Math year in review part 2 – Fold and Cut

I’m starting to write up some thoughts on the projects we’ve done in the last year.  The difference between the past school year and the ones before that is that this was the first year that we weren’t home schooling.  That change altered  some of what I was doing with the boys, but maybe not as  much as I thought.  Yesterday I wrote up our tiling projects:

Math school year in review part2 – our tiling projects

Today I want to look back on a second idea we came back to a few times – fold and cut.

Our year in math projects got off to a super fun start last September when I saw this incredible video from Numberphile featuring Katie Steckles:

This video led to several projects:

Our one cut project

Fold and cut project #2

Fold and cut part 3

One of my great mathematical thrills of the year was running into Martin Demaine over at MIT and showing him parts of these projects!

Our next interaction with the fold and cut theorem came when I stumbled on a “fold and punch” activity while preparing to run Family Math night at my younger son’s elementary school:

As you might imagine, this activity was one of the most popular ones at the Family Math nights. I tried it out with my younger son before trying it out with the larger groups:

Fold and Punch


A good (and fun!) thing that happened today – half a punch!

After seeing my tweet about the fold and punch activity, Joel David Hamkins created this incredible activity for kids:

Math for nine year olds: fold, punch and cut for symmetry

Later in the year Steven Strogatz shared the “Mathematical Etudes” videos on twitter:

We used one of their videos to look at a slightly more difficult fold and cut problem than we’d tried before:

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Using the Mathematical Etudes videos with kids

Finally, in April we saw an absolutely amazing public lecture from Tadashi Tokieda which led to two really fun projects that involve folding and cutting paper – one of the projects involves trying to pass the circle in the picture below through the much smaller square:

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Tadashi Tokieda’s “World From a Sheet of Paper” lecture

So, a fun year playing around with paper folding. I love how these activities engage kids with math. We’ve also explored a little bit in this geometry book that teaches geometry through paper folding and I plan to use it more this year to help the boys see a different side of geometry.