching math by both getting students excited about it and by showing some that they CAN do math when they thought they couldn't their whole lives, my world has been opened with TED-Ed.</span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">I'm a Libra, and I see a balance here. The harder life is, the harder I'll work to find something rewarding. It's my way, and it only works with the support of family, good friends, and good colleagues. I pray that I do for them what they all do for me. </span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">Happy Thanksgiving. If you've made it this far, thanks for giving me this venue to reflect on this year. I hope you have a wonderful time with those who give you unconditional love.</span><br />
<span style="font-family: "times" , "times new roman" , serif;"><br /></span> <span style="font-family: "times" , "times new roman" , serif;">~Lisa</span><br />
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Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com3tag:blogger.com,1999:blog-3454490001772574770.post-54176847836281601992018-10-13T07:34:00.000-04:002018-10-13T07:34:03.968-04:00Five Great Things This Week: Puzzles, Google Slides, Rubik's Cube, Spirit Week, and Math Community Service<div class="separator" style="clear: both; text-align: center;">
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Fifty! Phew! I made it! It was a fabulous birthday with a ton of surprises and so much to be grateful for! I'm also SO grateful for my job. Every day, I come home nourished (and tired!) and here are a few reasons why.<br />
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<span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif;">1. PUZZLE OF THE WEEK</span></h3>
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This is a fun weekly international competition that you can sign up for <a href="http://www.puzzleoftheweek.com/">here</a>. It's created by <a href="https://twitter.com/asharpeducator">@asharpeducator</a>. My Problem-Solving class and math club really enjoyed it. It's tough enough yet doable and got a lot of kids talking...particularly the calculus-loving student who doesn't get to see problems like this much. But really all kids can do it with a little help. I'm going to see if we can send this problem out to all students via email so that any student can access if they want. Even if only five students in the school open it, that's still more students talking about math! I'm hoping it will be a good problem for teachers to throw on the board if they have some time at the end of class. Sign up and give it a try!<br />
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2. WRITING LESSONS IN GOOGLE SLIDES RATHER THAN WORD</h3>
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I Started rewriting all of my lesson plans in Google Slides instead of word this year afer initially seeing <a href="https://twitter.com/mathycathy">@mathycathy</a>'s short ibook: <a href="https://itunes.apple.com/us/book/using-keynote-to-explore-math-relationships-visually/id1423274172?mt=11">Using Keynote to Explore Math Relationships Visually</a> Now I know I'm using Google Slides and note Keynote...our school uses everything Google, so it made it easier for me. But she really opened up my eyes about how much better it is than word. And then <a href="https://twitter.com/howie_hua">@howie_hua</a> tweeted <a href="https://twitter.com/howie_hua/status/1043914055285583872">this</a>:</div>
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Adding comments after the lesson is a GAMECHANGER!! <b>Every year</b>, I forget to change the one mistake on a lesson and don't remember until I'm in the middle of the class...no more!!</div>
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Here is a lesson I made on <a href="https://docs.google.com/presentation/d/1b5cEBz3KihsZSOwTFWNxxlos5CxmXCPe98iF-EtaOFc/edit?usp=sharing">Inverse Functions</a> that I taught to my Pre-Calculus AB class using Google Slides. Give it a try!</div>
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3. RUBIK'S CUBE</h3>
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<b>All</b> 13 of my Problem-Solving students solved the Rubik's Cube within 3 minutes after only a week and a half of learning how to solve it! I purchased <a href="https://www.amazon.com/gp/aw/d/B00P4KQFEG/ref=mp_s_a_1_1?ie=UTF8&qid=1479254962&sr=8-1&pi=AC_SX236_SY340_QL65&keywords=Mathematics+of+games+instant+video&dpPl=1&dpID=51C9sAIlhAL&ref=plSrch">Art Benjamin's version</a> on Amazon, and we watch the first four of eight algorithms together as a class. I find that Art Benjamin's method is the easiest for students (and me!) to learn. Then, I give students either <a href="http://eatplaymath.blogspot.com/2016/10/how-to-solve-rubiks-cube-20.html">the link to my blog post</a> on solving the cube with extra videos of me explaining how to solve, or I give them <a href="https://youtu.be/QzP1cI-1Oks">my Youtube playlist</a>. Some students really need me to go through every algorithm with them, which I do either on the side or during extra help, but others wanted to learn it on their own and were able to watch the videos at home. Anyone really can solve the Rubik's Cube...my favorite year was when I learned it <i>along </i>with the students, which I highly recommend! My class is probably the only one where the teacher allows the clicking of Rubik's Cubes all period as students solve problems...they are learning kinesthetically!</div>
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4. DRESSING UP FOR SPIRIT WEEK</h3>
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Kids love it when teachers dress up for spirit week! Even though it can be out of your comfort zone, you must do it! We had "Dress as a Movie Star" day, so my colleague and I dressed as Tina Fey and Amy Poehler from Baby Mama., but of course, we were "PreCalc Mama." So fun!</div>
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5. MATH COMMUNITY SERVICE</h3>
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For my math club, I reached out to <a href="https://www.ffcdc.org/">Florence Fuller Childcare Development Center</a> to see if they needed math tutors. They do! After a few weeks of emails, back and forth, we had two people from the center come out and talk to our club about how we can tutor their students during their aftercare program. They talked to our students about how meaningful it is both for their students and for ours. The club members seemed really interested. We are hoping to send a few students each week to meet with kids and help them with their math homework and hopefully to form a meaningful bond and mentorship program. Is there an economically challenged development center in your neighborhood? Reach out and see how your kids can help! Our math club is a lot about competitions, but it's equally about community service and peer tutoring. I hope this will be a meaningful experience for all involved!</div>
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It's been quite some time since I blogged, but it feels good to be back. Let me know if anything worked for you!</div>
<br />Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com2tag:blogger.com,1999:blog-3454490001772574770.post-46946066266915947012018-08-05T15:59:00.000-04:002018-08-05T15:59:16.736-04:00What to Expect on an Island Yoga Retreat with Yoga Girl<span class="" style="text-size-adjust: auto;">Ever since my son left for college, I have been doing something to nourish the soul during the summer. It has honestly been so rewarding. In 2016, I went on an incredible subsidized women's trip to Israel: </span><a class="" href="http://eatplaymath.blogspot.com/2016/08/a-jwrp-womens-trip-to-israel-that-has.html" style="text-size-adjust: auto;">part 1 blogged here</a><span class="" style="text-size-adjust: auto;">, </span><a class="" href="http://eatplaymath.blogspot.com/2016/08/a-jwrp-trip-that-has-changed-my-life.html" style="text-size-adjust: auto;">part 2 blogged here</a><span class="" style="text-size-adjust: auto;">, </span><a class="" href="http://eatplaymath.blogspot.com/2016/08/a-jwrp-trip-that-changed-my-life.html" style="text-size-adjust: auto;">part 3 blogged here.</a><span class="" style="text-size-adjust: auto;"> It was an experience of a lifetime. In 2017, I used </span>award<span class="" style="text-size-adjust: auto;"> money to fly solo to a few workshops in London and Cambridge, England, </span><a class="" href="http://eatplaymath.blogspot.com/2017/06/cambridge-teaching-seminar-and.html" style="text-size-adjust: auto;">blogged here</a><span class="" style="text-size-adjust: auto;">, and made side trips to Paris to visit a friend and Ireland to travel with family.</span><br />
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This year, the year of my 50th birthday, I decided to go on a yoga retreat to Aruba with 49 other women hosted by Rachel Brathen, more famously known as <a href="https://www.instagram.com/yoga_girl/?hl=en">@yoga_girl</a>. Rachel is a yoga teacher and entrepreneur that I have been following on Instagram for quite some time. I listen to her podcast, <a href="http://rachelbrathen.com/podcast-2/">From the Heart: Conversations with Yoga Girl</a>, every Friday and always feel motivated and inspired afterward. I have her book, aptly named <a href="https://www.amazon.com/Yoga-Girl-Rachel-Brathen/dp/1501106767">Yoga Girl</a>, on my coffee table. She often speaks about how she has gone through pain and loss, such as the sudden death of her best friend and her mother attempting suicide twice. Rachel has that <i>je ne sais quoi, </i>which is why she has over 2 million followers on Instagram and why several women of all ages flock to Aruba to attend her sold out <a href="http://rachelbrathen.com/retreats/">retreats</a>, take a class at her studio, or become a certified yoga teacher at her three-week <a href="http://rachelbrathen.com/retreat/200-hour-yoga-teacher-training-3/">teacher training.</a> As one Aruban cab driver told me, she has a "good heart," raising money for her animal adoption organization, <a href="http://www.sgtpeppersfriends.com/">Sgt Pepper's Friends</a> and creating an inexpensive online community platform consisting of classes and meditation on <a href="https://oneoeight.com/featured/">oneoeight.com</a>, for example. She is known for being authentic, honest, and for throwing out a "forking"curse or two (or three) on her podcast all while discussing a range of topics like #MeToo in the yoga world, body image, moving through pain, the fears and wonders of motherhood to <a href="https://www.instagram.com/loving.lealuna/?hl=en">@loving.lealuna</a>, and of course her enviable island life with husband <a href="https://www.instagram.com/dennisfromsalad/?hl=en">@dennisfromsalad</a>.<br />
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In person, she and her family are larger than life. When Rachel walks into a room with her genuine smile, long flowing hair, and kimono swaying, the retreaters cannot help but fangirl. And when Lea Luna comes trailing behind or the family's beloved dog Ringo nudges his way near you, everyone lights up as if it's a family member's beloved baby or puppy that we are seeing - because, if you follow Rachel, you see pictures of her family on her Instagram story as often as you would your own. And that's why we love her. It's a little crazy and a little surreal. As I heard many women on the retreat say, "It's like finally meeting your best friend who doesn't know you!" But, Rachel is warm, caring, and giving...it must be exhausting for her, being "on" constantly. Yet she has something here. On this retreat, she brought together 50 mostly separate women who were drained or hurting or just wanted to do a little yoga, and we came away as a more fulfilled and renewed group, changed for the better, with cups a little fuller and with new friends that you feel like you've known forever.<br />
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Here is what you can expect, from my viewpoint. I am blogging about this also for myself so I can remember. However, I may have forgotten some things as well!<br />
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<h3>
Day 1 (Arrival)</h3>
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<i>Bonbini</i>! I arrived alone at Queen Beatrix International Airport and easily made my way out to our driver, who held an Island Yoga sign. I had to wait about 10 minutes, as there were buses picking up attendees every hour. No worries, as I got to meet and chat with some of the other retreaters. We got on a bus and drove about 20 minutes to <a href="https://www.costaesmeraldaaruba.com/">Costa Esmeralda</a>, our villa for the week. This was a very cute place with two pools. The rooms were clean and spacious. Well, I can only speak for the single. I highly recommend the single! Several of the girls had to sleep on cots or a double bed in the shared rooms. I landed at 2:30pm which gave me an hour to shower, change into something dressy, go through a small gift bag (note: the salve is NOT lipgloss!), unpack, and meet at the pool at 5pm for a 3-minute walk to <a href="https://islandyoga.com/">Island Yoga</a>. Here, we were greeted with a mojito, and we chatted with our new friends in the beautiful backyard of the studio. This area is surrounded by cacti and the walls have gorgeous mandalas painted on them (more about that later).</div>
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Rachel, Dennis, Lea Luna, and Rachel's mother Shama arrived, and we all fangirled. I can't lie about that. Everyone on the trip, I think, is there because of Rachel, so to see her family in person, after seeing several pictures a day on Instagram, was a bit surreal. Rachel hugged and spoke to each of us. Dennis is TALL (and so handsome) and was super friendly to everyone. And Lea Luna had an audience of her own. The Island Yoga Team was incredible and accommodating, even giving us a WhatsApp number in case we had any questions...which I have to say, was always responded to within minutes, sometimes even seconds!</div>
