Problem Set 2 for my Problem-Solving Course

I've posted problem set 1 here and Chapter 0, which I've renamed Unit 1, here. Both are going to be part of a workbook I am creating for my students in my Honors Problem-Solving seminar. Thanks a million to @mrdardy for catching some typos and asking me great and thoughtful questions!


Here is my Problem Set 2.

In the 6 problems I give each week, I’m trying to include (and this has pretty much been in my head till now…I blogged about some of it, or wrote in the comments):

-one algebra problem

-one geometry problem

-one probability problem

-one problem based on what I will be doing in class that week

-one problem that may “recur” that they could see again somehow (like, my second problem set has a geo problem that ends up being the golden ratio)

-one logic problem

I think I have to write my weekly unit 2 before I create the next problem set, so it will all fit in well together...in other words, the unit and the problem sets kind of go hand in hand. 

Speaking of hands, below is the logic problem from problem set 2. 

Any feedback is welcomed :)

Chapter 0 Problem-Solving Workbook

If you have been reading this blog, you may know that I am working on a textbook this summer for my Honors Problem-Solving Seminar. Yesterday, I decided to call it a "workbook." There will be plenty of space for students to write ideas in it, as opposed to a textbook, which is usually pristine, with possible highlighting.

Last week, I posted my first Problem Set and got a lot of GREAT feedback on the blog comments and through Twitter. So many people shared resources with me, and I am not sure I will ever have the time to go through all of them.

I am hoping for some more constructive criticism on Chapter 0.

In Chapter 0, I explain the setup of the course:

• When to work collaboratively and when to work individually;  
• The need to be a supportive classmate when problem-solving; 
• For students to know that it can be both scary and frustrating to problem-solve--but also very rewarding; 
• That the class is broken up into three main parts; 
• How quizzes are structured; 
• How problem sets will be graded; 
• Other grades in the course; and finally, 
• An opening problem that I blogged about here and Angela Duckworth's Grit video and quiz, which I wrote about last year when I was thinking about how to run the course for its first year. 

I love having more structure in this course and am excited to have my own editable workbook. 

Please let me know your thoughts after you click on the link below.

Chapter 0

I probably will not be sharing everything about the workbook, as it is a little scary to share all my thoughts and ideas with #MTBoS...and I also know that what I do may not work for all and is very unique to how I learn and how I teach...so, please be gentle... :)

Math Teachers at Play #99 Blog Carnival

Welcome to the Math Teachers at Play #99 Blog Carnival, a "monthly smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math," originated by Denise Gaskins.  Let her know if you are interested in hosting in the future!

Here are some interesting facts about the number 99:

1. There is a Chinese Proverb that says, "If you wish to live to the age of 99, please walk 100 steps after each meal.
2. The sum of the cubes of 2, 3, and 4 equals 99.
3. 99 is the atomic number of Einsteinium. It was discovered in 1952, in the debris of the first H-bomb explosion and named after Albert Einstein.
4. Some famous songs involving the number are 99 Bottles of Beer, 99 Luftballons, and 99 Problems.
5. It is a Kaprekar Number, which means when you square it, it can be split into two parts that add to itself, meaning: 99x99 = 9801, and 98 + 01 = 99.
6. 99 is a Palindromic Number.

Here are some interesting posts that were either submitted or saved in my blog feed from the month of June so far:

Activities

• Head on over to Yummy Math's Coloring with Pascal's Triangle to color and see a bunch of activities involving Pascal's Triangle and the Binomial Expansion. 

• I love @benjamin_leis' Running a Math Club: My Experiences blog. In this post, about Art Math Intersection, he gives students a choice between investigating Ulam's Spiral or modular arithmetic circles, inspired by http://snip.ly/c7q7c#https://mikesmathpage.wordpress.com/2016/04/19/using-ann-marie-isons-incredible-math-art-with-kids/.

• I really enjoy the videos posted by @preshtalwalkar, such as this month's The Flower Math Problem. My students also love them. In this post, he claims, "Allegedly this problem comes from a test given to a Chinese kindergarten class. It caused a stir after it was posted online, with many adults debating the answer, some saying it was impossible. Can you figure it out?" 

• @emilygrosvenor declared June 17 as "World Tessellation Day" in 10 Ways to Celebrate World Tessellation Day, and the world listened. In her guest post, she shows "10 great ways to play with tessellations, learn about then, and introduce them to your children." Below is a video she posted to show how to make a simple tessellating pattern from a square. 

• Here is another awesome post about World Tessellation Day from @mathhombre. Check it out to see his gallery of tessellations!

