A 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.
Thanks to Meg Craig for this idea, which she posted about here.
With the start of the new year, here are 30 days of tech and..., to try something new. I'm hoping to blog this out to the faculty once we get back from break. It's all different levels, so even if you have been on twitter for years, there is something for everyone.
I'm starting logs in my Algebra 2 Honors class upon return from winter break. There's been a few great posts that I've found on these blogs from Wendy Menard,Julie Reulbach, and Kate Nowak. They are all fantastic, and I've used much of their ideas in my documents...so here's notes, links, etc. for exponentials and logarithms, that could go with any text, though I use Larson Algebra 2 and Trigonometry, 9e. Keep in mind that I teach in 90 minute blocks. Each note packet is for a day, but I haven't used them yet and so some could go over. These are linked to my dropbox, so you will need an account to open them.
When I find the time, I am going to throw in these two videos:
-- a Ted Ed video on how many folds of paper can get you to the moon
-- a Mythbusters video on paper folding
On Day 2, I will give them these Intro to Logs Notes.
--includes the Need for Logs (click on Wendy's and Julie's link, above)
--includes the fun puzzle from Kate (click on her link, above)
My plan is to use this Kahoot!as a good brain break that day.
On Day 3, I will hand out Laws of Logs Notes (nice way for students to figure out the laws in groups, by Kate.) We have a week of immersion before these notes (and no class), thus the big review in the beginning.
On Day 4, they will get A Huge Review of Logs and Exponents (I haven't checked answers! The last half is a review sheet that I once found, but I don't know where to give the credits to. The latter is for them to do on their own, if they want to)
What did I miss? Please send anything my way :)
~Lisa
I came across this on Pinterest yesterday and decided to give it a try for the 30 days after we get back from winter break. Maybe you will too? It's also a free download here.
Then I saw it on twitter, here...
I am going to give this a try. If all goes well, maybe we in the MTBoS can come up with another 30? Or maybe we can start it all over again.
It's midterm time here already, and I am tutoring a student in Pre-Calculus Honors. He texted me this question from his quiz last night when he was studying:
Given that the point (-3, 6) is on the graph of f(x), where does this point move to
given that h(x) = -f(2x+5) +3?
He had a wrong answer, and the teacher corrected it to (-11/4, -3).
We took horizontal stretches PLUS translations out of the curriculum except with trig (which we teach in a different way, using quarter- and half-periods) and except for in Pre-Calculus Honors. So I was trying to remember my way of doing it.
I factor out the 2 to get: h(x) = -f(2(x + 5/2)) + 3, and then make a rule. (x,y) --> (1/2x - 5/2, -y+3). Essentially, after explaining and using Desmos for discovery, students see that what happens on the outside of the function happens to "y" in the correct order (i.e., multiply by a -1 and then add 3--or reflect over the x-axis and shift up 1--see the "blue"), and what happens to the "x" happens oppositely (i.e., divide x by 2, then subtract 5/2--see "purple)"). So I took (-3, 6) and substituted into my rule (1/2x - 5/2, -y+3) and got the transformed point (-4, -3). Not the x-value my excellent colleague got.
So of course, I think I'm wrong. I text two other colleagues in the department. They both get x = -11/4. I am really confused at this point. I remember another way a former colleague used to teach the horizontal transformation. He would say, let x' be the transformed value, and let x be the original value. so 2x' + 5 = x and solve for x'. You get x' = (x-5)/2. This is the same thing that I got, but I just distributed the 1/2. So I'm really thinking I'm right because I got my answer two different ways. Still, for my highly esteemed colleagues to all agree on a different answer...I'm stumped. They are, too.
So out comes Desmos. The first equation I enter is f(x) = -2x, because the point (-3 6) lies on the graph. The next equation I enter is h(x) = -f(2x+5) + 3. .
And now I have proof that this method is correct. The orange point is not on the transformed function, but (-4, -3) is.
So thanks, Desmos. And it's not about being right, because I would have been satisfied knowing I was wrong, too. It's about being able to prove how to do it, so that we can collaborate on the answer and determine, perhaps the best way to teach it. And to know that at 10 pm, we can sleep peacefully and not stay stumped :)
Even though I was right, I find this one of the most difficult topics to teach. Students can understand it momentarily, but they really can't recall it after the test. If anyone has any ways that work for them, please leave a response at the bottom of this post. I would love to hear it!
Every year, our math club and math honor society, Mu Alpha Theta (MAO), designs a T-shirt for the year. When we compete in South Florida, we enjoy wearing them and looking at all of the other designs that the other schools have made.