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After our meet and greet, we walked inside to Luna Shala, which is where we practiced yoga each day. This gorgeous room with a beautiful wooden ceiling and lights that dim to a low red was set up with comfortable floor chairs in a tight circle. We all introduced ourselves. I believe the question Rachel asked us to answer was, "Why are you here?" Many people shared emotional reasons, others just wanted to do yoga. There were four, I believe, mother-daughter pairs as well as a few pairs of best friends. Most, like me, traveled alone.<br />
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After an hour or so, we knew most people's stories and had a lot to talk about during dinner outside. We were served a delicious (and included in the cost of the retreat) vegan dinner and could purchase wine for $7 a glass. A tab was kept for you for the week at the cafe, which made it very convenient. We did not do yoga this day, and we returned to our room to get a good night's sleep. Recommendation: if you come from a different time zone, such as California, I would arrive a day or two early to get used to the time change. Morning yoga is at 7:30am!</div>
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Daily Schedule</h3>
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Every morning, we started out with smoothies at 7am (optional) and yoga practice at 7:30am. Yoga usually lasted about 2 hours (sometimes 3, but not all of it was practice), and then we would have an included vegan breakfast consisting of delicious oatmeal, yogurt, fruit, breads, and something different each day: scrambled tofu, spinach arepa or breakfast burrito. There were lots of choices to sprinkle on the oatmeal or yogurt. Coffee or tea was also included with almond or soy milk, but if you wanted a latte or cappuccino, you could order one on your tab. Then we walked back to our rooms to get ready for our excursion of the day. After the excursion, there would be time to change and shower, and then smoothies were available at 4:30pm with a second yoga practice at 5pm. I loved that every smoothie throughout the entire week was different! These were all optional and included. After practice, we were on our own for dinner other than the first and last nights of the retreat, however, you could sign up to eat at Island Yoga's <a href="https://islandyoga.com/cafe/">Nourish Cafe.</a> Each day, you could examine the "Super Awesome Board" in front of Luna Shala to see which two meals were offered for dinner that night. If you chose to eat there, it was $15, and Rachel would be eating there as well. </div>
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Day 2 (First Actual Day of Yoga)</h3>
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We were shown to our own little cubbies for the week, so we did not have to bring our yoga mats and journals back and forth - so convenient! We could borrow blocks, straps, and blankets. Some people did borrow mats, but I was happy to have my own mat for the eight practices over the week. There were tape marks on the floor so that we could see where to put our 50 mats, as they were right next to one another. There was a little bit of room between, but I preferred the side wall, where there was extra space for blocks. We practiced a great flow, but what was really amazing, other than having Rachel teach us and having Dennis practice with us, was the music. Rachel has many gifts, and DJing is definitely one of them. Follow her on <a href="https://open.spotify.com/user/rachelbrathen">Spotify</a> - she shares a new playlist each month. I believe we started our eye gazing and sharing during this first practice. I was definitely out of my comfort zone, but I am glad I did it, mainly because over the course of the five days, I got to speak truths and listen to the stories of six of the 50 women. I don't want to ruin it for anyone who is going to go on this retreat, so I will briefly talk about it. Usually, toward the end of the flow, Rachel asks us to turn to face a partner we did not come with or know well. We had to sit very close, knees about touching, and just stare into each other's eyes for what seemed like an eternity. This was very hard for me. I looked away a lot that first time. But you do get used to it. She prompted us with a question, which could be the same one she asked us to write about in our journals before class or could be something else. Then only one of us could answer the prompt and the other could not speak at all until the sound was made to stop and switch. The idea behind this was to "make space for others." So often we cut people off in conversation and make a comment or talk about ourselves, but here, we could not. After both turns, we had to say thank you however we wanted to, which was often a hug, and then we would finish our practice. Out of the six eye gazes (all over the course of the week), there were tears in at least three of them for me and/or my partner. It was very intimate and meaningful, and I will never forget it. </div>
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After yoga, we had a huge (well I had a huge) breakfast at Island Yoga's beautiful outdoor space. Then we walked back to the hotel to get ready for the beach excursion. I should say that during many breaks, we shopped at the Island Yoga Boutique. Each day I found something I didn't see. By week's end, I purchased a ginormous water bottle with a fun saying, an Island Yoga long sleeve shirt, and a cute moon necklace, though I did want to buy more!<br />
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We went to the <a href="http://www.ritzcarlton.com/en/hotels/caribbean/aruba">Ritz-Carlton</a> beach by bus, which was beautiful. They offered us 15% off any service, but I'm not sure anyone took them up on that. We just spent the day on luxurious lounge chairs and in the water. If you go, bring lots and lots of sunscreen! Here is where we started to find our groups and connect. Though really, it was easy to connect with anyone. The ages ranged from twenties to sixties, I would think, though most were probably in their twenties and thirties. There was also a wide range of ability. Only a few, I think, were actual teachers. Most were not. </div>
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Rachel and her family stayed on the beach with us, so Lea Luna was a huge source of joy, as she could not wait to play in the water. She is so used to being around all of these women; I heard many say over the course of the week, "She is going to be such a strong woman when she gets older!"</div>
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We ordered food - the hummus was great; I did not love my fish tacos. Some people ordered drinks. A highlight was the waiter who balanced drinks without spilling while riding fast on his segway! Some of us grabbed a delicious ice coffee from the coffee shop inside and no one complained when we looked in stores in our bathing suits, though we were not allowed to peek in the casino that way! We stayed on the beach for a few hours and could have done local shopping, but we chose to go back to the hotel. We showered and took a quick excursion to Super Food for necessities like wine, La Croix, trail mix, cookies, coffee, cream, etc. We shared a cab which was about $12 each way, including tip. </div>
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By the time we got back, it was time for smoothies and another yoga practice. What was truly amazing is that no yoga practice was the same. I believe that it was during this evening practice when Rachel broke down handstand for us. Though I still can't do one, I did really understand <i>how</i> to do one (core, core, core!) and I also learned how to assist, which is important for when I teach. We broke into pairs for this, and Rachel's right-hand girl <a href="https://www.instagram.com/jessicarydh/">Jess</a> and Dennis demonstrated. I truly learned a lot, and hope one day to be able to do a handstand. One thing I really liked is that Rachel does not say "standing leg split," but rather, "standing L-shape," which makes much more sense! Again, the music was amazing. Her savasanas are incredible; people cry. After one full song in savasana, she also lets us lay in silence a bit before asking us to move. Her voice is extremely soothing, and it's easy to be in the present moment during class. </div>
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That night, I found my tribe: Yali, Kelley, Mary, and Jen, and we walked to <a href="https://papiamentoaruba.com/">Papiamento</a> for dinner, which is a must. It's a beautiful and quaint little place, with seating around the pool. I'm not sure how it happened, but we ended up at a special covered table - best seat in the house. I got the fish with almonds and it was delicious, but I would order the shrimp on the stone if I went back, as that looked amazing. Meeting and getting to know these women were the highlight of my trip. We ranged in age from 30s to 50, and we laughed all night, just getting to know one another and hear each other's stories. I am so, so grateful for meeting them.<br />
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Papiamento's is steps away from the hotel. Those who had roommates headed back to their rooms. The two of us in our single rooms sat on the patio and had another glass of wine by the pool, enjoying our time.</div>
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Day 3</h3>
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We left for smoothies and 7:30am practice again. I believe this was the practice where Rachel broke down vinyasa. Again, we worked in partners after she and Jess demonstrated. This is really important because so many people don't know how to properly do one - I didn't learn how to effectively do chaturanga until I attended to <a href="https://www.instagram.com/lara.heimann/">Lara Heimann</a>'s class in Princeton...one class and I mastered chaturanga for the first time in 19 years...and Rachel helped with that as well. So much of it is muscle memory, so we really have to forget what it is we have been doing wrong for so many years to learn the proper way. This will help us to avoid injury from doing it wrong as well. As an aside, I first discovered Lara from Rachel's podcast. She is an amazing yoga instructor and anatomy guru, so if you are ever in Princeton, you must take her class at <a href="http://yogastream.net/">Yogastream</a>! She also teaches the anatomy portion at Island Yoga's 200-hour YTT.</div>
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After breakfast, we left for a hike. I'm not sure where it was, but I'm pretty sure the beach we ended up at was on the North Shore. The buses to the hiking location were super fun, as they were colorful and did not have windows so we could feel the Aruban breeze. The hike was not difficult, but the terrain was uneven, so sneakers were a must (no flip-flops). After the hike, we hung out at a beautiful spot on the beach where there were waves hitting the rocks, but there were also shallow places to stand and swim in the water. Some practiced their newly found headstands. Rachel's sister was sick so Rachel did not join us, but Dennis and their friend (who also sews <a href="https://www.facebook.com/tangerinearuba/photos/a.310524702327666.71639.310502778996525/1688475101199279/?type=3">Tangerine</a> brand items right there in the Island Yoga Boutique) escorted us, along with some members of the Island Yoga team. We were supposed to go to the Natural Pools, but Dennis said the waves were too strong, and that sometimes groups cannot go due to this. So we stayed at the beach for an hour and a half. Snacks and sunscreen are a must! The Turkish towel in our goodie bags were great as a wrap as well. Hiking the way back felt harder going up the hill to the buses, but it also felt great.<br />
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I believe this is the day that Kelley and I ventured out to the area near the <a href="http://www.renaissancearubaresortandcasino.com/default-en.html">Renaissance Hotel</a>. This area has a lot of upscale shopping as well as kiosk-style souvenir shops. This hotel is not on the beach so they have their own private island where you are taken by boat to swim in the ocean with flamingos nearby. If you stay at the hotel, you can go to the island for free, but otherwise, it's a $125 fee. We went to Starbucks, where Kelley bought an Aruba mug, and we walked around the shops. A highlight for me was eating a spaghetti taco in one of the markets...unbelievably good! There was not all that much to do, but it was fun just walking around and seeing the outdoor shops. We went to a cool local artist shop called <a href="https://www.facebook.com/arubacosecha/">Cosecha</a> and took our picture by the huge "I Love Aruba" sign. If you take the cab back from the Renaissance, it was a bit more money.<br />
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We got back, changed, and got ready for 6:30pm yoga. Rachel knew how tired we would be and taught a yin class that night. We came into the shala all set up with mats, bolsters, blocks, and blankets. I actually fell asleep for a bit during class, and I think some others did, too. This was the hardest practice of all for me: to sit in a pose for so long. In two hours, I think we only did six or seven poses! But it was awesome to see how every yoga class that Rachel taught was different. </div>
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This night, as it was much later, a few of us ordered the Nourish meals to go (staffers boxed it up for you) while some of the others got a massage or cupping treatment from <a href="http://www.reikibystephanie.com/">Stephanie Moore.</a> Stephanie was flown out to offer massages, cupping, or Reiki to any of us during our free time for about $70 (plus tip.) More about that later! We ate our meals on the patio with the wine we bought from Super Food, debriefing about the day and learning more about each other.<br />
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Day 4</h3>
