Verifying Trig Identities (day 2 of 2)
Lesson 7 of 16
Objective: Students will be able to verify complex trigonometric identities by using the fundamental trigonometric identities.
Since today’s lesson is a continuation of the work done yesterday and in previous lessons, I chose to help students warm-up for the lesson by just reviewing homework. I like to give kids 2 minutes to compare their answers on the homework. Then I will take questions. I think it is important for students to compare their answers/solution methods to determine whether or not they have questions. I also think it is a great way for students to catch their silly mistakes and tends to encourage students to help each other out on the homework. I am a huge proponent of study teams and working together on homework. I do not see homework as a summative assessment of students’ knowledge in anyway. Instead, it is part of the learning process. So I encourage them to work together and to be constantly self-assessing whether or not they would be able to do this on their own and whether or not they understand the material.
For the middle part of today’s lesson students will play the Whiteboard Review Game. This game requires every student to have their own whiteboard and their own marker. Although the game is played in teams, students are expected to do their own work. For today, I will have my students sit with the team that they will take the group quiz with later this unit.
Before the class period begins, I will have prepared a method to randomly call on students. I used to use Popsicle sticks which I wrote students name on, but this year I assigned students a number (which they use all year long) and I use a random number generator to call on students. You can find a random number generator on www.random.org that is easy to use.
To start the game I will put a problem on the board from the Problem Bank: Whiteboard Review Game. Students will simplify or verify the trigonometric identities over a given time frame. I like to set a timer and say you have x minutes to solve this one. I adjust the time based on how difficult the problem is. The game is summarized for students on page 2 of today's flipchart, Verifying Trig Identities (day 2 of 2) flipchart.
When time is up, I randomly select a student. This student will bring their whiteboard under the document camera and present their work. Their team earns 2 points for making a presentation. If they have correctly and completely simplified the identity (or verified it correctly) they earn another point. If there is a mistake in this student's work, the first student who raises their hand to point out the mistake will earn a point for their team (MP3, MP6).
Sometimes, students become too aggressive trying to point out mistakes. Because of this I typically deduct a point from a team whose members incorrectly point out a mistake. If I sense a need to draw a little more energy from students, I make the game a little more fun by allowing students to ‘gamble’ the points they earn. When a student is awarded points, they can gamble the points (double or nothing) by doing something fun. Here are some of my favorite gambles:
1) Throw a piece of paper into the trash can from 10 feet away.
2) Answer a trivia question.
3) Throw a piece of paper behind your back and catch it.
4) Correctly guess a coin flip.
I have learned that it is better for me to make up the Gambles, than to let students come up with their own ideas.
As a closure to today’s lesson, I had students write down one thing they learned today on their whiteboard. Then I had them hold it up and show me. Did I read them all? NO! Did I care what they said? Not really. I just felt it was important for students to recognize that although there was not a new learning target for today, they still probably learned something from their peer’s presentations.