Yesterday, we unveiled our secret design, created by 3 seniors:
This was a play on Watch Me Whip, Watch Me Nae Nae, which is a popular song and dance out right now. So cool when on twitter, @pamjwilson tweeted this within days after the students and I came up with the idea "watch me flip, watch me translate."
Great minds think alike.
My students and I whipped and nae-nae'd for a while with excitement when we finally came up with the idea. OK, so they whipped and nae-nae'd...I would try, but I can't dance. At all. (My friends always tell me "less is more," but I don't get it, so I often refrain...especially in front of students!)
We are lucky to have talented artists in the club, and that we have a great local company that makes the shirts for us at an affordable price. The color is beautiful and the shirt is soft this year, as we used a different brand. We always have our school mascot, Scotty, on the shirt in some way, and we usually take some pop culture idea and go with it.
Last year, a senior came up with the idea "AB/BC" (Calculus), a play on words with AC/DC. We had SO much fun coming up with mathematical names for their songs. Here's how that shirt came out:
In 2013 - 2014, we did a parody with Monsters University:
Here's the artist's rendition..and how it turned out...we also make a digital scrapbook each year...the cover is the bottom left picture.
This was on the back of the T-shirt. At that time, we had student names on the back at that time, which I did not add.
In 2012 - 2013, "Oppa Gangnam Style" was big. My son, a freshman at the time, came up with idea "Cosine Tangent Style." The math club went to the mall after a competition once, and we were stopped constantly. People wanted to buy our shirt!
And below is our first shirt--we have come a long way! It says, in math symbols, "I'm Mathy and I Know it!," a parody of "I'm Sexy and I know It!" with a line from the song on the back, "I workout"...Problems.
We never know what we will come up with until we meet with the kids and come up with an idea after the summer. "Taylor Swift Series" was a close one this year, but I'm glad we came up with something specific to 2015.
If you are not part of http://www.mualphatheta.org/, which I have written about here, here, and here, what are you waiting for? It has made a huge difference in my life as a teacher, and I think it has made a difference in the lives of my students. Maybe it will make a difference in your and your students' lives as well.
It is awesome. I have given this problem before, but this was a great little video that was very fun to watch. The characters, script, and editing make it all the more fun. I played it this morning for my students and paused at the exact moment so they could begin working. This is NOT a puzzle for the meek...but it certainly is a fun one. I don't know if it's true, but the internet boasts that only 2% of people can get the answer to this riddle.
Here's the version I have given:
But Dan's twist is that the fish is stolen...who took it?
Here's some of my students' work:
There's more, but I don't want to show you the answer. It will be fully explained, after the pause when students do work on the problem. It's a great activity, but I do recommend a full class period. If a student wants to give up, do it with them on the board...very fun!!
Great job, Dan!
I blogged about the bridge riddle here--we love Alex Gendler and the narrator! It's another great problem.
I hope these keep coming. They are fun and counterintuitive in many cases. They open my students' eyes to problems that I was exposed to at some point, but that they have never seen. I know your students will love them as much as mine did.
It's ironic that I have a half marathon halfway through the school year, where I feel like I've almost completed the 2015 - 2016 half marathon. I feel like I've completely let go of the "eat" and "play" of my blog title, so here's a little play...this is my playlist, in case if you ever are in need of some upbeat music for a half-marathon or a workout. It goes over my time, but just in case I decide in the middle of the song that I downloaded that I want to switch it, I figured I'd add more at the end. I tried to make every fourth song, towards the beginning at least, a major motivation song for me. I couldn't snap a picture of the entire playlist, but here it is in two pictures.
Also, here is a recipe that was a hit at Thanksgiving...from my Pinterest, where you will also find a ton of high school math resources. It is No Bake Mini Pumpkin Cheesecakes, and they are out of this world. The only thing I would do differently is double the amount of graham cracker mixture because I had a lot of leftover mousse (not to worry--it was all eaten without the graham crackers.) I also used graham cracker crumbles which made it easier. And there are little plastic shot glasses at our local grocery store that makes it very easy to make a lot of little desserts.
It all started when my 17-year-old son came home from his summer teen tour and had some much needed down time. The normal teenager would probably just sleep or watch videos, but AJ decided he wanted to solve the Rubik's Cube. I remember playing with one as a child and could get one face complete pretty easily. But in "those days," the directions were all on a folded piece of paper (the horror!), and I did not have the GRIT needed back then...at least not with this puzzle. But he watched a video over and over again, and by the next day, he had it down. (As I am writing this, I hear the clicks from him solving his cube...it's a good "brain break" for him between homework assignments.)