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I am not sure which practice it was, morning or afternoon, but it was the best flow yet if that was even possible. I think Rachel put in every asana. And the music!! I know if I hear a song from any of the flows, I will be brought right back to Luna Shala. I think this was the day that Rachel broke down crow pose for us. It's hard to remember, as the days were hard to separate. During breakfast, <a href="http://www.sgtpeppersfriends.com/">Sgtpeppersfriends.com</a> came to visit us! This is Rachel's <span style="background-color: white; color: #28323f; text-align: justify;"><span style="font-family: "times" , "times new roman" , serif;">non-profit animal rescue organization founded and located in Aruba. They brought several puppies for us to play with! One of the dogs was taken home by Kait, a woman on our retreat. Sgt Peppers Friends pays the $250 to fly the animals to a loving home. If you are traveling from Aruba and want to transport a rescue dog or cat back </span></span><span style="background-color: white; color: #28323f;"><span style="font-family: "times" , "times new roman" , serif;">to the USA, Canada, the Netherlands or Sweden, you can</span></span><span style="background-color: white; color: #28323f; font-family: "times" , "times new roman" , serif; text-align: justify;"> </span><a href="http://www.sgtpeppersfriends.com/flight-volunteer-form/" style="background-color: white; font-family: Times, "Times New Roman", serif; text-align: justify;">fill out this form.</a><br />
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This excursion day was the best, as we set sail on the Pelican with Rachel. The crew provided fruit skewers and tofu and tomato snacks (I normally HATE tofu, but every time I had it in Aruba, it was delicious.) and drinks at no charge. We climbed out to the bow of the ship and sat on nets and saw the beautiful ocean below us. We stopped twice to snorkel, once at a shipwreck. Rachel was generous with allowing anyone who wanted to snap selfies with her. She also chatted with anyone eager to ask questions. Dennis and Lea Luna swam out to meet us, and "Luni" did downward dog for us a few times, to much applause. It was a happy, happy day. I could not tell groups that day; everyone talked with everyone. The music was loud, the sun was bright, the ocean was inviting, and we all just really felt relaxed!<br />
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Some of us opted to stay at the beach for a bite near the hotels after the excursion. It was nothing special, but the view and the company were perfect. We did a little shopping, though much was closed due to it being Sunday. There were plenty of kiosks to buy souvenirs. We got a coffee at Starbucks and hailed a cab to go back to the hotel in time to change and grab a smoothie before practice. I will never forget the barista writing "Wala" for Yali's name, and that nickname has stuck :)</div>
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I was nervous for yoga at 5pm that night, given that I'd had an Aruba Arriba on the boat, a beer at lunch, and that it was our third day of sun. But Rachel started off slow and got us moving to the music. I forgot I was tired. In fact, I forgot everything except for the in the moment flow. It was the best. </div>
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For dinner, we made reservations at <a href="http://www.barefootaruba.com/">Barefoot</a> after three of us separately heard how good it was. It did not disappoint. The staff was incredibly nice. (I should also say that the cab driver was so funny and in general the cab drivers are great - also, Arubans speak at least four languages!) We sat at a table on the beach and took our shoes off and dug our toes in the sand. There were wine specials, and I believe we all ordered fish of some sort. It was delicious. We laughed a lot. And we couldn't decide on one dessert, so instead we ordered the top three desserts on the menu, which were all fabulous!<br />
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Day 5</h3>
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This day, instead of practicing in the Shala, we all did <a href="https://islandyoga.com/sup-yoga/">SUP yoga</a> (Stand Up Paddleboard) by the Ritz. Buses took about 13 of us each hour to do an entire yoga class on the paddleboards. If you have not done this, you really are in for a treat. If you fall in, you fall in...the water is only about waist deep. The wind made the boards bang into each other now and then, which is half the fun when you are balancing in a pose. And the teacher (not Rachel this time, since there were about four different groups) explained how to adjust your pose so that you could find your center of balance. Savasana on the water is something that just can't be explained. It's beautiful and pure to hear the ocean after a full practice. The trip honestly kept getting better and better. We could have breakfast before or after, and I LOVED the hanuman smoothie: peanut butter and chocolate protein...oh how I want one right now!!</div>
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This day, we had a little time to ourselves. I have been to Aruba before, and since we did go into town a few times already, I decided to book a Reiki session with <a href="https://www.instagram.com/mindbodyspiritinbalance/">Stephanie</a>. I had absolutely no idea what to expect - the only reason I decided to try Reiki was that I get regular massages and had tried cupping before, so I thought I'd try something new.</div>
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I stepped into the room and got up on the table. You don't need to undress for Reiki (I didn't know this.) Stephanie stood over me and was extremely tender and warm. She asked me why I was here and what I was feeling. I told her I was sad that my best friend had died in April. She handed me tissues and we talked a bit about that. She then touched my heart and made me go deeper. Literally and figuratively she touched my heart. She helped me with some private issues, and I came away with a deeper understanding of what I needed to do to be happier. As my friend said, Reiki was like "therapy and acupuncture at the same time," and at this point, I had definitely felt the therapy. </div>
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Stephanie put an eye pillow over my eyes and told me she would not be speaking to me during the Reiki treatment, as she meditates, but that she would be moving around my body. I would know I was done when she put her hand on my shoulder,</div>
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I honestly had no idea what to expect. Suddenly, I saw an aura of blue swirling above me. I didn't know if maybe she was shining lights (she wasn't), but I couldn't get enough of it. Then, the aura turned green...I can't explain it other than it was swirling and swirling over my face. Then it turned yellow! I saw orange, kind of, after that, but it wouldn't fully come. It was teasing me. Then nothing...I did not know what any of this meant. Finally, I saw purple and white for a little while, and then nothing. When she touched my arm I opened my eyes and told her I saw colors. She was very excited and said this happens to people, but not all the time. I asked if I could see the Chakra colors (shown below), and I was "chak'd" haha shocked that they corresponded to where she was creating energy around my body! I did not know the chakras in order, nor even the colors prior to this session, but now I will never forget them.<br />
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The fact that I saw or didn't see certain colored chakras after I looked up their meanings was very telling to me. It was incredible! It felt so spiritual and magical. I didn't feel anything directly after the session other than a need to tell everyone about the colors, but by the end of the night, I definitely felt much, much lighter. </div>
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I went to Nourish Cafe for lunch and ate with a lovely aunt that I had done eye-gazing with and her equally lovely niece. Since I had shared with her intimate details of my life and vice versa, I immediately felt like I had a connection with her. It was such a nice lunch - I had a sweet potato and bean chili - and then I shopped a bit more in the boutique and packed a bit. </div>
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At 2pm, we had an optional Mandala Workshop given by <a href="https://www.instagram.com/courtneybetts/">@courtneybetts</a>. Courtney is the one who painted the gorgeous mandalas on the outside of Island Yoga as well as the ones in front of Luna Shala that depicted a female in a series of Vinyasa poses. She is amazing and self-taught. The cost for this workshop was $20, and well worth it. It was truly therapeutic to learn how to create this piece of beauty. All that was required was: paper, pencil, compass, protractor, eraser, and marker. Rachel and her mother joined us here, and it was just a fun way to chill. I am definitely going to do this with my students, and I will blog a more mathy post on it when I do!<br />
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After Mandala drawing, we had our final evening smoothie, and after another amazing practice, we got in a circle and shared the answer to, "What will you take home with you?" This probably took about an hour and a half to get through everyone. There were tears and as Rachel would say, "epiphanies." I came home with #newoldfriends (thanks, Yali, for that hashtag), new physical things to work on, like bringing my foot to my hand from downward facing dog without lifting my palm off the ground, new self-improvement things to work on, such as how to be a better listener and a better partner, and I just came home "lighter." The school I work at has a mission of educating students in "mind, body, and spirit," and I feel like I was able to home in on each of these things during this retreat.<br />
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We did not have time to change (though a few people did), and we went to the outside room and picked up a yummy sangria as Rachel toasted. (Note: the night before, although we didn't go, Dennis made and served Pomegranate Margaritas.) We were served a delicious meal of tofu and some type of peanut sauce (allergies were asked about beforehand) and we ordered wine or beer and just laughed and talked with many more of the girls we had not really spoken to before. If only we had more time. We were encouraged to rip the pages out of our journal where we wrote what we wanted to "let go" and throw them into the fire pit. We got more selfies with Rachel (are there ever enough?) and finally headed back to the pool area with a large group and some wine and (more!) food. We opened up to each other once more, a final debriefing and group therapy session before heading to bed at 1am!</div>
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Day 6</h3>
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Yes, up again for 7:30am yoga!! I did not want to go after such a festive night, but I was glad I did. Lea Luna showed up for the last class for a few minutes (I forgot to mention that Ringo joined us one day as well.) The savasana at this class was the best yet, with the song <a href="https://open.spotify.com/track/4cAsKEGHGZ2nMxwSduCgVb">Let It Be - Long Version</a>. The chills that went through my legs made it feel like I was floating. <a href="https://open.spotify.com/track/7mptueK99zxqmgIdT3SaWF">Spirit Bird</a> was another song she played on a different day during savasana that was incredible...there were so many great songs! But this gospel version of <i>Let It Be</i> brought out strong emotions. I watched Rachel press her hands to someone's forehead, who, for lack of a better word, lost it with the emotion of the song. Immediately, her crying calmed. Rachel is a healer. It was an incredible moment, and there were many tears to wipe after class. We made sure we all wrote our intention on the Island Yoga wall before leaving this incredible place.<br />
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We went to our last breakfast and sadly, back to pack and get ready for the staggered buses to take us to the airport. Quick note: you clear customs in Aruba, at least to the USA, but it is quite lengthy. After checking your bag, you need to grab it again through customs and then put it on a belt once more. They do have Global Entry in Aruba, so if you have it, you will skip a long line. And do not buy water until you are completely at the gate, or else you will have to throw it out when you go through security for the second time.</div>
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We left more balanced, happier, and for some, worried about returning home and back to chaos. But for a short moment in life, we experienced peaceful bliss with strong, open women who have our backs. I feel more at peace now than I ever have before. I am so thankful to Rachel and her team for providing us with this incredible opportunity. TAKE ME BACK!</div>
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Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com6Noord, Aruba12.5642591 -70.035487199999977-12.957775400000001 -111.34408119999998 38.0862936 -28.726893199999978tag:blogger.com,1999:blog-3454490001772574770.post-57065368119924143892018-04-30T19:53:00.000-04:002018-08-14T06:14:23.629-04:00Algebra 2 and Precalculus Unit Circle Projects 2018<div class="separator" style="clear: both; text-align: center;">
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Every year, I <span style="background-color: white; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px;"> assign my </span><span style="background-color: white; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px;">Pre-Calculus and Algebra 2 Honors classes a </span><a href="https://www.bloglovin.com/blogs/secondary-classroom-can-be-fun-too-5775125/unit-circle-art-3053936483/" style="background-color: white; color: #6699cc; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px; text-decoration-line: none;">Unit Circle Art</a> project,<span style="background-color: white; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px;"> which I got from Miss Rudolph. I loved her guidelines and rubric, and I have used it in my classes since <a href="http://eatplaymath.blogspot.com/2015/05/the-unit-circle-of-life.html">2016</a> and <a href="http://eatplaymath.blogspot.com/2017/04/algebra-2-honors-unit-circle-projects.html">2017</a>. I don't have pictures of the projects I got prior as I probably wasn't blogging then. The toga really stands out from the student who graduated <b>college</b> last year! So I've been doing this a while, but Miss Rudolph really helped me with her rubric. I assign this as a 30 point project, and the top three win 1, 2, and 3 points extra credit. The winners are chosen by another teacher and sometimes his/her students. </span><br />