• Here's a shameless plug for my blog, where, this week, I talk about how I am writing a textbook this summer for my Honors Problem-Solving class. It's a semester class made up of bright students grades 9 - 12. Here is my first Problem Set that students will work on individually as a week-long homework assignment. I got a lot of great feedback on it and added a few diagrams, etc, and hope it will be a great first set for my students--thanks to the help of #MTBoS.

Review:

• I really like these review games from @TheMathGiraffe, who's Twitter cover page rightly claims "The perfect mix of fun and rigor!" I love that for my classroom, but it's hard to come up with neat review ideas. These are perfect for grades 6 - 12 and they are clever and different. I also follow Math Giraffe on Pinterest, and you should too :)

• @ScaffoldedMath never disappoints with their beautiful graphic organizers. This month's Graphing Rational Functions Reference Sheet is awesome, and I love their "freebies!"

Things that make you go, hmmmm....in teaching:

• In Why Do We Ask Word Problems In Math? from @MIND_Research, mathematician Brandon Smith asks you to "think deeply about why we ask word problems in the first place," and offers "actionable tips for how you can create better word problems for your students."

• My friend @mrdardy wrote up a nice list of How To Succeed in Math Class. I will be sure to share this with my students next year, as often students who are not strong in math think they just "can't do it." But they don't realize that there is a method to the madness of "studying" for math. 

• @ddmeyer is always writing awesome posts that get you to THINK about the most effective ways to teach math. In his recent blog, Your GPS is Making You Dumber, he discusses that teachers should avoid "GPS-ing" their students, that is to say, don't give them step-by-step instructions for how to solve a problem. I know it's easier to use a GPS, but will you really know how to get from point A to point B by yourself if you use one? It's a great read and certainly makes me think, why is it that students seem to forget everything from the last unit once we start the new unit? This post and the comments are a fascinating read. 

Something for the younger kids:

• Crystal Wagner (@Tri_Learning) explains how to help young kids learn math in Five Math Skills Kids Need to Master. Here, she shows how you can help students master these skills with games and practical applications. 

• Here is Denise Gaskins' latest in her Math FAQ for Parents: FAQ: He Won't Stop Finger-Counting. Denise discusses how counting on one's fingers is not a 'bad' habit, it's a crutch. She offers ideas to try to help kids "develop that transfer of skills" to begin to count mentally. 

I am going to leave you with one more thing, since my blog IS called eatplaymath...here's a recipe for what I made for Father's Day today, Raspberry Tiramisu, chosen by my husband...let's hope it tastes as good as it looks!

My First Problem Set for My Problem-Solving Class

Year one of Honors Problem-Solving Seminar is in the books. It was an amazing year, and I learned A LOT. Now that I've taught it for two semesters, I've figured out (so far) what works and what doesn't. My students gave me a some really good feedback. I did not have a textbook, which was both good and bad. The good was that it was a very flexible class, and as things came up (i.e., in blog posts, Twitter, anything #MTBoS), I could stick it in whenever wherever. The bad was that there wasn't as much structure, and I think my other students would say (from Pre-Calculus and Algebra 2 Honors), I am a VERY structured teacher...so that was hard for me.

This summer, I am writing a textbook for the class. Today I wrote my first problem set, which I am sharing with you all. I would LOVE any feedback. Last year, I gave seven or eight problems on a problem set. I gave one problem set just about each week. Students would get them at the beginning of the week and they would be due at the beginning of the next. One thing they said I should do is keep it to six problems. They thought anything more was too much, especially when one or two problems are often really tough.

Last year, they wrote solutions in composition books, but this time, I would like it to be on the paper I give them so that it is more structured. If they need more paper, they can staple it to the page. The back of the page is for things they learn from other students when we go over the problems (so this should not be double-sided when copied). I should explain that we go over the solutions Exeter style, which is to say, each student picks a problem at the beginning of the class and writes the solution on the board. Then that student presents it, and anyone can chime in to explain a different solution or approach. It's awesome, and I learn more from them, perhaps, than they learn from me. There are so many times that they have found a more elegant solution than me!

Some of the problems are famous ones, but many are calendar problems from Mathematics Teacher. In each set, I try to include one geometry problem, one probability problem, one number theory problem, and then the rest are just interesting problems.

I added a reflection page at the end that I will likely change after each problem set. I think I will hand the Problem Sets out each week, separately from the text, so students can't go ahead (I have some students who would do that, I think), especially as some of it will coincide with the curriculum I will be teaching them. So, without further ado, here is the link via dropbox: Problem Set 1 and below is a picture of the first problem.

