# Pascal’s Triangle, Patterns, and Binomial Expansion

Today the CPM lesson in my Algebra 2 book started with a lesson from my MS past, Pascals Triangle. I only have two new lessons of the year left before our final assessment and then exam review begins. So I gave them extra time to discover the patterns and then play with Pascals Triangle after their quiz. They’ve had a stressful week (it is May!) and the quiz was tough, so coloring was definitely the right call! Some kids got so into coloring they didn’t even care about the patterns. I didn’t mind at all because they were coloring one of the patterns!

After discovering and then sharing the pattens by groups, we moved on to the main part of the CPM lesson, discovering binomial expansion within the Triangle, then using substitution to extend it to more then (a + b)^n.

I don’t know if it was the all of the cool patterns or the coloring, but my students really got into this lesson today. We usually work in groups in my class, but a couple of students got really involved in the math and extended what they were learning. I usually bring students back to group work when they go off on a tangent, but they were so excited that I just let them go! I’m so glad I did bc they developed these beautiful ideas. Drake was so proud of his that he labeled it and left it for the rest of my classes to see!

My students also created beautiful triangles. Next year I am going to make the Triangle larger so they can see the Sierpinski pattern even more through their own coloring. We decided to do a Pascal’s triangle photo shoot in a couple of my classes. What an amazing way to end the week.

## 2 thoughts on “Pascal’s Triangle, Patterns, and Binomial Expansion”

1. I love reading your posts about all of the cool and wonderful things happening in your classroom. I also teach CPM algebra 2 (and algebra 1 and precalculus) in a private school on St. Croix in the US Virgin Islands. I was wondering how you use the checkpoints in CPM in your classroom? How long have you been teaching CPM?

Thanks for any information you would like to share. I am looking for other teachers who teach using CPM so I can get a better idea of how to implement the curriculum in my classes. Keep on blogging!

Cheers,

2. Nice idea. Before, I only write the pattern in a clean sheet without them expressing their creativity. You approach will make your students enjoy Math.