<span style="background-color: white; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px;"><br /></span> <span style="background-color: white; color: #333333; font-family: "arial" , "tahoma" , "helvetica" , "freesans" , sans-serif; font-size: 14.85px;">This year, the winner was the HQ-nit circle, a play on the trivia game HQ, which we try to play every so often in one of my classes. </span></div>
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<a href="https://4.bp.blogspot.com/-US3pi3LaaEE/Wuemmb0LOqI/AAAAAAAAEg0/lbb40CGWjMwCTeTnvmIPzHxmPjUoixkoACLcBGAs/s1600/IMG_7614%2B2.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1600" data-original-width="1108" height="320" src="https://4.bp.blogspot.com/-US3pi3LaaEE/Wuemmb0LOqI/AAAAAAAAEg0/lbb40CGWjMwCTeTnvmIPzHxmPjUoixkoACLcBGAs/s320/IMG_7614%2B2.JPG" width="221" /></a></div>
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It was fun to tweet to <a href="https://twitter.com/hqtrivia">@hqtrivia</a> and get a <b>ton</b> of likes.</div>
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<a href="https://3.bp.blogspot.com/-cdphl3Vsy3E/WuencxZodUI/AAAAAAAAEhI/sWI7VsTLOoo6u6SqSuWW0CMvwxoVAlp3gCLcBGAs/s1600/Screen%2BShot%2B2018-04-30%2Bat%2B7.31.26%2BPM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="157" data-original-width="692" height="72" src="https://3.bp.blogspot.com/-cdphl3Vsy3E/WuencxZodUI/AAAAAAAAEhI/sWI7VsTLOoo6u6SqSuWW0CMvwxoVAlp3gCLcBGAs/s320/Screen%2BShot%2B2018-04-30%2Bat%2B7.31.26%2BPM.png" width="320" /></a></div>
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And then <a href="https://twitter.com/ScottRogowsky">@ScottRogowsky</a>, the host, posted on Instagram!</div>
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<a href="https://2.bp.blogspot.com/-LqXOUfsgIIs/WuepkxhWy1I/AAAAAAAAEhU/qlmNRO71Acc9uUEtc6XI6-9YPvdC8NLNgCLcBGAs/s1600/IMG_6C92B772D967-1.jpeg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="1334" data-original-width="750" height="320" src="https://2.bp.blogspot.com/-LqXOUfsgIIs/WuepkxhWy1I/AAAAAAAAEhU/qlmNRO71Acc9uUEtc6XI6-9YPvdC8NLNgCLcBGAs/s320/IMG_6C92B772D967-1.jpeg" width="179" /></a></div>
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<span style="text-align: left;">That was fun today...here are some other creative projects.</span></div>
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<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-7pojfGxY7Us/WuelcJjCO8I/AAAAAAAAEgE/kxP2BkDK-Coxt0OBdS-qY58ph-R4Vm0wwCLcBGAs/s1600/IMG_8899.JPG" imageanchor="1" style="font-size: medium; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1280" height="320" src="https://3.bp.blogspot.com/-7pojfGxY7Us/WuelcJjCO8I/AAAAAAAAEgE/kxP2BkDK-Coxt0OBdS-qY58ph-R4Vm0wwCLcBGAs/s320/IMG_8899.JPG" width="256" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Swimming lines/lanes!</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-FGuAecTFMCY/WuelfghvvxI/AAAAAAAAEgM/1MSkRLcLmHoEns4hypzeRElryhN8L-m6wCLcBGAs/s1600/IMG_9219.JPG" imageanchor="1" style="font-size: medium; margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1200" data-original-width="1600" height="240" src="https://1.bp.blogspot.com/-FGuAecTFMCY/WuelfghvvxI/AAAAAAAAEgM/1MSkRLcLmHoEns4hypzeRElryhN8L-m6wCLcBGAs/s320/IMG_9219.JPG" width="320" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The details of this web are incredible!! See the x and y on the spiders??</td></tr>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-EJ_UCR45cdg/Wueml3MaAcI/AAAAAAAAEgw/XY6R_40NRdoDIEYHvbqoyRDd1XQP4zwNACLcBGAs/s1600/IMG_2970%2B2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" data-original-height="1600" data-original-width="1286" height="320" src="https://4.bp.blogspot.com/-EJ_UCR45cdg/Wueml3MaAcI/AAAAAAAAEgw/XY6R_40NRdoDIEYHvbqoyRDd1XQP4zwNACLcBGAs/s320/IMG_2970%2B2.JPG" width="257" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Bowling - the bowling ball slides back and forth! I had this as a boomerang, but I lost it...<br />
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<tr><td><a href="https://1.bp.blogspot.com/-5XmHNUBY6wg/WuelL6GvJuI/AAAAAAAAEfY/WtAlK3Oq84wvVyfHZdK0Se7AvpJ1e5o1QCLcBGAs/s1600/IMG_5553.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-5XmHNUBY6wg/WuelL6GvJuI/AAAAAAAAEfY/WtAlK3Oq84wvVyfHZdK0Se7AvpJ1e5o1QCLcBGAs/s320/IMG_5553.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="font-size: 12.8px;">A good use of the unit circle "bow tie!"</td></tr>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-uWnBe9QQ5sQ/Wuek-kGRTtI/AAAAAAAAEe4/dClUDC8QewwxK_Hz7WoZrSr6XtG4FOzLwCLcBGAs/s1600/IMG_0698.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://4.bp.blogspot.com/-uWnBe9QQ5sQ/Wuek-kGRTtI/AAAAAAAAEe4/dClUDC8QewwxK_Hz7WoZrSr6XtG4FOzLwCLcBGAs/s320/IMG_0698.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">watermelon</td></tr>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-WEnBlPqrkMY/Wuek_aJeb2I/AAAAAAAAEe8/hAdYXZjj4cYFyqxMT43h7Tmu7qgQlVfVgCLcBGAs/s1600/IMG_0797.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://3.bp.blogspot.com/-WEnBlPqrkMY/Wuek_aJeb2I/AAAAAAAAEe8/hAdYXZjj4cYFyqxMT43h7Tmu7qgQlVfVgCLcBGAs/s320/IMG_0797.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">surfboard</td></tr>
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<tr><td style="text-align: center;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://4.bp.blogspot.com/-6EwiDvNR9tc/WuelEXV5k7I/AAAAAAAAEfA/QEF7RPVf_SU30nl7PLSeLN5LmEOT1OYHgCLcBGAs/s320/IMG_1149.JPG" style="margin-left: auto; margin-right: auto;" width="240" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Fortnight</td></tr>
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<a href="https://4.bp.blogspot.com/-6EwiDvNR9tc/WuelEXV5k7I/AAAAAAAAEfA/QEF7RPVf_SU30nl7PLSeLN5LmEOT1OYHgCLcBGAs/s1600/IMG_1149.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><br /></div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-i1l-OfzCmPU/WuelEsRNn9I/AAAAAAAAEfE/MqoLLMLaqzUe9VRi0TF86ohBlbnaEY9NwCLcBGAs/s1600/IMG_1669.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://4.bp.blogspot.com/-i1l-OfzCmPU/WuelEsRNn9I/AAAAAAAAEfE/MqoLLMLaqzUe9VRi0TF86ohBlbnaEY9NwCLcBGAs/s320/IMG_1669.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Lake Okeechobee</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-cG_B2PpmhlA/WuemmZi6yyI/AAAAAAAAEg4/MZ1hskXLN2w7kkCaeoZ0rCNTTYbW7jGpACLcBGAs/s1600/IMG_9588%2B2.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1317" height="320" src="https://1.bp.blogspot.com/-cG_B2PpmhlA/WuemmZi6yyI/AAAAAAAAEg4/MZ1hskXLN2w7kkCaeoZ0rCNTTYbW7jGpACLcBGAs/s320/IMG_9588%2B2.JPG" width="263" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">I scream for the Unit Circle!</td></tr>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-E67pCU1aPAk/WuelLpCO7RI/AAAAAAAAEfU/6C-PmIMZ8pEkxeD-QcxJ3gVwJGit_F9kgCLcBGAs/s1600/IMG_3094.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://3.bp.blogspot.com/-E67pCU1aPAk/WuelLpCO7RI/AAAAAAAAEfU/6C-PmIMZ8pEkxeD-QcxJ3gVwJGit_F9kgCLcBGAs/s320/IMG_3094.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Where will I put this in my house?? </td></tr>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-JJXGNbnbM_c/WuelLSMJPYI/AAAAAAAAEfQ/X9mOyD8sTbcPF5ID3kh0UIqFDruz4IrdwCLcBGAs/s1600/IMG_3866.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://4.bp.blogspot.com/-JJXGNbnbM_c/WuelLSMJPYI/AAAAAAAAEfQ/X9mOyD8sTbcPF5ID3kh0UIqFDruz4IrdwCLcBGAs/s320/IMG_3866.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">The student's nickname who made this is Mr. 300</td></tr>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-gpeGkpwcoEk/WuelRYp6EMI/AAAAAAAAEfo/HmRqgxMucyE9eslOcT2awKZm2GO1jJxXwCLcBGAs/s1600/IMG_5790.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://4.bp.blogspot.com/-gpeGkpwcoEk/WuelRYp6EMI/AAAAAAAAEfo/HmRqgxMucyE9eslOcT2awKZm2GO1jJxXwCLcBGAs/s320/IMG_5790.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">This was clever...a doodle bug!</td></tr>
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<tr><td style="text-align: center;"><a href="https://1.bp.blogspot.com/-76blIo3HO6w/WuelRet1jxI/AAAAAAAAEfk/KA-iGtPA6LU-WAt464jYFicic-yALq0FgCLcBGAs/s1600/IMG_6069.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-76blIo3HO6w/WuelRet1jxI/AAAAAAAAEfk/KA-iGtPA6LU-WAt464jYFicic-yALq0FgCLcBGAs/s320/IMG_6069.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">licorice...not supposed to bring food, but it was sweet...</td></tr>
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-FBzGiSa0xvU/WuelR2p-SjI/AAAAAAAAEfs/QeJwJlTsE7wf5SOnDuwkFj2A6vtxe5P7ACLcBGAs/s1600/IMG_7437.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-FBzGiSa0xvU/WuelR2p-SjI/AAAAAAAAEfs/QeJwJlTsE7wf5SOnDuwkFj2A6vtxe5P7ACLcBGAs/s320/IMG_7437.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">More food...happy students.</td></tr>
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-WkZpu5nn7Q0/WuelX3WqWMI/AAAAAAAAEf0/quFDT0CP9LcJLM0IwDQHCLfp9ZFgqqqOQCLcBGAs/s1600/IMG_7516.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-WkZpu5nn7Q0/WuelX3WqWMI/AAAAAAAAEf0/quFDT0CP9LcJLM0IwDQHCLfp9ZFgqqqOQCLcBGAs/s320/IMG_7516.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">I used this a lot to demo when students were confused. </td></tr>
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<tr><td style="text-align: center;"><a href="https://2.bp.blogspot.com/-ypjzNXvlY9E/WuelYPsp0NI/AAAAAAAAEf4/iJCMwIEJYq4DamXCx0Aykr_mvVImog96wCLcBGAs/s1600/IMG_7684.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://2.bp.blogspot.com/-ypjzNXvlY9E/WuelYPsp0NI/AAAAAAAAEf4/iJCMwIEJYq4DamXCx0Aykr_mvVImog96wCLcBGAs/s320/IMG_7684.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Pokemon with a sigma</td></tr>
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<tr><td style="text-align: center;"><a href="https://3.bp.blogspot.com/-dZjP6mqlGMs/WuelffEP5MI/AAAAAAAAEgI/OfYTWcacLYUBIxGRmP9gB13DOIg6Ia1gwCLcBGAs/s1600/IMG_9215.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://3.bp.blogspot.com/-dZjP6mqlGMs/WuelffEP5MI/AAAAAAAAEgI/OfYTWcacLYUBIxGRmP9gB13DOIg6Ia1gwCLcBGAs/s320/IMG_9215.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Big Ben</td></tr>
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<tr><td style="text-align: center;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://1.bp.blogspot.com/-ZaJLwc3YdNc/WuelituzIJI/AAAAAAAAEgU/EaHQrNYjVwUoRgXaG7X9hgFLMDqwUQjTgCLcBGAs/s320/IMG_9315.JPG" style="margin-left: auto; margin-right: auto;" width="240" /></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Pac Man on the computer!</td></tr>
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<a href="https://1.bp.blogspot.com/-ZaJLwc3YdNc/WuelituzIJI/AAAAAAAAEgU/EaHQrNYjVwUoRgXaG7X9hgFLMDqwUQjTgCLcBGAs/s1600/IMG_9315.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a><br /></div>
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<tr><td style="text-align: center;"><a href="https://4.bp.blogspot.com/-VKY9YbKVamE/WuhZZJJLs5I/AAAAAAAAEho/1yJti8iHMasn9lxXPzqE3g4DBstJBA3qACLcBGAs/s1600/IMG_4592.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto; text-align: center;"><img border="0" data-original-height="1600" data-original-width="1200" height="320" src="https://4.bp.blogspot.com/-VKY9YbKVamE/WuhZZJJLs5I/AAAAAAAAEho/1yJti8iHMasn9lxXPzqE3g4DBstJBA3qACLcBGAs/s320/IMG_4592.JPG" width="240" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;">Famous building in Brazil</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Our crest!</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Cool sun artwork</td></tr>
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<tr><td class="tr-caption" style="text-align: center;">Wheel of Fortune!</td></tr>
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Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com12tag:blogger.com,1999:blog-3454490001772574770.post-25776245565844792582018-04-28T15:53:00.000-04:002018-04-28T20:35:24.921-04:00A Few Weeks of Relative Maximums and Relative MinimumsThe title of this post is my math play on words for these last couple of months, as I have been away almost every weekend for some highs and lows.<br />
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Three weeks ago, I lost <a href="http://notgonnabeadebbiedowner.blogspot.com/">my childhood best friend to ALS.</a> She asked me back in 2016 if I would write one of her eulogies. A few weeks before she died, I visited her and was able to read my eulogy with her. It was a gift I will never forget: to tell a person how much you love her and how much she impacted your life. We cried. Ugly cried. We hugged. Well, I hugged because she couldn't. She spelled out for me, with her laser pointer, "I am not worthy." If she only knew how worthy she was. Over 600 people were in attendance and four other very close people in her life wrote very different, yet equally if not more impactful eulogies. The funeral was beautiful, starting with Debbie picking out the song <a href="https://www.youtube.com/watch?v=8N0QOVBefzA">Thank You by Jennifer Nettles</a> and having it played for all of us. I was numb. I was lost. I had no time to mourn.<br />
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I flew back to Florida a few hours later and immediately finished prepping for our first <a href="https://www.saintandrews.net/page/news-detail?pk=947271">TEDxSaintAndrewsSchool event </a>three days later. I went from possibly the lowest point in my life to probably the highest (professional) moment within a matter of days. The <a href="https://sites.google.com/saintandrews.net/tedxsaintandrews/home">fifteen students and three guest speakers</a> absolutely blew me away. They did better than I ever could have imagined, and more importantly, I watched as the students shined. Four months earlier, they started the <a href="http://eatplaymath.blogspot.com/2018/01/a-very-busy-second-semester-gratitude.html">TED-Ed class</a> with little idea of what it was about and no idea that they would do a TED talk. And they all ended with an impactful idea worth spreading. Their and their parents' smiles said it all. Yet every moment when I wasn't busy, every moment I was alone, all I could think of was Debbie.<br />