Relaxing, Renewing, Reflecting, and Writing this Summer!

High Five!! Today is my first official day of summer. Sort of. I have two meeting days Thursday and Friday, but until then, I'm off. My finals are graded, my grades are, in the word of a former student who said this phrase at the end of every class, "DUNZO." Whew. What a long, strange year it's been.

Rather than focus on the craziness of our school year, I've decided to focus on this summer. Here is a list, more for me to get down on paper, of things I plan to do this summer.
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1. Celebrate my son graduating from high school and help to get him ready to go to college. We are driving up to Preview Day tonight, and he will meet his roommate. He's my "one and done," and this is an exciting time. I am so proud of him, and can't wait to see what awaits him next! His graduation present is a trip to Climb Mount Kilimanjaro. Because this kid loves challenges. I love this boy!

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2. Write a textbook for my Problem-Solving class. This is definitely going to take up a bulk of my time this summer. I will likely dedicate a few hours a day. My plan is to make a chapter of problem sets. My students recommended six problems a week; I normally gave eight. Maybe I will settle for seven. Then I have to break up what I do into chapters. Off the top of my head, I'm thinking a unit on Figurate numbers, probably one on just "problem-solving" itself, solving the Rubik's Cube, cryptography, probability, and I will probably have "famous problems" strewn throughout as warm-ups. And there has to be a miscellaneous chapter because there is a lot more to include, even though this is a semester class! I am hoping to have a recent graduate design the cover.
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3. Go to the library to get books. I used to feel that I had to finish every single book I read. I would get so bored with some books that I would just stop reading because I couldn't get through the book. One day I just said to myself, it's OK if you don't finish what you started. Wow. Revelation. Freedom. But now, I buy books on Amazon and don't finish them...what a waste. So I am going to get them from the library this summer. My friend just posted on facebook that if you want a book that is on a waitlist, see if it's available in large print. I like that idea, especially since I am just starting to need reading glasses (sigh.) I just finished The Widow...a page turner for those who liked Gone Girl, but creepy. I am going to get Yaa Gyasi's novel Homegoing next. It's about slavery in Ghana and America over a 300 year period.

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4. Continue my workout regimen. After spring break, I started with a trainer who trained a former student of mine. She lost 55 lbs! I decided to bite the bullet and spend the pricey amount to see him three times a week. And I'm glad I did. Putting in that amount of money ahead of time, for me, meant that I could not cheat. I knew I'd let myself down if I did, but more, how could I tell my husband that I just blew all that money on nothing? Well, after 10 weeks, I'm 13 pounds down, and could not feel better. Basically, it's a workout that consists of lifting very heavy weights three times a week plus cardio. I have always been an active person who works out a lot, but I was doing the wrong workouts...too much cardio, not enough weight training. He also put me on a diet where I eat 5 meals a day and hardly any carbs and no sugar. After the first month, so many people told me I looked younger...I know it's because of the effect of the sugar on my skin. I feel great, and my husband bought me these Beats yesterday, and I can't wait to use them at the gym today. So I am weaning myself off of training three times a week and will go myself. However, my trainer suggested I continue to work out once a week with him to maintain. At first, I did not want to spend the money. But I decided I'm worth it. And if it means I have to tutor one more time a week to make up for it, so be it. Email me if you want to hear more about the diet and exercise plan I am on. 

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5. Plan my trip to Israel! I am going with a group called JWRP, which stands for Jewish Women's Renaissance Project, and is for mom's in their 40's with children under the age of 18. I met the 10 other women I'm going with, and I can't wait. It is my first time going to Israel, and has been a dream of mine to go since I was a little girl. Women going with other women--it sounds so amazing. We will be there with 400 other women coming from around the world at that time. I will be going in late July, and I am told it will be a life-changing experience.

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6. Get ready for PD. This summer, I am pumped to go to Twitter Math Camp again (can't wait!) and also we have a summer institute at my school. The last day of our summer institute is called "Ignite, Innovate, Inspire," and volunteers from our faculty will be presenting on best practices, mostly involving technology. I will be presenting on how to create a PLN using blogs and Twitter (surprise, surprise) as well as on visible random grouping, which I blogged about here, and Zaption, which I blogged about here. My student designed a cute logo (below), which we made into computer stickers and also got made on cups for participants. 

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7. Organize, organize, organize. I do this every summer, and it feels good to put things back in their proper places after shoving them in shelves over the year in a made rush of cleaning. The book, The Happiness Project, has a chapter about cleaning that I love. That's as far as I got in that book...I have to finish reading that one!

