My students worked on proving trigonometric identities for homework, so I will take some time at ths start of class to go over any of the problems that were challenging for students. There will usually be some identities that students are unable to prove. If possible, I will have a student who successfully completed the proof present their work to the class.
A good strategy is to go through each of the proofs and make a note about what made each one difficult and the students' first attempt to simplify. The list below sums up the major strategies that students will encounter while working on these problems.
1. Combining two fractions with a common denominator
2. Factoring and cancelling common factors
3. Too many trig functions so writing everything in terms of sine and cosine
4. Too many trig functions so simplifying using one of the identities
After generating these strategies, students will have a tool they can use when they get stuck on a proof. They can go through this list and see which one(s) apply to the problem they are working on.
Student Work Day
It is nice to take a breather and give students a day to have an extended time to work on some math and to take the time to check in with students individually. Today will be once of those days as students can finish up their Car Talk problem or work on proving the identities from the last few days. For today, I am going to bring laptops into the classroom so that students can work on their final write up for the Car Talk problem. If a group has completed this assignment, they can keep working on the rest of the identities to prove from yesterday's worksheet.
Since students will be working independently for most of the hour, it is a nice time to check in with each students and have a short conference about their progress. In this video I discuss some possibilities for these individual meetings.