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Around the same time, I helped one of my best friends with her ice cap through her chemotherapy. It's a cap she uses so she won't lose her hair. She's doing OK, but she feels sick for a week after and gets chemo every two weeks. That's not much time to feel like herself. All while she's still teaching. We watched part of the first episode of the <a href="https://www.imdb.com/title/tt5580540/">Santa Clarita Diet</a> as the poison seeped through her veins, and we had to turn it off as we both got nauseated - from the show, not the chemo! We sent tons of pictures of raw meat back and forth to each other with the throw-up emoji for days, just giggling about it as I'm thinking about it now. Highs and lows.<br />
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The next week, I took 30 kids to Mu Alpha Theta states. It was so much fun. I laughed with my incredible colleagues and students even as the kids competed constantly for almost two days straight. We started out at Universal Studios and went on a few rides and giggled when some of the adults turned a bit green. I heard a freshman exclaim, "Mrs. Winer! I won!" when his name was called for an award, and immediately watched him call his mother afterward. I constantly laughed while playing trivia with the students and cheered with them when we came in 3rd place out of over forty schools. I watched the kids sit in a huge circle outside of my hotel room late after awards because they weren't allowed to have boys in girls rooms and vice versa. They sat and played cards with the newest member of the math department, a male teacher who is equally as nerdy as me. I watched them grow to love him and learn more about him and realize they had a lot in common with him. I felt proud of him and of my students.<br />
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What no one knew is that when they were competing, I had some downtime. At Starbucks, waiting in line, I sobbed, quietly, into my MAO sweatshirt of all things. I read and answered texts from Debbie's friends and family while in line-- none of us sure we even believe that she is gone. How could I no longer see my sweet friend?? And then, a kid would appear in line, and just like that, I snapped out of my pain and into proud momma mode.<br />
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How can one go through a series of relative maxes and mins so fast? A sine curve? With a period of π/10000 for us math folk. Up down up down...<br />
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And the last maximum so far...I just got back from NCTM Annual. It was amazing. <a href="https://twitter.com/saravdwerf">Sara VanDerWerf</a> is my hero. She has superpowers for sure. I think she makes everyone she speaks to feel important. I am going to do math talks and make sure students can "see it before I show them" and that students will "say it before I tell them." I will try to teach with a "full stack" like <a href="https://twitter.com/ddmeyer">Dan Meyer</a>. I will try to do all of the things I learned. The biggest relative max of all was when I gave my first talk ever on <a href="http://eatplaymath.blogspot.com/2017/05/find-student-taught-math-lessons-and.html">Students Teaching Students</a>. I ran out of handouts. That means I had over 200 people in attendance, and they were so engaged and interested. And I did it...I used to hate public speaking, but I was able to speak without having all my notes written down in front of me, and I didn't fail. It was actually amazing. I had an awesome time with my former colleague <a href="https://twitter.com/Mfredgrassi">Mary.</a> We laughed the whole time with my other colleague Ari. I bumped into my son's Kindergarten teacher from 15 years ago as well as a former student. I helped a group of pre-service teachers when the session we were at was at a lull, and it was so cute to watch them take copious notes on everything I said. It was so much fun.<br />
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But there was a low. A dear friend of mine whom I met for a drink there told me she has Parkinson's. She was there for me when I had my medical issues in 2004, climbing Philmont with her son in my honor. And to hear this news - to hear that my avid runner friend, my brilliant author friend - is having to deal with such a huge burden...it's almost too much.<br />
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So now, I'm home and...it's time to mourn. It's time to mourn all the things around me that are falling apart and at the same time to be thankful for everything I have. It's time to be grateful I can make it to yoga this afternoon and know that my body will do what my instructor tells me to do. Well, mostly. It's time to be there for my students and let them know I'm here for them in a month when I've been out of school much more than I care to admit. It's time to thank G-d for being alive and not worry about petty things.<br />
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Who knows how long my domain will last. It's my range of actions that I need to be most proud of in the big function f(x) = life.<br />
<br />Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com0tag:blogger.com,1999:blog-3454490001772574770.post-89732285576230626342018-01-28T20:26:00.000-05:002018-01-28T20:26:31.457-05:00Like a Good Puzzle? Try the TED-Ed Dark Coin Riddle<iframe allow="autoplay; encrypted-media" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/pnSw8g3DPHw" width="560"></iframe><br />
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Have you seen the new Dark Coin Riddle? Give it a try, but also check out the TED-Ed <a href="https://ed.ted.com/lessons/can-you-solve-the-dark-coin-riddle-lisa-winer">lesson</a> to go even further with it.<br />
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Want to try some more? Give these a try with your classes!<br />
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<iframe allow="autoplay; encrypted-media" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/c18GjbnZXMw" width="560"></iframe> <iframe allow="autoplay; encrypted-media" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/ZKh6z0X6KRw" width="560"></iframe> <iframe allow="autoplay; encrypted-media" allowfullscreen="" frameborder="0" height="315" src="https://www.youtube.com/embed/ADR7dUoVh_c" width="560"></iframe>Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com0tag:blogger.com,1999:blog-3454490001772574770.post-64750465321586074582018-01-06T10:11:00.002-05:002018-01-06T10:26:11.651-05:00A Very Busy Second Semester (Gratitude)I have so much going on right now, I feel the need to blog about it so that I can see it all in one place. So, as it is for many bloggers, this is more for me to just put it all down somewhere, organize it, and hold myself accountable!<br />
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TEDx and my new TED-Ed class</h4>
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I have put in an application to host a <a href="https://www.ted.com/participate/organize-a-local-tedx-event">TEDx </a>event at my school. This is really exciting, but it is also nerve-wracking at the same time. I've decided that one of my New Year resolutions is to give students a voice. I read recently that one of your New Year resolutions shouldn't be about you. I like that, and so I spent a few days during winter break really thinking about how I can commit to that. I planned my TED-Ed class for two weeks, curating TED talks to watch, assigning small assignments, explaining the purpose of the class, etc. I'm getting excited. The irony is that I am a math teacher who at one time was so paralyzed by public speaking that I can't believe I am the one to teach students how to give a TED talk!! But I see it as an opportunity to give students a way to spread an idea that is unique to them and that makes their hearts beat faster. I'm pumped. I'm nervous, but it's a good nervous. And after 27 years of teaching, it's exciting to have something new to do!</div>
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I have been preparing by using the amazing modules provided by <a href="http://eatplaymath.blogspot.com/search?q=ted+ed+club">TED-Ed clubs</a> (click the link to find out how to get the valuable resources) and by reading <a href="https://www.amazon.com/TED-Talks-Official-Public-Speaking/dp/1328710289/ref=sr_1_1?ie=UTF8&qid=1515246943&sr=8-1&keywords=ted+talk+chris+anderson">Chris Anderson's TED Talks book</a>. He's the curator of TED. I met him in person at <a href="http://eatplaymath.blogspot.com/2016/12/an-incredible-ted-ed-weekend-for.html">TED-Ed Weekend</a>, which is enough to inspire me to help my students do incredible things. Stay tuned!! The video below explains TED-Ed clubs. Watch below!</div>
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A Math Fair</h4>
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I wish I could remember how I figured out about the <a href="http://jrmf.org/">Julia Robinson Math Festival</a>. Each year, I've charged my <a href="http://eatplaymath.blogspot.com/2017/11/an-untraditional-route-for-veteran-math.html">Mu Alpha Theta</a> vice-presidents to come up with a school-wide community service project, and this is the first year that I have students who followed through! The goal is to have a math fair, grades JK - 8, for students and their parents, with our club members facilitating. I've listed some info below. The goal is to have our 85+ club members work with younger students to inspire them to enjoy mathematics. I hope that this will be a yearly festival! </div>
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Speaking at NCTM</h4>
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Again, never would I have thought that I could do public speaking. A sudden calm came over me in the last few years. I seriously used to get so nervous when I found out that I had to speak (not in the classroom, of course!), that I would be sick to my stomach for weeks, obsessing about what could go wrong. However, in the last year or so, this feeling has dissipated. I don't know why. But I'm not going to question it. I spoke publicly twice last year, once in front of a a group of alum and once in front of maybe a hundred and fifty people, telling my story about my love of my school and my job. It was extremely rewarding, which is another reason why I want to help students share their unique stories.</div>
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I applied to speak at <a href="http://www.nctm.org/Conferences-and-Professional-Development/Annual-Meeting-and-Exposition/">NCTM Annual in Washington DC</a> last year and was happy to hear that I was selected to speak about my <a href="http://blog.ed.ted.com/2017/10/08/boost-school-engagement-through-students-teaching-students/">TED-Ed project Students Teaching Students</a>. I have yet to plan this talk, but hey, that's what spring break will be for!! This is another first that I'm excited about, but it feels stressful not having it ready yet. </div>
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Competitions</h4>
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There are a lot of MAO competitions coming up as this is our season. We have three regionals: January 20, February 3, and March 3, along with States. This year, we are hoping to take students to Universal Studios the night before states (by student request), and all of this takes so much time to organize. It's very enjoyable, and for January 20th, we have over 70 students signed up to go! This also means giving up 3 Saturdays and one weekend as a chaperone, but it is totally worth it. </div>
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Spirituality</h4>
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There is one thing that really helps ground me other than working out, and that is attending things that help me spiritually. Here are some of the things I am going to/going to do this year:</div>
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<li><a href="https://www.instagram.com/glennondoyle/">Glennon Doyle</a> Jan. 16</li>
<li><a href="https://www.eventbrite.com/e/6th-annual-womens-day-of-wisdom-tickets-38927950548?aff=es2%5C">Women's Day of Wisdom</a> Jan. 21</li>
<li><a href="http://www.jwrp.org/people/adrienne-gold-davis">Adrienne Gold</a> Feb. 4</li>
<li><a href="https://www.facebook.com/events/1208823182566220/permalink/1208823212566217/">#YouDoYou </a> retreat Feb. 23-25 (Atlanta)</li>
<li><a href="https://www.instagram.com/yoga_girl/">Rachel Brathen</a> yoga retreat in July (Aruba)</li>
<li><a href="https://www.instagram.com/hauteyogapb/">Local yoga classes</a> and those on <a href="https://oneoeight.com/featured/">oneoeight</a>, especially <a href="https://www.instagram.com/lara.heimann/">Lara Heimann</a></li>
<li>Weekly discussions with my spiritual guide Bruchy :)</li>
<li>Will finish my 200 hr yoga teacher training this summer!! </li>
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I'm also reading <a href="https://www.amazon.com/You-Are-Badass-Doubting-Greatness/dp/0762447699">this book.</a></div>
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<a href="https://3.bp.blogspot.com/-EaPQd_SUg-w/WlDhTHkzdjI/AAAAAAAAEPs/UzS2RTBLS-0VchNud5-jMe0ihl488fAQwCLcBGAs/s1600/download.webp" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="293" data-original-width="186" src="https://3.bp.blogspot.com/-EaPQd_SUg-w/WlDhTHkzdjI/AAAAAAAAEPs/UzS2RTBLS-0VchNud5-jMe0ihl488fAQwCLcBGAs/s1600/download.webp" /></a></div>
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I also listen to <a href="http://rachelbrathen.com/podcast-2/">Rachel Brathen's podcast "From the Heart"</a> weekly. </div>
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And I try to do something with at least one girlfriend a week - this is so necessary for my soul. </div>
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After writing all of this down, I do feel better. I can see what's ahead. I know I have a lot to accomplish, but it's all doable. And I'm grateful for my family for supporting me through it and for this venue to share it. I am thankful for my health, my home, my friends, my job, and my students. I am thankful I can write this, and that my body is able to do the things I ask it to do each day: wake up, take me where I need to go, work out, and know when to relax (working on that last one!).<br />
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I'll leave you with this Glennon Doyle post from Instagram, in which my two worlds of math and spiritually collide: </div>
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<blockquote class="instagram-media" data-instgrm-captioned="" data-instgrm-permalink="https://www.instagram.com/p/BdnLM7vFlek/" data-instgrm-version="8" style="background: #fff; border-radius: 3px; border: 0; box-shadow: 0 0 1px 0 rgba(0 , 0 , 0 , 0.5) , 0 1px 10px 0 rgba(0 , 0 , 0 , 0.15); margin: 1px; max-width: 658px; padding: 0; width: 99.375%;">
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<a href="https://www.instagram.com/p/BdnLM7vFlek/" style="color: black; font-family: "arial" , sans-serif; font-size: 14px; font-style: normal; font-weight: normal; line-height: 17px; text-decoration: none; word-wrap: break-word;" target="_blank">In which my nephew Bobby mansplians geometry but my niece Alice reclaims her damn time.</a></div>
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A post shared by <a href="https://www.instagram.com/glennondoyle/" style="color: #c9c8cd; font-family: Arial,sans-serif; font-size: 14px; font-style: normal; font-weight: normal; line-height: 17px;" target="_blank"> Glennon Doyle</a> (@glennondoyle) on <time datetime="2018-01-06T14:56:44+00:00" style="font-family: Arial,sans-serif; font-size: 14px; line-height: 17px;">Jan 6, 2018 at 6:56am PST</time></div>
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Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com1tag:blogger.com,1999:blog-3454490001772574770.post-81377263048741941052017-12-24T08:16:00.000-05:002017-12-24T08:16:01.048-05:00Six Good Things in 2017 #MTBoS12daysI saw <a href="https://pamjwilson.wordpress.com/2017/12/21/yule-blog-challenge-mtbos12days/">Pam's Yule Blog Challenge</a> and decided it was time to write about the good things that are going on this year in my classroom, 2017.<br />
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Escape Rooms - in and out of the classroom. </h4>
1. My department purchased a <a href="https://www.breakoutedu.com/">Breakout Edu</a> box, and my <a href="http://eatplaymath.blogspot.com/2015/06/math-schools-out-for-summer-and-i.html">Honors Problem Solving Seminar</a> students "broke out" twice this semester, once in the beginning of the semester and once at the end. I have to say that most students loved these challenges, and I plan to do it in my Algebra 2 Honors classes at the beginning of second semester. We ended the semester by going to a local escape room for a field trip. We had a blast!!<br />
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<iframe allowfullscreen="true" allowtransparency="true" frameborder="0" height="372" scrolling="no" src="https://www.facebook.com/plugins/video.php?href=https%3A%2F%2Fwww.facebook.com%2Fsascots%2Fvideos%2F10155008249504001%2F&show_text=0&width=560" style="border: none; overflow: hidden;" width="560"></iframe><br />
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Play Table. Again. </h4>
2. I have always had a few puzzles laying around my classroom for students to pick up and touch, but this year, I have a <a href="http://eatplaymath.blogspot.com/2017/08/my-goals.html">play table</a>. I think the biggest hit has been <a href="https://www.amazon.com/dp/B0752CFJSM/ref=sspa_dk_detail_0?psc=1&pd_rd_i=B0752CFJSM&pd_rd_wg=yq5QT&pd_rd_r=SDPZYXTPA4XT7KFG2TNW&pd_rd_w=kGfdy">Connect Four</a> because it brings back some childhood memories for students...however, the cool thing is that now that kids are older, they are really understanding the strategies behind winning the game. Students also love the <a href="http://tavernpuzzles.stores.yahoo.net/puzzle.html">metal Tavern Puzzles</a> (for lack of a better name...I believe they were played in taverns back in the day), where they have to separate what seems like one piece into two.<br />
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HQ</h4>
3. My period G class falls at the end of the day. At first, this class came in quite sleepy and not as engaged. I always find that my least engaged students become my most engaged students at the end of the year. I think it's because I work harder at getting them motivated, but who knows. Anyway, we started talking about the viral game <a href="https://itunes.apple.com/us/app/hq-live-trivia-game-show/id1232278996?mt=8">HQ</a> and played once during our brainbreak. What a hit. While we can't play a lot (what could really be a 2 minute game can easily turn into 20 minutes with the commentary of my new fave <a href="https://twitter.com/ScottRogowsky">Scott Rogowsky</a>), I thought it was worthy to donate to the MS Society and have Scott do a cameo video for the class...SO FUN!!<br />
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<iframe allowfullscreen="true" allowtransparency="true" frameborder="0" height="372" scrolling="no" src="https://www.bookcameo.com/v/5a310aa8b5a9f3003d6dfaec" style="border: none; overflow: hidden;" width="560"></iframe><br />
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"Breakfast Club"</h4>
4. My <a href="http://eatplaymath.blogspot.com/2014/11/why-i-love-advising-my-math-club-mu.html">Mu Alpha Theta</a> students have been peer tutoring a lot (I require 10 hours a year), but we have been holding a special session on Thursday mornings called "Breakfast Club." I got the idea from <a href="https://mathequalslove.blogspot.com/2017/10/cookie-club.html">Sarah's post about Cookie Club.</a> Math teachers don't offer extra help Thursday mornings, so I pick up donuts and about 10 - 15 of our members either help each other or are available to help any students who pop in. We've averaged only about 3 non-club member students a week, but it is a start. My officers want to continue it next semester. My classroom is not centrally located so we may move it to a better location, such as the new Entrepreneurial Center. However, no food is allowed there so we may need to rename the club! In February, the club will be hosting its first Math Games Night for either the Lower School, the Middle School, or both...stay tuned!! I'm very proud of my officers this year!<br />
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3D Printers</h4>
5. Our school bought three 3-D printers, and I'm excited about the prospect of having students create. I am not sure I want to sacrifice my <a href="http://eatplaymath.blogspot.com/2017/03/a-great-conics-project-using-desmos.html">conics project on Desmos</a>, and it's too late to do something with parent functions, like what I read about in <a href="https://growingexponentially.wordpress.com/2015/06/29/3d-desmos-designs/">Heather's post</a>, but I am psyched for the future. I am hoping to get <a href="http://www.classroomchef.com/chefs/">John Stevens</a> to do a workshop for us. Stay tuned on this as well!<br />
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Former Students</h4>
6. This is the time of year when former students come back to visit. What a treat! It's great to hear what they are up to. I love seeing the babies or marriages on Facebook, or just getting a quick rundown in person. I have one former student that I closely consider to be the daughter I never had. We see each other maybe once a year (she lives across the country), but we catch up here and there with a quick text or through social media. She was one of those students who laughed at every joke and whose eyes lit up during that lesson that you prayed would work. I taught her in Algebra 2, and she quickly rose to the top, getting A's on her exams and skipping over the next math class to get directly into Pre-Calculus. I actually first met her during her freshman year, on our Pathfinder school trip. I was trying to roll up my sleeping bag to fit in this impossibly small bag (something my husband always does for me), and to no avail, I could not do it. She quickly earned the name "Macgyver" as she rolled it up in about a second and proudly displayed the sleeping bag in its case, holding it by the string.<br />
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We have kept in touch ever since. Perhaps the hardest time seeing her after she graduated was when she flew back for a classmate's untimely death. The funeral was unbearable, for a life lost too soon. He was one of her best friends, and we still talk about his antics. That was a sad day, indeed.<br />
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I caught up with her last week, listening to her delightful stories of rubbing elbows with stars in LA (I am easily starstruck). It was a lovely start to winter break.<br />
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These are just a few of the cool things going on this year. Nothing remarkable. Which is just the way I like it.<br />
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<br />Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com2tag:blogger.com,1999:blog-3454490001772574770.post-85857989472292503482017-11-25T08:41:00.000-05:002017-11-25T08:48:01.542-05:00An Untraditional Route for a Veteran Math Teacher--What's Next?Every year I think I'm going to slow things down and start saying "no." And every year, I think I take on more.<br />
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I see the parallel in my son's life, a sophomore in college. Each time he thinks he can't handle anymore, someone comes to him with an amazing opportunity, and he can't say no. The apple doesn't fall far, I guess.<br />
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I have been teaching high school mathematics for 28 years now. No year is like the last, so in that respect, nothing is ever boring. However, in the last few years, I have been feeling "what else?" Don't get me wrong...I love my job and love how Twitter and MTBoS have changed my teaching exponentially, as my department has grown from 10 people in the classrooms next door to me to thousands (tens of thousands?) globally. But, 28 years is a long time to be in the same career...from what I hear, most people change jobs 7 times...and though I changed schools once, I've been teaching some of the same topics every year, 3 or 4 times a year, for 28 years (completing the square, anyone??)<br />
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MU ALPHA THETA</h4>
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Six years ago, I started a <a href="http://eatplaymath.blogspot.com/2014/11/why-i-love-advising-my-math-club-mu.html">Mu Alpha Theta</a> chapter in my school, and that kept the fire in my soul, in addition to teaching. I love it, and that was really just what I needed to keep things the same yet different. It gave me a new outlook each day, something more to look forward to. Again, I look forward to teaching my students each day, but I can't help the feeling I had that something was missing. Advising this amazing group was the antidote.<br />
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Honors Problem-Solving Seminar</h4>
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Then, three years ago, I began teaching the elective <a href="http://eatplaymath.blogspot.com/2016/06/my-first-problem-set-for-my-problem.html">Honors Problem-Solving Seminar</a>. It was just something different and new, and what I LOVE about it is that we can stop the curriculum and talk about a cool problem or video that just came out (I'm biased and love <a href="http://eatplaymath.blogspot.com/2016/04/can-you-solve-locker-riddle-ted-ed.html">TED-Ed riddles</a>). This never happens in math. I envied history teachers for years, as they could talk about current events, and I know someone out there can say we can relate a math problem to the real-world and talk about current events, but for me at least, it does not come up organically. It comes up organically every day in problem-solving because I'm not constantly focusing on finishing a curriculum to ensure that next year's teacher finishes the curriculum to ensure that students pass their BC Calculus class the year after, etc. Whew. I'm exhausted just thinking about it.<br />
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This year, Honors Problem-Solving Seminar is going strong. The students are all motivated, and best of all, they are funny. They thrive on humor and get excited when I give them just about any problem. Their final exam is to make a Numberphile or Vi Hart type video on any of the following topics:<br />
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<a href="http://4.bp.blogspot.com/-IGpeKxQb54g/WhbKHpYBVII/AAAAAAAAEME/9kzEnUS1Pd8e13tE43ZpPM3X6htlfKVSwCK4BGAYYCw/s1600/Screen%2BShot%2B2017-11-23%2Bat%2B8.15.39%2BAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://4.bp.blogspot.com/-IGpeKxQb54g/WhbKHpYBVII/AAAAAAAAEME/9kzEnUS1Pd8e13tE43ZpPM3X6htlfKVSwCK4BGAYYCw/s320/Screen%2BShot%2B2017-11-23%2Bat%2B8.15.39%2BAM.png" width="298" /></a></div>
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<li>Sierpinski's Triangle and the Chaos Game (see picture for a <a href="http://eatplaymath.blogspot.com/2016/01/why-my-problem-solving-class-could.html">project from two years ago</a>.)</li>
<li><a href="https://www.youtube.com/watch?v=xlZHY0srIew&feature=youtu.be">Koch Snowflake (perimeter and area and...)</a></li>
<li><a href="http://eatplaymath.blogspot.com/2016/11/making-jacobs-ladder-with-chocolate-bars.html">Jacob's Ladder</a> (we did not get to it this year) </li>
<li>The Mandelbrot Set</li>
<li><a href="https://mathigon.org/origami">Math Origami</a> (looks so cool)</li>
<li>Graph Theory and the 4 color Graph Theorem (usually I get to this in the class, but Hurricane Irma "blew" that away)</li>