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I hope you all have a restful, renewing summer where you can relax, reflect, travel, and spend time with loved ones!

My Top Ten Math Blogs I Follow, Plus Two Bonuses

I follow (gulp!) 232 blogs on https://www.bloglovin.com/. I know some are defunct, and some are possibly renamed from older blogs, but I can't let go of any of them. I know it's geeky, but every morning, with coffee in hand, I browse through my blog feed and get ideas from great people from around the world.

http://www.fishing4tech.com/mtbos.html is an awesome place to search through blogs for a particular topic, but I truly love "happening" upon an interesting lesson or thought each day. I learn from so many people everyday, MTBoS is my virtual classroom.

ALL of the blogs are AWESOME, truly, whether they are about a lesson or even just a teacher's difficult life moment. I want to share with you my personal list of top ten blogs...ones that personally connect with me almost every single time. They are in no particular order, but generally, each time these bloggers post, I save them. They make me go, "hmmmmm." Maybe they will resonate with you, too.

1. Fawn Nguyen's Finding Ways. The first time I heard of Fawn was at TMC '15 . She gave perhaps the most passionate talk I've ever heard. Fawn is so brutally honest and true, and I think she connects with everyone. She can make you laugh and cry in the same sentence. She is fiercely protective of her students, like a momma bear with cubs. And get out of her way if you do anything to hinder the performance of her students. Every time I read her blog, I feel cathartic. Like it's everything I wanted to say but could never get it out nor could have the courage to say it. She is courageous, and it's no wonder everyone loves her.

2. Sarah Carter's  Math Equals Love. If you haven't heard of the Sarah formally known as Mrs. Hagan, you could be living under a rock. Sarah has been featured on NPR's All Things Considered and even found her husband Shaun Carter on hard material. When you see her posts, you think, now why didn't I think of that? She is extremely relatable and it's no wonder her students love her.

MTBoS. Sarah does great things with Interactive Notebooks and planners, but she also finds easy, uncomplicated ways to teach and provides links to fantastic handouts.

3. Julie Reulbach's I Speak Math. Julie teaches Algebra 2, and if you need great resources and ideas, she's got them. She also will answer your questions on Twitter, and she taught me how to use Kahoot! at TMC '15...which, by the way, many of the teachers in my school now use!

4. Sam Shah's Continuous Everywhere But Differentiable Nowhere. Sam has unique ideas that I've never seen anywhere. I've used the fist bump problem (a take on the handshake problem), which I blogged about here and here. I use a lot of his problems in my problem-solving class. His posts are thoughtful, kid-tested, and there is always humor. And they are thought-provoking and genuine. I love them!

5. Meg Craig's Insert Clever Math Pun Here. Do you need ANY and ALL resources for Pre-Calculus, Algebra II, or Geometry? Meg's got them. All of them. She makes awesome review sheets and we both preach not to Kill a Kitten with our students. She is also the Queen of Gifs and cheering people up who need cheering. The world is a better place because of Meg! And who can resist her cute hat profile picture on Twitter??

6. Jo Morgan's Resourceaholic. I particularly like her gems, which truly are little nuggets of helpful links and resources that she finds by scouring Twitter and other places so you don't have to. I find nifty puzzles and facts there every post. She is also an amazing resource for England's math GCSE test that I don't give, but I do like to follow.

7. Amie Albrecht's  Wonder in Mathematics. I've only just discovered Amie's blog, and it is chockful of fantastic ideas. I particularly love her Friday Five series, where she, like Jo, finds awesome ideas so you don't have to.

8. Sara Vanderwerf's Saravanderwerfdotcom. Sara is also more of a recent find for me. She has great resources, and everyone loves her (secret)5x5 Most Amazing Just for Fun Game.

9. Ok, you get two here because I confused Alex Overwijk's Slam Dunk Math with Bob Loch's Math Coach Blog. I met both at TMC '15, and loved working with Bob in the Desmos workshop. He has great AP Stats resources. If you are into Visible Random Grouping, then Alex is the one for you. I had the pleasure of participating in his TMC '15 session, and it was fantastic...plus, he is pretty famous for something pretty cool, as you can see in this video!

10. Pam Wilson's The Radical Rational. Again, this is just another awesome site with great things posted...and she wears my math club's T-shirt.

Two bonus blogs. 

I save posts from http://www.freetech4teachers.com/ and http://www.educatorstechnology.com/ all the time, as they often have great tech ideas to incorporate in the classroom. Though not necessarily math related, I use their ideas to get ideas across to students using technology.

In keeping this list to a top 10, I know I left several blogs out that I adore. What are your favorite blogs?