**Exploring Triangles and the Triangle Inequality Theorem**

Do your 6th grade math students understand the Triangle Inequality Theorem? Do they know what that is?

Mine did not, and although we’re trying to get through quite a bit of material before our state testing, we took some time today to explore triangles and the discuss the triangle inequality theorem.

Maybe you’ve done this exploration already, but it was quick and fun, so I thought I’d share.

The goal of the activity is to help students discover that not all line segments can meet to form a triangle.

**Discovering Triangle Inequality Theorem**

Without explaining triangle inequality to my math students, I gave each group three straws I had cut to different lengths and asked them to use their straws to make a triangle.

- In my first math class, I used straws that were cut to 2 inches, 3 inches, and 5 inches.
- These lengths, using straws, made it
**almost**possible to make a triangle, even though it shouldn’t be possible. So, I had to insist that their straw ends be lined up*perfectly*. I used 3, 5 and 2 inches to show that even these dimensions won’t make a triangle, because the sum is equal to the longest side, not longer than it. - After understanding how precise they had to be and that they couldn’t leave segment parts sticking out of the end of the triangle, they came to the conclusion that it couldn’t be done.

Next I gave the groups a new set of straws that were cut to 3 inches, 3 inches, 5 inches. In this case, they were excited to make their triangles in about 30 seconds!

We then discussed why the 3, 2, 5 didn’t work and worked our way to “creating” the triangle inequality “rule.”

**Lesson Adjustment**

For my next math classes, I trimmed the 3-inch straws to 2 inches, so these classes would have more difficulty getting the ends to meet. It was so funny to hear their comments:

- “This doesn’t work.”
- “Is this a trick question?”
- “This is impossible!”

And then, their excitement when they made the 3, 3, 5 triangle, and their exclamations of “We did it first,” was great to hear!

Again, we discussed the idea that the sum of the two smaller sides of a triangle must be greater than the longest side.

Students then applied the Triangle Inequality Theorem to their homework.