I was inspired to have some more fun with folding by a question from this year’s *American Invitational Mathematics Examination *(AIME) that turned triangles into tables and asked “How high can the table go?”. (You can find the question here).

Investigating the problem seemed like more fun than solving it, so I cut out a triangle from some foam board and scored lines near the vertices.

Then I folded the corners and made the following table with an irregular hexagonal top!

I made a few, to see what kinds of heights I could get.

There are so many fun questions to explore here! What comes to mind?

**Related Posts**

This would make an interesting investigation for students to explore…range of exit points…Year 3 through to 12.

I’d probably start with an equilateral triangle with younger kids, and move to an isosceles or scalene with older kids.

It’s a bit artificial lack in a context, but a challenge could be to have a ratio of the area of the top to the height as 1:1 (ignoring the units, like when considering surface area to volume ratio).