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My colleague introduced a great way to practice these identities. She said that in a prior lesson, she would have introduced the identities themselves and how they are derived. Students, apparently, are generally alright with learning the identities, but when it comes to actually working with them to solve left side/right side problems, that's where they get worried. Perhaps it's because it can take a few tries to solve one of these problems correctly? The students get discouraged and don't want to finish the problems. This is where the practice method my colleague used comes in. She provided us with the following sheets which we had to cut into individual pieces:
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With this activity, all the answers are there, you just need to put everything into the correct order. The squiggly lined boxes are starting points, and all the others are steps in the problems. In the end, you have 4 fully worked out trig problems. Honesty, I think we might have had too much fun with this activity! But even for students who are hesitant to try to solve trig identity problems, I can see how this activity would seem more "doable". As my instructor said, it feels much better to rearrange than it does to erase.
I think this is a great starting point for students who "hate" trig identities. I do believe it's important for them to also practice solving these problems from scratch, but it's quite possible that activities such as this one will help them gain the confidence they need in order to stick with it. I would be excited to use an activity like this in my classroom.
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