Four math projects for kids to build analytical muscle

Saw this tweet from Jose Vilson today:

It was a well-timed tweet for me because I’ve been thinking about easy to implement, and especially not-so-computational-focused math ideas that you can do with kids.

Here are four that came to mind – hopefully all you need is an internet connection plus pencil and paper (and scissors for the last one).

(1) Using Richard Green’s google+ post about Octagons:

Richard Green’s Google+ post about Octagons

This was how I used Green’s post with my son back in April:

Using a Richard Green google+ post to talk about geometry with my son

I would love to hear kids talk about the Octagon tilings – and hopefully kids would also be intrigued to see the various pictures associated with the octagon tilings. Another nice idea here is showing kids that math that math professors like Green do / look at / find interesting / share isn’t just computational stuff.

(2) Larry Guth’s “No Rectangles” problem

Here’s another project coming from a research mathematician – this time Larry Guth of MIT. The problem is stated this way:

“Suppose I have an NxN grid of points in the plane. I can color some of
the points red, but I have to obey the following “no rectangles” rule: the four corners of a rectangle cannot all be colored red. I want to have as many red points as possible. How many red points can there be?”

The general problem is pretty challenging, obviously, but starting with a 3×3 square, and moving up to larger squares is a great project for kids. Here’s our project after I saw Guth’s lecture:

Larry Guth’s No Rectangles Problem

Although our project did take a little computational turn, looking at it now I’d love to talk through the 4×4 case with them.

(3) Anna Weltman’s loop-de-loops.


We’ve had a ton of fun with Weltman’s loop-de-loop idea and it especially captured my younger son’s imagination. Nothing but pencil and paper required, and some neat (and challenging) ideas for kids to think through. Here are our two projects:

Anna Weltman’s loop-de-loops part 1

Anna Weltman’s loop-de-loops part 2

(4) Numberphile + Katie Steckles’s video about the Fold an Cut Theorem.

Just pencil, paper, and scissors required for this incredible project:

Here are some of the projects we did after seeing this video:

Our Fold and Cut project

Fold and Cut part 2

Fold and Cut part 3

Anyway, that’s the four that came to mind today as I was thinking about projects that would be fairly easy to share with kids.

A Robert Talbert inspired conversation about Fibonacci numbers

Saw this interesting tweet from Robert Talbert yesterday:

The whole lesson is really interesting read. I decided to try out one small piece of it with the boys today – which Fibonacci numbers are even. The idea was to hear how they would approach “proving” that every third number in the list was even.

Here’s what my older son had to say – one interesting thing in this discussion was his thoughts about the proportion of the even and odd Fibonacci numbers. The confusing idea here is that both sets are infinite. I put off the details of that discussion for another day:

And here’s my younger son – he picks up on the two odds, one even pattern and has a pretty good explanation of why the pattern continues:

So, a fun little exercise. It is always interesting to me to hear the language that kids use to describe advanced mathematical ideas.