Over same summer, I was planning for my new Problem Solving Seminar, and I thought I would make solving the Rubik's cube an assignment for the class around Thanksgiving. I thought it would be a good time for kids to practice...and perhaps get encouragement from their families over break. I decided I would have them watch the video my son learned from, and I would facilitate, but that I did not have to really solve it...after all, it was an assignment for them, and maybe I didn't really have to (gulp) solve it?! It felt really daunting to me, and yet, I knew my kids could do it. I just didn't necessarily want to--which I know does not make a whole lot of sense right now...but it somehow did to me then.
I asked the bookstore to stock Rubik's cubes...the only thing they needed to purchase for the course, and after avoiding lots of "when are we going to solve the Rubik's cube?" questions, we finally watched the above video together last week. I broke down the first few steps as such:
The white cross on top with yellow in the middle
The white cross flipped to the bottom with white in the middle and a partial matching T
The entire white face with one full layer (top) complete
The entire second layer complete
As we were watching the video and pausing A LOT, I noticed that many of the students were having trouble visualizing. Ironically, one of the top students in the class could not follow the directions at all at first. But most kids were still very interested...solving the Rubik's Cube is like a fun party trick to pull out-out of nowhere, so most were determined. Some asked me to share the video via Classroom Google, so they could watch at their own pace, which I did.
Oddly, I was able to see how to do the first three of the four steps, above, pretty easily. I say oddly because my spatial reasoning is my weak point as a math teacher. You could spin me around in my own driveway, and I will get lost. But I guess having played around with the cube a lot as a kid, I could do these steps fairly quickly. So once I realized my kids needed help, and I could help them, I started to want to solve it myself. But it was not until then that I felt the need to solve it. They needed my help in explaining it, and that I could do. But I didn't know how far I could get...that second layer blew my mind.
Then luck happened. I got an email from the Mathematical Association of America (MAA) highlighting an article about Dan Van der Vieren (known to students as Mr. VDV), a teacher who wrote his undergrad thesis on the Rubik's cube. I immediately followed him on twitter and asked if he was willing to skype with my class...and he said yes! And then the magic happened.
Via skype, and with pictures like the one to the left, he showed us how to get the entire second layer complete. This involved an algorithm. My students struggled through this (as did I), making mistakes and having to redo it all over again, but once they finally got it on their own the texts with pictures started pouring in...on a Saturday night?! And it coincided with me getting that layer complete as well. We felt so accomplished!
Mr. VDV, is skyping with us again on Wednesday (the day before Thanksgiving break) to get us to the next stage. This, more than anything else that I have ever taught, is teaching the kids tenacity and grit and stick-to-it-tiveness. I do have a student who wants to give up. I hope more than anything else, I can encourage him to stick with it and solve it. He will learn more from that, I think than anything he has learned in my class. If he learns how to do it, which will come not only from my helping him but also from his willingness to learn from his mistakes, I will feel like I have done my job.
Mr. VDV has tweeted with me regularly, sharing pictures like these to help me help my students--so incredible. I am so thankful to him...funny this is the case right around Thanksgiving.
Lastly, Mr. VDV has told me that his class has made mosaics with Rubik's Cubes, and now, of course, we HAVE to do this...next semester. I can't wait. He told me to register at http://www.youcandothecube.com/, which I did, and someone got back to me Sunday morning! They will ship all the cubes to you for the mosaic making; all we have to do is pay for shipping back.
I am looking forward to my post when we actually create this. Another challenge, Mr. VDV told me, is to make our school logo as a mosaic. There is an app for that! The possibilities are endless.
I am not there yet...I haven't solved the puzzle fully. I'm 2/3 done, but I can do the entire 2/3 from memory...by Thanksgiving break, I hope to have it fully done, along with the rest of the students in my class. I finally am learning about the grit I have been talking about to my class. And it feels great.
If you don't follow Richard Byrne, whose blog is Freetech4teachers, you must NOW. I have gotten a lot of great ideas from him, and today he did not disappoint. In this blog, he wrote about Zaption. Zaption is a site where you can take any video and add questions to it to make it interactive. Zaption calls these videos "learning tours". In about 5 minutes, I learned how to add multiple choice and free response questions to videos. Here's the video I watched to learn--so easy, I pinky swear.
