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# Changing Ferris Wheels

Lesson 4 of 11

## Objective: SWBAT describe how changing the parameters of a Ferris wheel affect the graph associated with that Ferris wheel.

## Big Idea: How do changes to the Ferris wheel affect the graph? Without having studied transformations of trigonometric functions, students can develop their own generalizations about this using Ferris wheels.

*70 minutes*

During today's investigation I offer my students two different sets of tasks.

Each set gives students a lot of chances for deeper thinking. In today's lesson I really want students to apply the knowledge they have been developing over the course of the week so far.

Comparing Ferris Wheels is more abstract and it gives students the chance to use **MP2. **Students may have to create graphs to understand how to answer the questions, but they are not given numbers so they will need to choose numbers to help them illustrate the second situation.

Ferris wheel graphs key information is more challenging and may be used as an extension or a challenge for students who can easily tackle the first task. The idea is for students to develop a formula to determine the maximum and minimum points on the Ferris wheel by using the given information. This is a good chance for students to use **MP7** and **MP8** to develop a generalization.

The overall purpose of these tasks is for students to think about the Ferris wheel graphs in different ways and to begin to develop a more generalized understand of how the functions work. The better that they understand the functions without the abstraction of the equations, the more concrete of an understanding they will have.

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#### Closing

*10 min*

The close of this lesson is a moment during the unit when it is good to ask students to share their knowledge because they may have figured out different things than other people in the class. Today, I will ask students to quickly find a person that they didn't talk to during class. This way, they can choose somebody they are comfortable talking to. I ask them to share their learning for the day with that person and then to ask each other questions about what they figured out.

Afterward, I ask them to write a quick note about what they learned from talking with their partner. If time allows, I ask a few people to share their notes before I collect them. Approaching the close in this way helps to sustain a classroom culture where we share our learning with each other and are comfortable learning from lots of different people.

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- UNIT 1: Linear and Nonlinear Functions
- UNIT 2: Piecewise Functions
- UNIT 3: Absolute Value Functions and More Piecewise Functions
- UNIT 4: Introduction to Quadratic Functions through Applications
- UNIT 5: More Abstract Work with Quadratic Functions
- UNIT 6: Rational Functions
- UNIT 7: Polynomial Functions
- UNIT 8: Exponential Functions
- UNIT 9: Ferris Wheels
- UNIT 10: Circles
- UNIT 11: Radical Functions
- UNIT 12: Cubic Functions

- LESSON 1: Introduction to the Ferris Wheel Problem
- LESSON 2: Ferris Wheel (Graph) Symmetries
- LESSON 3: Graphing Ferris Wheel Heights
- LESSON 4: Changing Ferris Wheels
- LESSON 5: Ferris Wheel Speeds
- LESSON 6: From Degrees to Radians, Ferris Wheel Style
- LESSON 7: Ferris Wheels and Triangles
- LESSON 8: Ferris Wheels and Trigonometry
- LESSON 9: Ferris Wheel Function Rules
- LESSON 10: Ferris Wheel Unit Review
- LESSON 11: Ferris Wheel Summative Assessment