Trig Graph Match-ups

When we were working through our first trigonometry unit in Precalculus, I wanted students to be able to make the connection between the equation of the trig function and the graph. Before I'd ask students to graph the trig equations themselves, I wanted students to practice finding amplitude, frequency, period, midline, and phase shifts and be able to look for those in a graph. I found a card set of trig functions and their matching graphs on TES here...

Trig graph match ups.  https://www.tes.com/teaching-resource/transformations-of-trigonometric-graphs-match-up-6407000

There are three sets of functions and graphs, so I copied each set on a different color of paper. I had teams of students work with one color and when their matches were made correctly, they moved onto another color. 

As I would check student matches, I'd ask questions such as: How did you decide that this graph matched with this equation? What part of the equation gives you a clue to how tall your graph will be? What's the difference between the frequency and period and how can you explain the difference using this graph and equation?

I know these concepts are all learned in Algebra 2, but students sure do need the refresher when they get to Precalculus.

Composition of Trig Functions Leap Frog

As I was preparing to teach the concept of compositions of trig functions, I read this post on Math = Love. Sarah explained how to play the game of leap frog to help students practice finding the values of trig functions using the unit circle. When I looked at Sarah's answer bank for the activity, I knew that I could easily adapt it to the compositions of trig functions I wanted to practice with my students. 

The bulk of the work was putting together slides for the questions so I could switch to the next question with just a click. Now, I love all things Google, but there is no equation editor in Google Slides. So, I put all of the expressions in a Google Doc and then cut and pasted them into the Slides presentation. It was a lot of work, but I was happy with the end result. It was also a big hit in class, and by the end, the light bulb had turned on for the whole class for this concept. 

I did this in February, before Coronavirus sent us all home. Since we were together, I actually had them leave the answer cards behind and just move seats and use the answer cards that were at the next seat.  If we are together this coming school year for this, I may need students to carry their answer cards with them to whatever seat they are moving to to minimize sharing of supplies. 

So, here are my files:

Google slide with all of the questions, one per slide.

Google doc with all of the expressions together.

Answer sheet from Math = Love.

Hands-On Law of Sines and Cosines

I love when teachers freely share ideas and materials online. Although I appreciate the work available in TPT (I use All Things Algebra's Precalculus curriculum and love it), freely shared resources are my favorite.

We were working on the Law of Sines and the Law of Cosines in class today and I was trying to decide what we would do for practice. This class is flipped, so my students had already done the notes.  Even doing a jigsaw with the homework questions seemed kind of dry. Happily, I found this lesson plan on the Utah Education Network.

I didn't do part one of the lesson, which was making a triangle reference model to give a concrete picture of which sides correlate to which angle, although given more time, it may have been wise to do it.

We did part 2 and started part 3 in class. We'll have to finish part 3 next class. Normally, we would have been able to get through part 2 and 3 in one 80 minute period, but we had a quiz and went over it, so the 60ish minutes we had wasn't quite long enough.

I love the hands-on aspect of this lesson--that students are using the Law of Sines and Cosines to find the missing information in the triangle and then actually measuring with rulers and protractors to verify. When we moved onto part 3 I handed out half sheets of tablet paper and several of my students were working hard to make the hardest triangle to solve--as in with the smallest angle possible for one of the vertices. We had just made it to the part of the lesson where students give their constructed triangles with three measurements to other groups to solve when we ran out of time.  Ideally, if students are choosing three different measurements differently for each of their constructed triangles, the students solving them should get an assortment of Law of Sines and Cosines practice.