# Noticing and Wondering with Trigonometric Identities

### Friday

I had a sub Friday in Precalculus. My students were set to take a group of mini-assessments for Chapter 3. I expected they would have some additional time at the end of class, so (out of love for the substitute, and a desire not to waste class time) I wanted to launch Chapter 4 with an exploratory activity. I think it has some potential for improvement, but this is what I scraped together while getting my sub plans ready.

### Monday

Today my goal was to move toward proving trigonometric identities (see below for a handout), but first I wanted to debrief from their experience on Friday. I gave students three minutes to share their observations and questions in their groups, then I asked each group to share one noticing and one wondering. We ended up with this:

### Onward

My favorite part of all of this? Built on their questions, we’re now headed into Chapter 4 with a bit more motivation than we might have otherwise had. Also, there were a few wonderings that surprised me (at least in subtle ways), and these will almost certainly enrich our conversations over the coming days.

P.S. Up next, this.

P.P.S. That last handout is far from my best work, but it helped us transition from the noticing and wondering into some basic proofs.

1. Zach, thanks for the comment (and double thanks for the link to your blog). After seeing your approach, I’m tempted to revise mine so that students have a chance to sort pairs out of a larger group. Or maybe I’ll leave my first task in place, but I’ll include a new second activity where kids must use Desmos to sort ten graphs into five pairs, and THEN we’ll dive into proving them as identities.

Thanks again for stopping by the blog!

2. Oh I like the idea of using Desmos to have students sort through a set of graphs to find identities. I’ll have to remember to try that this year also. Nice idea.