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# Ferris Wheel Function Rules

Lesson 9 of 11

## Objective: SWBAT write algebraic functions to model the height of a rider on a Ferris Wheel over time.

## Big Idea: How can we complete the multiple representations of this relationship? Is there a function rule for this situation? Students will write and test function rules using online graphing tools.

*70 minutes*

#### Warm-Up

*30 min*

I designed today's Find Ferris Wheel Functions Warm-Up to give my students a good chance to consider functions describing the motion of a Ferris wheel using multiple representations. One strategy I used in this worksheet was to keep some problem formats the same so that students can develop confidence with particular problems. Of course, I also vary other problem formats so that students don’t just memorize a single algorithm (spurred on by repetition).

I will make use of graphing technology in this lesson, specifically the trigonometric features of desmos. I will make sure my students understand how to use them. The most important thing they need is to be able to change the axes to “degree mode” and to change the scale of the axes so that they can see what is going on in the graphs. I want my students to check their graphs and tables electronically.

Today's lesson will be difficult for some of my students. When I come across a student who is struggling, I will be sure to tell them, “*It’s okay, we are still in the process of figuring this concept out.*”

#### Resources

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#### Closing

*10 min*

In this lesson it is a good idea to close the lesson by providing a summary presentation of the models for trigonometric functions. I will use these sample functions with parameters:

- y= a*sin(b*x)+d
- y= a*sin(b*x+c)+d

When I make this presentation, I give students a chance to think about what these generalized formulas represent:

- How do each of the parameters affect the graph?
- How do each of the parameters relate to the Ferris wheel?

Now that students have spent several lessons exploring these functions using the context of a Ferris wheel, they can better understand an abstract representation of these functions in order to create their own generalizations. I plan to have my students write on their own, first. Then I will have them share some ideas and I will ask students to add to what they have already written. I will use this brief writing task as a quick, informal assessment of how well students are able to make generalizations about how the functions work.

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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