Saw an interesting tweet last week and I’ve been thinking about pretty much constantly for the last few days:
I had a few thoughts initially – which I’ll repeat in this post – but I’ve had a bunch of others since. Below I’ll share 10 ideas that require very few materials – say scissors, paper, and maybe snap cubes – and then 5 more that require a but more – things like a computer or a Zometool set.
The first 4 are the ones I shared in response to the original tweet:
(1) Fawn Nguyen’s take on the picture frame problem
This is one of the most absolutely brilliant math projects for kids that I’ve ever seen:
Here’s how I went through it with my younger son a few years ago:
(2) James Tanton’s Mobius strip cutting exerciese
This is a really fun take on this famous scissors and paper cutting exercise:
You will honestly not believe what you are seeing when you go through Tanton’s version:
Here’s the link to our project:
(3) Martin Gardner’s hexapawn “machine learning” exercise
For this exercise the students will play a simple game called “hexapawn” and a machine consisting of beads in boxes will “learn” to beat them. It is a super fun game and somewhat amazing that an introductory machine learning exercise could have been designed so long ago!
(4) Katie Steckles’ “Fold and Cut” video
This video is a must see and it was a big hit with elementary school kids when I used it for “Family Math” night:
Here are our projects – all you need is scissors and paper.
(5) Along the same lines – Joel David Hamkins’s version of “Fold and Punch”
I found this activity in one of the old “Family Math” night boxes:
Joel David Hamkins saw my tweet and created an incredible activity for kids. Here’s a link to that project on his blog:
(6) Kelsey Houston-Edwards’s “5 Unusual Proofs” video
Just one of many amazing math outreach videos that Kelsey Houston-Edwards put together during her time at PBS Infinite Series:
Here is how I used the project with my kids:
(7) Sharing the surreal numbers with kids via Jim Propp’s checker stacks game
Jim Propp published a terrific essay on the surreal numbers in 2015:
In the essay he uses the game “checker stacks” to help explain / illustrate the surreal numbers. That essay got me thinking about how to share the surreal numbers with kids. We explored the surreal numbers in 4 different projects and I used the game for an hour long activity with 4th and 5th graders at Family Math night at my son’s elementary school.
This project takes a little bit of prep work just to make sure you understand the game, but it is all worth it when you see the kids arguing about checker stacks with value “infinity” and “infinity plus 1” 🙂
Here is a summary blog post linking to all of our surreal number projects:
(8) Larry Guth’s “No Rectangle” problem
I learned about this problem when I attended a public lecture Larry Guth gave at MIT. Here’s my initial introduction of the problem to my kids:
I’ve used this project with a large group of kids a few times (once with 2nd and 3rd graders and it caused us to run 10 min long because they wouldn’t stop arguing about the problem!). It is really fun to watch them learn about the problem on a 3×3 grid and then see if they can prove the result. Then you move to a 4×4 grid, and then a 5×5 and, well, that’s probably enough for 80 min 🙂
(9) The “Monty Hall Problem”
This is a famous problem, that equally famously generates incredibly strong opinions from anyone thinking about it. These days I only discuss the problem in larger group settings to try to avoid arguments.
Here’s the problem:
There are prizes behind each of 3 doors. 1 door hides a good prize and 2 of the doors hide consolation prizes. You select a door at random. After that selection one of the doors that you didn’t select will be opened to reveal a consolation prize. At that point you will be given the opportunity to switch your initial selection to the door that was not opened. The question is -> does switching increase, decrease, or leave your chance of winning unchanged?
One fun idea I tried with the boys was exploring the problem using clear glasses to “hide” the prizes, so that they could see the difference between the switching strategy and the non-switching strategy:
Here’s our full project:
(10) Using the educational material from Moon Duchin’s math and gerrymandering conference with kids
Moon Duchin has spent the last few years working to educate large groups of people – mathematicians, politicians, lawyers, and more – about math and gerrymandering. . Some of the ideas in the educational materials the math and gerrymandering group has created are accessible to 6th graders.
Here’s our project using these math and gerrymandering educational materials:
(11) This is a computer activity -> Intro machine learning with Google’s Tensorflow playground.
This might be a nice companion project to go along with the Martin Gardner project above. This is how I introduced the boys to the Tensorflow Playground site (other important ideas came ahead of this video, so it doesn’t stand alone):
Our complete project is here:
(12) Computer math and the Chaos game
The 90 seconds starting at 2:00 is one of my all time favorite moments sharing math with my kids:
The whole project is here, but the essence of it is in the above video:
(13) Another computer project -> Finding e by throwing darts at a chess board
This is a neat introductory probability project for kids. I learned about it from this tweet:
You don’t need a computer to do this project, but you do need a way to pick 64 random numbers. Having a little computer help will make it easier to repeat the project a few times (or have more than one group work with different numbers).
Here’s how I introduced the project to my kids:
Here’s the full project:
(14) Looking at shapes you can make with bubbles
For this project you need bubble solution and some way to make wire frames. We’ve had a lot of success making the frames from our Zometool set, but if you click through the bubble projects we’ve done, you’ll see some wire frames with actual wires.
Here’s an example of how one of these bubble projects goes:
And here’s a listing of a bunch of bubble projects we’ve done:
(15) Our project inspired by Ann-Marie Ison’s math art:
This tweet from Ann-Marie Ison caught my eye:
Then Martin Holtham created a fantastic Desmos activity to help explore the ideas:
It is fun to just play with, but if you want to see how I approached the ideas with my kids, here are our projects:
(16) Bonus project!!A dodecahedron folding into a cube
This is a an incredible idea from 3d geometry.
We studied it using our Zometool set – that’s not the only way to go, but it might be the easiest:
Here’s the full project: