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# Unit Circle and Graphing: Formative Assessment

Lesson 6 of 14

## Objective: SWBAT demonstrate understanding of the unit circle and graphing trigonometric functions.

*45 minutes*

#### Ferris Wheel Match

*20 min*

For the first activity today, each student will be given one card from the Ferris Wheel Match cards. Each of the 15 rows of cards are a pair. Each pair will have one equation and either one diagram of a Ferris wheel or a description of a Ferris wheel.

**Note**: for all of the Ferris wheels, we will assume that the rider will always board at the lowest point.

Students will each get a card and will have to walk around the room to find their match. Keep a copy of the cards before they are cut out so you can quickly check that students found their correct pair.

After students find their correct match, they are to look at their Ferris Wheel diagram or description and change one of the numbers. Then, they are to write a new equation that will describe the new Ferris wheel after the number has changed. I talk more about this in the video below.

Once all (or most) of students have completed a revised equation, discuss how each of the measurements affect the equation.

- Ask a group that changed the radius or the diameter of the Ferris wheel to describe how it affected their equation. Ask the students to be specific about which transformation had to change (the vertical stretch in this case).
- Do the same for the length of one rotation.
- Do the same with the height of the Ferris wheel off of the ground.

Summarize how each measurement transforms the equation.

#### Resources

*expand content*

#### Quiz

*25 min*

After the matching activity, students will take a short quiz over the unit circle and the graphs of trigonometric functions. The questions included in the document below are sample questions for the quiz. I am not allowing calculators for this quiz because I want it to be an assessment of whether they understand these concepts. For example, for Question #1 a student could get the correct answer using a graphing calculator with very little understanding of how a cosine function behaves and how the transformations affect the graph.

#### Resources

*expand content*

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- UNIT 1: Functioning with Functions
- UNIT 2: Polynomial and Rational Functions
- UNIT 3: Exponential and Logarithmic Functions
- UNIT 4: Trigonometric Functions
- UNIT 5: Trigonometric Relationships
- UNIT 6: Additional Trigonometry Topics
- UNIT 7: Midterm Review and Exam
- UNIT 8: Matrices and Systems
- UNIT 9: Sequences and Series
- UNIT 10: Conic Sections
- UNIT 11: Parametric Equations and Polar Coordinates
- UNIT 12: Math in 3D
- UNIT 13: Limits and Derivatives

- LESSON 1: Riding a Ferris Wheel - Day 1 of 2
- LESSON 2: Riding a Ferris Wheel - Day 2 of 2
- LESSON 3: The Parent Functions are Related to Sine and Cosine
- LESSON 4: Transforming Trig Graphs One Step at a Time
- LESSON 5: Tides and Temperatures - Trig Graphs in Action
- LESSON 6: Unit Circle and Graphing: Formative Assessment
- LESSON 7: The Drawbridge - An Introduction to Inverse Sine
- LESSON 8: Inverse Trig Functions - Day 1 of 2
- LESSON 9: Inverse Trig Functions - Day 2 of 2
- LESSON 10: The Problems with Inverse Trig Problems
- LESSON 11: Inverse Trig Functions: Formative Assessment
- LESSON 12: NPR Car Talk Problem - Day 1 of 2
- LESSON 13: NPR Car Talk Problem - Day 2 of 2
- LESSON 14: Trigonometric Functions: Unit Assessment