What makes a triangle?

Last weekend we went to a wonderful family camp with an Ancient Greece theme. I was tasked with coming up with a fun, hands-on geometry lesson for 5-7 year olds.

These were my criteria for the activity:

1) Easy prep of materials.
2) Easy mechanics of working with materials.
3) Opportunities for kids to make interesting observations.
4) An opportunity for the kids to discover some cool math fact.
5) At least a loose connection to Ancient Greek geometry.

So, here it goes: Little kids discovering the triangle inequality using pipe cleaners.

Prep: Cut up pipe cleaners into pieces of various sizes (our range was probably from 1 to about 7 inches).

The lesson:

I began the lesson by asking the kids how many sides a triangle has. Of course they all knew that it was 3. I then proceeded to take 3 pipe cleaner pieces of about equal lengths and make a triangle out of them. And then came the key question: will I always be able to make a triangle no matter which three pieces I take? If some sets of three pieces cannot make a triangle, can you come up with a rule for when triangle can and cannot be made?

There were six kids and we split them up into two groups of three. Each group was given plenty of pipe cleaner pieces. The kids were encouraged to experiment with the pieces, make observations, and discuss them among each other. Each group was also assigned an adult scribe to write down the kids’ observations.

Here are some pictures of the process:

 

Pretty soon I heard kids in both groups saying things like, “If there is one long piece and two short ones then it won’t work.” Naturally, at this point, I encouraged them to try to formulate more precisely how short is “short” and how long is “long.” I hinted that a good way to do this could be to fix the long piece and then try out longer and longer “short” pieces until you can make a triangle.

And then I saw this and heard the following wonderful formulation:

“If the two short pieces are placed along the long one like this and they don’t reach each other, then you can’t make a triangle.”

And there you have it, a 7 year old’s formulation of one of the most fundamental theorems in geometry!