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# Model Trigonometry with a Ferris Wheel Day 2 of 2

Lesson 14 of 19

## Objective: Students will be able to model the movement of a Ferris Wheel using trigonometry.

*48 minutes*

#### Warm-up

*5 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-Ferris Wheel Day 2 which asks students to identify things that could be modeled with sine or cosine.

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

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This is a complete lesson found on the MARS (Math Assessment Resource Service) website. I have broken it up into two days. Since this is already a wonderful complete lesson, I will share my pacing and key portions but the original should be read if you plan on trying this lesson. In the previous lesson, the students completed a formative assessment that I have looked at to identify any areas of struggle.

The first goal for today is a paired matching activity (**Math Practice 2**). Each student will receive the A and B cards from the lesson, a big sheet of paper, and a glue stick. The instructions from the lesson are as follows:

*Take it in turns to match and place cards. Place them next to each other, not on top, so that everyone can see.**When you match two cards, explain how you came to your decision.**Your partner should either explain that reasoning again in his or her own words, or challenge the reasons you gave.**You both need to be able to agree on and explain the placement of every card.**If you cannot find a card to match, then make one up yourself.*

These are located in my PowerPoint. The key to this portion is that they alternate justifying each other's reasoning (**Math Practice 3**). I may want to model this behavior if they seem unsure. I walk round listening to the sharing, keeping kids on track, and asking formative questions if anyone is struggling. There is a beautiful list of questions in the MARS lesson plan on page 4.

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#### Adding in the Model

*10 min*

Once most of the groups have completed their work, I pause them to introduce then next portion of the activity. We look at the slide with the diagram of the Ferris wheel (**Math Practice 4**). Here are the suggested directions from the MARS lesson plan:

*Each of the functions you have been looking at models the motion of a Ferris wheel.**I now want you to try to match the correct wheel description to the graphs and functions on the table.**On these graphs the heights are given in meters and the times in seconds.*

I ensure that the students understand axles. The students then finish their chart by adding in the wheel descriptions. Again, I walk around, keep students on track, and ask guiding questions to anyone who is struggling. There is a terrific list on page 7 of the MARS lesson plan.

#### Resources

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#### Class Discussion/Conclusion

*15 min*

The goal of this portion is not to check that everyone got the correct answer. It is to give students an opportunity to share their thinking and to formalize, as a class, how each separate portion of the cosine function is represented in our Ferris wheel model. While they provided a slide to aid in this, I chose not to use it. I pulled the image out and will use it without the extra calculations. I think they may distract from the students providing their own thinking. I ask the students to write a conclusion statement in their notes talking about the similarities between the functions on their graphs. I will then have the students share their conclusions.

After everyone has shared, I ask leading questions to get to any remaining information. One important thing is why cosine is being used rather than sine (**Math Practice 7**). Next, we will make sure that the important features of each Ferris wheel have been completely covered. As a class, we determine how the diameter, height of the axle, and rotation time are represented in the function. Finally, a general form is either written by the students(higher level) or written together. This form is where y represent the height of the rider and t represents seconds. Another good question is why there is a minus sign in the general form.

#### Resources

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The assignment for this lesson a similar problem to the original assignment that my students did in the previous lesson. The goal is to see the growth in their knowledge and understanding. If there is any time after the class discussion, class time may be used. This assignment is on page 16 of the MARS Ferris Wheel Lesson Plan.

#### Resources

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#### Exit Ticket

*3 min*

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

This Exit Ticket assesses students' ability to transform a tangent function.

#### 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