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# Period Puzzle

Lesson 10 of 19

## Objective: Students will be able to identify the amplitude of a sine graph given the parent graph.

*27 minutes*

#### Warm-up and Homework Review

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Period Puzzle which asks students to use a trigonometric model to answer questions about a respiratory scenario.

I also use this time to correct and record the previous day's Homework.

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#### Quiz on Trigonometry

*10 min*

The lesson includes a quiz that covers the previous material in my Trigonometry Unit. I have included two versions of the quiz as I alternate quizzes like a checkerboard. Please see this short document for more information on my Quiz Procedures.

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#### Period Puzzle

*5 min*

Once the students are finished with their quiz, they are to work on this puzzle*. I really like this puzzle for a couple of reasons. First of all, it gives students practice with **Math Practice 7**. Given the graph of the parent function for sine, students must figure out the period of other sine functions. The key is that there are no unit marks and the x axis. Students have to use that they know about periodic functions and period itself to figure each one out.

The second reason I really like this puzzle is that it is highly differentiable. The author of the puzzle suggests that one uses the purple graph as the parent graph. This will make for the easiest conversions to other periods and will be an acceptable challenge for most students. The green function has a period that is half the length of the purple and would be a bit bigger of a challenge but still doable for many students. For those high level students, the gray function would provide a serious challenge. It has two thirds the period of the purple function.

I do not have access to a color printer at school so I highlight the parent function. I choose beforehand which student gets which parent function. I inform the students that they will be getting different parent graphs in advance. They will work on this alone and then possibly in pairs once everyone is finished with the quiz. For those students who finish faster than I expect, I will extend the lesson by assigning them a new parent function and have them re-evaluate the period of each function (**Math Practice 7**).

*This puzzle comes from nrich.math.org.

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#### Exit Ticket

*2 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

This Exit Ticket checks ask the students to answer, "What strategies or tricks did you use to solve the puzzle?" This will provide a look into their thought process as they attempted to make sense of the puzzle.

#### Resources

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Angle and Degree Measure
- LESSON 2: Trigonometric Ratios
- LESSON 3: Trigonometric Ratios of General Angles
- LESSON 4: Radians Day 1 of 2
- LESSON 5: Radians Day 2 of 2
- LESSON 6: The Unit Circle Day 1 of 2
- LESSON 7: The Unit Circle Day 2 of 2
- LESSON 8: Graphs of Sine and Cosine
- LESSON 9: Period and Amplitude
- LESSON 10: Period Puzzle
- LESSON 11: Transformations of Sine and Cosine Graphs
- LESSON 12: Graph of Tangent
- LESSON 13: Model Trigonometry with a Ferris Wheel Day 1 of 2
- LESSON 14: Model Trigonometry with a Ferris Wheel Day 2 of 2
- LESSON 15: Modeling Average Temperature with Trigonometry
- LESSON 16: Pythagorean Identity
- LESSON 17: Trigonometric Functions Review Day 1
- LESSON 18: Trigonometric Functions Review Day 2
- LESSON 19: Trigonometric Functions Test