<li><a href="https://www.ted.com/talks/arthur_benjamin_does_mathemagic">Calendar Math and Cool Mental Math Problems</a></li>
<li><a href="https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/">The Monty Hall Problem and Marilyn Vos Savant's Column about the Three Children</a></li>
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</h4>
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TED-Ed Class</h4>
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Next semester, rather than teach a second section of this class, I will be teaching a TED-Ed class. Instead of holding a traditional <a href="http://eatplaymath.blogspot.com/2017/07/how-to-start-ted-ed-club-in-your-school.html">TED-Ed club</a> after school (because I advise Mu Alpha Theta and JSU already), we will be having it as a class. This is new for me and I'm both frightened and excited. But I feel like this is exactly what I am supposed to be doing next. </div>
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I love the quote: Do something every day that scares you. Yep, that's me! 🙋🏻</div>
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I am a mathematics teacher and truly hate public speaking. But I'm a <a href="http://blog.ed.ted.com/2017/11/01/24-game-changing-ideas-from-educators/">TED-ED Innovative Educator</a> (the only math teacher, I believe), and I have learned how to cultivate the best in my students. So while I do not like to speak publicly, I will show how, through the amazing TED-Ed modules, to give students a "voice with choice"--in other words, what are they passionate about? What is their idea worth spreading?</div>
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What is next up for me? I'm proposing that we host a <a href="https://www.ted.com/participate/organize-a-local-tedx-event">local TEDx event</a>, something I do not know much about. However, there are so many people out there who want to help and have helped tremendously. So in 5 months, we may actually have our students, at all grade levels (we have TED-Ed clubs starting in the Middle and Lower schools), do their very own TED talk in our brand new 180-seat theatre. This is so exciting to me! </div>
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Someone asked me when they heard about it, are YOU giving a TED talk? No, that's not the point. At least not now. This is and always has been about opportunities to showcase our students, not ourselves. </div>
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Our students have so much to say. Much of it could be bottled up and much of it students don't even know how to tap into. But now they will have their own voices and a platform. </div>
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Maybe this is my calling? Well, math teaching was and is my calling...but it's time for something else. And what I love is that I'm not giving up my math teaching...I'm adding to it, in a way that is global and that allows for students to grow. And maybe, just maybe, a student will talk about their love of math at our TEDx event. And then my two worlds will collide.<br />
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What's next for you? </div>
Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com0tag:blogger.com,1999:blog-3454490001772574770.post-83936270956055362192017-09-07T18:27:00.000-04:002017-09-07T18:27:15.867-04:00Life is what happens to you while you're busy making other plans<span id="goog_1382478270"></span><br />
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This is one of my favorite quotes from one of my favorite movies. It's from John Lennon's <a href="https://www.google.com/search?q=beautiful+boy+lyrics&oq=beautiful+boy+lyrics&aqs=chrome..69i57j0l5.2937j0j4&sourceid=chrome&ie=UTF-8">"Beautiful Boy,"</a> and I remember it from <a href="http://www.imdb.com/title/tt0113862/">Mr. Holland's Opus.</a> From what I recall, Mr. Holland, played by Richard Dreyfuss (supposedly a very distant cousin of my husband's), "sings" it to his deaf son in sign language...I believe after refusing to really acknowledge his son much at all since music was Mr. Holland's "thing." Ah what a great movie.<br />
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But I digress. I had big plans this week/weekend. I am only one week into school, and I am just at that sweet spot where the kids are starting to open up and trust you. My Mu Alpha Theta officers made an amazing promo video to show to the entire school that was funny and cool and full of geeky but great Rubik's Cubes and "marker drops." I had a plan to begin yoga teacher training this weekend, something I have been wanting to do for years, and the stars finally "aligned" (and my studio's owner and the manager gave me the extra push I needed.) My son is back up at UF, and while last year was trying at the beginning, he is now in a good place, happy and satisfied, and just got a major research project that he had been patiently vying for since April. I got back on track eating-wise and health-wise after a summer of gorging on processed foods made with sugar and flour since I was lucky enough to travel most of the summer and try all these new treats made with them. All sounds good, right?<br />
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And then...the hurricane. Irma, I'm talking about you. As I look at the window at this beautiful Florida sky, I cannot believe that within 48 hours, I am not sure if I will have a house with a roof on it. Perhaps I should be packing things up and trying to keep things dry, but I am frozen. I am doing just what my husband tells me to do: clean out the closet at the bottom of the stairs for a "safe space," go to the pet store, etc. I truly am completely frozen. And a bit petrified.<br />
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Why wouldn't I leave? Well, I have been through a few hurricanes before. It's been rough, and at least we do get a warning. I can't answer why I don't want to leave. We don't have hurricane shutters. It's crazy, I know. It was so expensive so we never got them. And after last year's scare with Matthew (which turned last minute, thankfully), we vowed to get them this year...but we...forgot??? How?? We live in a townhouse with a house on either side and are somewhat protected. We are praying for the best.<br />
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On this gorgeous Florida day, school is closed so families could prepare and leave. One family told me they were flying to Canada. Another to Colombia. Many are "buttoning up" their houses and leaving. But I'm going to stay. My son is safe in Gainesville, so I am feeling good about that. Most of my family is here...my husband and two cats, my sister-in-law and brother-in-law down the road, my other brother-in-law around the corner, and my mother-in-law also down the road...I will stay with her when it gets really bad, but my husband wants to stay with the house and the animals.<br />
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So, Irma has other plans for me this week. No "method of finite differences" for my Problem Solving kids after spending several days on figurate numbers. No reviewing for the second quiz (first quiz was on <a href="http://eatplaymath.blogspot.com/2015/08/save-teaching-time-at-beginning-of-year.html">prerequisites</a>) for Algebra 2H and Pre-Calculus AB. No showing of the awesome Mu Alpha Theta promo video in the all-school assembly. No Back to School night (I'm OK with this one!) No weekend of yoga. And I know it will be OK...no matter what, we have insurance and we will figure it out. And if you haven't been to one, a hurricane party is always fun :)<br />
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<br />Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com73tag:blogger.com,1999:blog-3454490001772574770.post-39874635403593515372017-08-06T18:03:00.001-04:002017-08-06T23:00:00.584-04:00My GoalsI'm a few hours late with the #MTBoS blog initiative this week for #SundayFunday, which is to write about my goals, but I do want to jump on the bandwagon so that I can think through what I want to set out for next year.<br />
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Math (i.e, teaching) Goals: </h3>
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(I noticed after I wrote them that they really don't apply much to math at all, but more about making students feel even more comfortable in class.)</div>
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<b>Goal 1:</b> After listening to <a href="https://twitter.com/susancain">Susan Cain's</a> Ted Talk on the Power of Introverts, I am convinced that not all students ALWAYS have to work in groups. She claims that many students are introverts who do better when they can think and work on their own. I am going to really make note of this as well as having students think on their <i>own</i> while solving a problem FIRST (cue this tweet:)</div>
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I need to teach this skill and have students (especially in Problem-Solving, but all classes really) know it's NOT okay to blurt the answer (I need to have WAIT time and not tell them the answer so fast, too.) I have been a big proponent of vertical non-permanent surfaces (#VNPS), and my classroom is supposed to have more board space when I walk in next week, so if some kids do not want to always work in groups when up at the boards or in their pods, I have to be okay with that and support them, too.<br />
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<b>Goal 2:</b> I love this post from <a href="https://twitter.com/mgolding">Megan Hayes-Golding</a>, <a href="https://kalamitykat.com/2017/05/02/perfect-teacher-move-to-support-lgbtq-students/">Perfect Teacher Move to Support LGBTQ Students</a>. Here is a snippet.<br />
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It really got me to think, if we could all just do one small thing to make all of our students just a little bit more comfortable, wouldn't you do it? I am going to try to go out of my way to make a student like Ev feel good. It might make the difference for one student. </div>
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<b>Goal 3:</b> Last year, I had some games set up on the back table: Towers of Hanoi puzzles and Rubik's Race. My kids loved them and played them during Brain Breaks and before and after school/class. My goal is to have more kids playing next year. </div>
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This is how we spend our break during block <a href="https://twitter.com/YouCanDoRubiks">@YouCanDoRubiks</a> <a href="https://t.co/EkRF7slQFt">pic.twitter.com/EkRF7slQFt</a></div>
— Lisa Winer (@Lisaqt314) <a href="https://twitter.com/Lisaqt314/status/847798937885040642">March 31, 2017</a></blockquote>
After reading <a href="https://twitter.com/saravdwerf">Sara Vanderwerf's</a> post on <a href="https://saravanderwerf.com/2017/05/29/you-need-a-play-table-in-your-math-classroom/">You Need a Play Table in Your Math Classroom</a>, I bought <a href="http://talkingmathwithkids.squarespace.com/store/spiraling-pentagons">these spiraling pentagons</a> to leave on the back table for play. </div>
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Play Goals:</h3>
<b>Goal 1:</b> I am going to get my yoga certification this fall, which will be fantastic and crazy all at the same time. I will basically be giving up entire weekends for 6 weeks, but I am looking forward to growing with the group I am going to be working with. And it will help me to heal as I am feeling the pain of my childhood best friend, who was diagnosed with ALS last year. Here is her blog, <a href="http://notgonnabeadebbiedowner.blogspot.com/">http://notgonnabeadebbiedowner.blogspot.com/</a> which is beautiful and unbelievably written, but also hard to read. She is so raw, and she blows me away with her strength and the things she notices.<br />
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<b>Goal 2:</b> I am hoping to go for a walk at night after dinner and listen to some podcasts. I finished my first podcast ever, <a href="https://stownpodcast.org/">S-Town</a>, and now I'm listening to <a href="https://serialpodcast.org/">Serial.</a> I'm also listening to some other ones, such as the one from <a href="http://www.quickanddirtytips.com/grammar-girl">Grammar Girl</a> and others. I'm new to Podcasts and am a bit overwhelmed with all of the options! I also hope to listen to them in the car to and from work on most days.<br />
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Eat Goals:</h3>
Last year, I lost 15 lbs which was amazing. I've put some of it back on, so I hope to go back to the healthy diet I was following when the pounds came right off. It's 80% diet, 20% exercise for me, so now that I am finished with vacation and eating whatever I wanted (pretty much), I am hoping to get back on track!<br />
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<br />Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com2tag:blogger.com,1999:blog-3454490001772574770.post-83641779035170268542017-07-31T08:39:00.002-04:002017-07-31T08:39:46.954-04:00How to Start a Ted-Ed Club in your School<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt; text-align: center;">
