Four math projects for kids to build analytical muscle

Saw this tweet from Jose Vilson today:

Too much of math pedagogy isn centered on flexing students' numerical muscle instead of their analytical muscle.

— José Luis Vilson (@TheJLV) October 14, 2015

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: