# Triangles, Toothpicks and Patterns

Standard

This was our visual pattern in Algebra 1 today.
They were upset because there were so many triangles. And so many toothpicks.  Which then means…there were so many patterns.

But the way they saw it was much different than how I saw it.  So I listened.

J: But where are you getting the triangles?  Here’s what I see…

And there was a discussion of the center “upside down” triangles (yep, they said it)…do we count them? They’re like bonus triangles, you really don’t build those, they just happen.  Hmm? Really.

Someone would make a suggestion for finding toothpicks and we would try it…if not, let’s look again.

Z: It’s easier if we don’t count them to find the pattern for number of toothpicks.  You add the new step # to last triangle # then each one takes 3 toothpicks.

Okay…so what about step 27? And step 43?

And it was fun watching them struggle a little.

K:  If you add the step # to the steps before, you get triangles you build.

And I see using triangular numbers and arithmetic series discussion in our future?

Why? Because it’s next in our curriculum? No. Because they are engaged in this question.

They kept seeing patterns and describing them.  They were playing with their math.  And it made me smile.