Objective

Warm-Up

Finding Ferris Wheel Functions Investigations

Closing

Ferris Wheel Function Rules

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.

Lesson Author

Hilary Yamtich

Oakland, CA

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

trigonometric functions (Graphing)

Precalculus and Calculus

Trigonometric functions

modeling

Standards

HSF-IF.B.4

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.*

HSF-TF.A.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

HSF-TF.A.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

HSF-TF.A.3

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for Ï/3, Ï/4 and Ï/6, and use the unit circle to express the values of sine, cosines, and tangent for x, Ï + x, and 2Ï â x in terms of their values for x, where x is any real number.

HSF-TF.A.4

(+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

HSF-TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.*

MP1

Make sense of problems and persevere in solving them.

MP2

Reason abstractly and quantitatively.

MP3

Construct viable arguments and critique the reasoning of others.

MP4

Model with mathematics.

MP5

Use appropriate tools strategically.

MP6

Attend to precision.

MP7

Look for and make use of structure.

MP8

Look for and express regularity in repeated reasoning.

Warm-Up

30 minutes

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.”

Finding Ferris Wheel Functions Investigations

30 minutes

Closing

10 minutes

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.

Previous Lesson

Next Lesson