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">From Ted-Ed Clubs: We want every student in the world to share an idea on the TED platform (because, quite frankly, we need help figuring some stuff out -- like </span><a href="https://www.youtube.com/watch?v=Yj7FrBz1UHU&t=3s" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">redefined gender roles</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> and </span><a href="https://www.youtube.com/watch?v=3aMD78ppXcw&index=1&list=PL71qiWRg4XP8vWNpUxnxpcgh8ZOCDzCWX" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">feline Batman conspiracies</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">). </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">As a <a href="http://blog.ed.ted.com/2016/09/27/meet-the-third-cohort-of-ted-ed-innovative-educators/">Ted-Ed Innovative Educator, Cohort 3</a>, I am lucky enough to have started a Ted-Ed club in my school...in fact, I am super excited to teach it as a class second semesterl!! </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">BUTTTT don't be scared that this is a daunting task...it's not...I promise! Ted-Ed has the entire curriculum ready for you to use (you get it once you get approved), and you only have to meet weekly, or whenever you can as a club. </span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">TED is looking for fresh new student voices to share from the TED stage. Our student voice initiative, TED-Ed, is launching the </span><a href="https://youtu.be/U2PG_R4wl-0" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">TED-Ed Clubs</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> Challenge to surface student stories from around the world. So far, more than 25,000 students have given </span><a href="https://www.youtube.com/playlist?list=PL71qiWRg4XP-ZpAiSg9Bp_wHByqYoDA2J" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">TED-style talks</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> in their schools and communities through </span><a href="http://ed.ted.com/clubs" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">TED-Ed Clubs</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. We are inviting students, ages 8-18, to share what they would say </span><a href="https://youtu.be/3IKlF2dSQWU" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">if the world were listening</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, and we want to include your answer!</span></div>
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<a href="https://calendly.com/tededclubs/student-voice-411" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Sign up</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> for a quick video chat to learn more. You’ll speak directly with a member of the TED-Ed team to learn everything you need to know about the Challenge and how to get involved with this </span><a href="https://youtu.be/VununkhWjj4?list=PL71qiWRg4XP922UwSbaYQ84-c7pvHNgq0" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">awesome global community</span></a><span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. </span><span style="background-color: magenta; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><b>TED-Ed has asked that you m</b></span><span style="color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><b><span style="background-color: magenta;">ention my name, LISA WINER, when you sign up. As a TIE, this will hopefully get you through the process a little faster.</span> I went to the TED Weekend event last year, where kids were invited to give their talk based on their TED-Ed Club TED Talk...and it was absolutely amazing to see what OUR kids can do!!</b></span></div>
<b style="font-weight: normal;"><br /><img alt="Screen Shot 2017-07-10 at 1.59.34 PM.png" height="246" src="https://lh6.googleusercontent.com/7Tg61L574gzbCku30_1mfS9llZzSG96hNjgj-m2QOfd4g64Me_YjfN3L3uTYwNJqh53TNNMfh9kmJoDCgGYmQdGljFcWQroN-4Fft1SmZfSB68RCRIRjnTBE0Xro-LHVdGmnZt97" style="-webkit-transform: rotate(0.00rad); border: none; transform: rotate(0.00rad);" width="450" /></b><br />
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> </span></div>
<h2 dir="ltr" style="line-height: 1.38; margin-bottom: 6pt; margin-top: 18pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Questions? Email me at <a href="mailto:lisa.winer@saintandrews.net">lisa.winer@saintandrews.net</a></span></h2>
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<span style="background-color: transparent; color: black; font-family: Arial; font-size: 16pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">TED-Ed Club Resources:</span></h2>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">TED-Ed Clubs: Celebrating and amplifying student voices around the world video: </span><a href="https://www.youtube.com/watch?v=U2PG_R4wl-0&feature=youtu.be" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">https://www.youtube.com/watch?v=U2PG_R4wl-0&feature=youtu.be</span></a></div>
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<ol start="2" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Website: <a href="http://ed.ted.com/clubs">ed.ted.com/clubs</a></span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Video call sign up link: </span><a href="https://calendly.com/tededclubs/student-voice-411/07-11-2017" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">https://calendly.com/tededclubs/student-voice-411/07-11-2017</span></a></div>
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</ol>
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<ol start="4" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What would you say if the world was listening video: </span><a href="https://www.youtube.com/watch?v=3IKlF2dSQWU&feature=youtu.be" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">https://www.youtube.com/watch?v=3IKlF2dSQWU&feature=youtu.be</span></a></div>
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<b style="font-weight: normal;"><br /></b>
<ol start="5" style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Playlist of TED-Ed Weekend talks: </span><a href="https://www.youtube.com/playlist?list=PL71qiWRg4XP-ZpAiSg9Bp_wHByqYoDA2J" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">https://www.youtube.com/playlist?list=PL71qiWRg4XP-ZpAiSg9Bp_wHByqYoDA2J</span></a></div>
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</ol>
<b style="font-weight: normal;"><br /></b>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Global connect video: </span><a href="https://youtu.be/VununkhWjj4?list=PL71qiWRg4XP922UwSbaYQ84-c7pvHNgq0" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">https://youtu.be/VununkhWjj4?list=PL71qiWRg4XP922UwSbaYQ84-c7pvHNgq0</span></a></div>
</li>
</ol>
<br /><br /><br />Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com1tag:blogger.com,1999:blog-3454490001772574770.post-1058226430875760032017-06-19T10:38:00.000-04:002017-06-22T07:40:10.167-04:00Cambridge Teaching Seminar and MathsConf10 - My Summer of Professional Development<div class="separator" style="clear: both; text-align: center;">
<a href="https://2.bp.blogspot.com/-NTkFuaaJ84c/WUffGJIcfYI/AAAAAAAAD8o/uYVPcoEKpawYCh7ku_OwjyTTByasQzB6wCLcBGAs/s1600/Screen%2BShot%2B2017-06-19%2Bat%2B10.26.08%2BAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="566" data-original-width="875" height="206" src="https://2.bp.blogspot.com/-NTkFuaaJ84c/WUffGJIcfYI/AAAAAAAAD8o/uYVPcoEKpawYCh7ku_OwjyTTByasQzB6wCLcBGAs/s320/Screen%2BShot%2B2017-06-19%2Bat%2B10.26.08%2BAM.png" width="320" /></a><a href="https://1.bp.blogspot.com/-jGYwyvfEKBI/WUffoYxLM3I/AAAAAAAAD8w/TcUjLNW3Z-U-eV4gN-zWO-GQAFbO8FL6gCLcBGAs/s1600/Screen%2BShot%2B2017-06-19%2Bat%2B10.28.27%2BAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="515" data-original-width="559" height="183" src="https://1.bp.blogspot.com/-jGYwyvfEKBI/WUffoYxLM3I/AAAAAAAAD8w/TcUjLNW3Z-U-eV4gN-zWO-GQAFbO8FL6gCLcBGAs/s200/Screen%2BShot%2B2017-06-19%2Bat%2B10.28.27%2BAM.png" width="200" /></a></div>
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I'm procrastinating packing for Europe. I'll be traveling for about three weeks without my son or my husband - mostly alone. Doing what? Well certainly traveling to countries that I have never been to, but the main reason for my trip is to attend two workshops in England: The day-long <a href="https://completemaths.com/events">Complete Maths workshop</a> (<a href="https://www.eventbrite.co.uk/e/mathsconf10-a-complete-mathematics-event-tickets-32797536314">MathsConf10</a>) in Rainham, London and the week-long <a href="http://www.oxbridgeprograms.com/ForEducators/TeacherSeminars.aspx">Oxbridge Teacher Seminar</a> entitled "Thinking Mathematically" in Cambridge. I am using my <a href="https://www.saintandrews.net/page/news-detail?pk=767988">Patten Family Foundation Grant for Sustaining Teacher Excellence</a> to fund most of the trip as well as a fellowship I received from Oxbridge.<br />
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I'm super excited because <a href="https://twitter.com/mathsjem">Jo Morgan </a>(her award-winning blog is <a href="http://www.resourceaholic.com/">http://www.resourceaholic.com/</a>) will be meeting me at the train station and will help me to navigate to Rainham the morning of MathsConf10, and then I will be taking workshops on:<br />
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<a href="http://gdaymath.com/courses/exploding-dots/">Exploding Dots</a> (WATCH THE ANIMATION!!),<br />
<a href="http://www.artfulmaths.com/mathematical-art-lessons.html">Using Art in the Math Classroom</a> from <a href="https://twitter.com/c0mplexnumber">@c0mplexnumber</a>,<br />
<a href="http://www.cambridgemaths.org/espresso/">Cambridge Math Espressos: Filtered Maths Education Research</a>, just to name a few.<br />
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Also included in this workshop:<br />
<ul>
<li>Speed Dating: sharing your favorite maths idea with others</li>
<li>"Tweet-ups" during lunch</li>
<li>Maths Cakes competition (unfortunately, I won't be able to bring one across the pond, but I will post pictures, I'm sure!)</li>
</ul>
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After this workshop, I will take a train to Paris to visit a friend and to do an in"Seine" day tour of basically every site there. I didn't mention that the day I land, I will be doing the same thing in London. It will be a whirlwind few days, but then when I arrive back in London, I will be going on a tour of Stonehenge, Bath, and Windsor Castle. I've got tickets to <i>Kinky Boots,</i> and I do get some time to just discover a bit. </div>
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I have a day planned to go to <a href="https://www.bletchleypark.org.uk/">Bletchley Park</a>, or "Home of the Codebreakers," which is where Alan Turing and his team cracked the Enigma Code. (The movie <i>The Imitation Game</i> is based on this.) We talk about this in Problem-Solving, and I really want to thank Jo Morgan for encouraging me to go to this. I think it will be great, and I can't wait to bring all I learned back to my students.</div>
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The next day, I travel to Cambridge for the weeklong seminar <i>Thinking Mathematically.</i> </div>
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<a href="https://4.bp.blogspot.com/-TKcKSutrt-4/WUfdOLZf-5I/AAAAAAAAD8c/1mMSqN08zjYB33zlID1WOZoT8Sj4FbvjgCLcBGAs/s1600/Screen%2BShot%2B2017-06-19%2Bat%2B10.18.02%2BAM.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" data-original-height="394" data-original-width="800" height="196" src="https://4.bp.blogspot.com/-TKcKSutrt-4/WUfdOLZf-5I/AAAAAAAAD8c/1mMSqN08zjYB33zlID1WOZoT8Sj4FbvjgCLcBGAs/s400/Screen%2BShot%2B2017-06-19%2Bat%2B10.18.02%2BAM.png" width="400" /></a></div>
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This seminar sounds super exciting because although it is mathematical, it sounds more humanities based, and therefore I will be using my right side of the brain in addition to the left. There will be talks on Brexit, the Cambridge system, how to re-read literature and why, readings with a poet laureate, how poets ended slavery, Oliver Cromwell and more, as well as a viewing of an outdoor Shakespeare play and of course, daily 4:00 pm tea. I'm sure there will be lots of networking here as well. </div>
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Following this seminar, I will be lucky (as in, luck of the Irish) to meet my mother-in-law and sister-in-law for a few days in Ireland, as they were already planning a visit. </div>
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I do feel lucky. I hope to post more about the math ideas I will have learned in the next few weeks.</div>
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By the way, the picture below is of our new Bengal kitten, Arthur, who has a knack for knowing exactly when I'm working and therefore when to plop himself right down on me when I'm doing so. (One of these days I'm expecting him to send unfinished emails as he is also always walking along my keyboard!)</div>
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Here's to summertime! Though I won't have the typical amount of summertime at home with my family, I am excited about this once-in-a-lifetime experience, and I'm so thankful to my family for being so supportive and for my school for providing me this amazing experience. </div>
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Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com3tag:blogger.com,1999:blog-3454490001772574770.post-21554075129439010172017-06-17T08:51:00.001-04:002017-06-17T08:51:53.416-04:00The Case of the Missing Fractals<div class="separator" style="clear: both; text-align: center;">
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I happened upon this 2014 lesson called <a href="http://ed.ted.com/lessons/the-case-of-the-missing-fractals-alex-rosenthal-and-george-zaidan#digdeeper">The Case of the Missing Fractals </a>when I was looking for something else, and wow what a gem! I am definitely going to share it with my students next year. One year I was lucky enough to start talking about fractals in my Pre-Calculus Honors class. I posed the question, what fractal will have 0 area as the number of iterations goes to infinity? And then, and what fractal will have infinite perimeter as the number of iterations goes to infinity? This Ted-Ed lesson explains exactly that in a very cute way. Kids will be hooked as gumshoe "Manny Brot" answers riddles about fractals.<br />
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The "Dig Deeper" section in the lesson has terrific links, including another Ted-Ed lesson about <a href="https://en.wikipedia.org/wiki/Flatland">Flatland</a> shown below:<br />
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There are so many great lessons on <a href="http://ed.ted.com/">ed.ted.com</a>, and you can customize them as you see fit. </div>
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What great Ted-Ed lessons have you found and used in your math classroom?</div>
Lisa Winerhttp://www.blogger.com/profile/11156444965825197383noreply@blogger.com1