My five-year-old had fun playing with foam sheet triangles I cut out—and we even introduced Pythagoras’s theorem for right triangles.

I was inspired by some sample materials offered by *Math Expressions* (start on page 14 of this pdf). One thing this source recommends is to discuss the difference between “turning” a triangle piece and “flipping” the piece.

I made up some right triangles with sides of lengths 3, 4, and 5 inches, and I figured I might as well work this up into a lesson about Pythagoras. Before I did this, we measured the sides of different triangles to see that the longest side is not always a round inch (when the other sides are round inches). So the 3-4-5 triangle is a special sort of triangle.

By cutting out and marking squares with sides 3, 4, and 5 inches, we could see that the square of the shortest side, plus the square of the middle side, is equal to the square of the longest side. I did not try to write down the formal equation or to demonstrate the universality of the theorem. This is just an illustration of the theorem for a particular triangle. But at this stage I thought that was the perfect level of complexity.

We also peaked at some basic facts about Pythagoras and looked up on Google maps where he lived.

You could use card stock for your triangles. For this, though, I really like the feel of foam sheets. The foam pieces stick to each other just enough to be helpful.

We were lucky in that Grandma had dropped off some foam sheets. If you need some Amazon sells various sets (here’s one that seems good—paid link).

Incidentally, you can also use foam sheets to make up your own fraction wheels; see the pdf for patterns.