I thought, nah, no math, I'm sure...but right when I checked it out, I saw a choice of a rational graph video, which I just taught, so it caught my attention. I had hoped to get to converting to vertex (standard) form of a parabola in my class today. Students had a test, and then they worked on this Desmos activity to introduce them to parabolas. But we did not get as far as completing the square.
Insert Zaption. I searched for a completing the square vertex video, and luckily, the first one I saw had an instructor who does it the same way I do. I was able to add a multiple choice question and two free response questions in a video that was less than 4 minutes. I added it to their homework assignment, and students will have to answer the question before they move on. Twice, I asked them to predict the answer, and then once I asked them to solve a problem on their own after watching the video. Afterward, I can look at the analytics and see their responses and how they did. I am assigning this for homework in addition to a light assignment on what we did get to cover.
Here is the video:
And here are the analytics, though none of my students have done it yet--though I can't wait to see it for myself.
The gallery is quite amazing. They have all different subjects and topics. Try it for yourself. If you do a flipped classroom or a modified flip, I think you will love it.
If you are interested in learning how to use Explain Everything for your flipped classroom, click here.
This is a crosspost from the technology blog I write with ProfeSeiden, called Tech4Scots.
Classtools.net is probably one of the coolest things out there. It's really unique and students enjoy it. You can use it just for fun or as a learning tool. In a nutshell, you can create free games, fun activities, and diagrams in literally seconds. Here are some examples.
Breaking news generator:
I made this in about 30 seconds.
or use a pre-made picture from Anchorman:
Star Wars Movie Text:
Use this to scroll directions, for example, or to introduce something exciting (or otherwise not exciting, but you want to add some pizzazz...)
Fake Tweet:
To generate interest in a topic...haha I made this one up!
Fakebook:
Use "Fakebook" for character development, to give a series of historical events, to give debates and relationships between people...this would make a great assignment. Here is an example from Classtools.
BrainyBox:
This is really cool. You have to see it to believe it. There are six sides to a box, so there are six key events that students can write about...one side can be a video, one side can be a slide...click here to see it in action.
Fake Texts:
This is just for fun...
Random Name Picker:
This would be great for our department, as currently, we play "nose goes."
click here to watch it spin--when a name is picked, you will hear applause. You can also remove the student so that they are not picked next time.
Fruit Machine:
This is a slot machine...you can use as a random name generator, but I think it's great for a vocabulary word list. Put in words and spin, and when a word comes up, students need to define it Countdown Timer:
This is nice to display, and you can select a soundtrack as well:
Timeline:
Need a timeline tool for students? There are a number to choose from:
Arcade Generator:
Need one? No problem. There are some pre-made ones as well:
Fishbone or Burger Diagram:
Because, why not? Who wouldn't want this?
There's more, too. Just go to http://classtools.net to check it out. There is a paid version as well for no ads.
Make something fun? Let us know in the reply section.
"CRAYONS!? We are COLORING? Wait, can I snapchat this????"
Yes, yes you may.
Here are the directions I gave to my Problem-Solving class the other day:
Take any map and color it so that no two adjacent states are the same color. Keep in mind that you want to use as few colors as possible so that coloring the map is not too expensive. It turns out that any map can be colored in at most 4 colors! And that this was the first proof proven using a computer.
Here is the map I gave them, without telling them that they needed 4 colors...you may want to provide extras.
Here is the quick video I showed them after they colored, that talks about the four-color theorem.
After coloring the map, we drew the graph at the right, where each vertex represents a country and an edge connecting two vertices means those countries are adjacent. Then we colored the vertices and found the "chromatic number," that is, the least number of colors we can use. We needed at least three, as you can see by the red triangle drawn between Bolivia, Paraguay, and Argentina. The chromatic number for this map was 4. (And remember, for any map, this is the most it will ever be.)
Then we went on to scheduling committees, and I showed how you could make each vertex a club and each edge would represent any club that had a member in common, so a conflict in time. The chromatic number, in this case, would be the least number of club meetings required. We also answered some interesting problems that related to the Handshake Problem.
Here are my notes from class that day, that I took from my book.
All in all, a fun class with a theorem that they have never heard before. And I am sure that they will never forget.
Today, we did the awesome Pumpkin-time-bomb-activity from Mr. Orr. Very fun predictions, and we were only 4 off from what we guessed! I highly recommend that you read his post, check out the data, and also watch the video from Jimmy Fallon.
The explosion took us by surprise so we didn't get a picture, but one student ended up with pumpkin all in her hair! I was amazed at what the rubberband clump looked like at the end! We didn't do anything to it. That's what it looked like after the explosion!
