Ferris Wheel Unit Review

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Objective

SWBAT assess their strengths and weaknesses related to the content of this unit and to reflect on their application of the Practice Standards throughout this unit.

Big Idea

A thorough, leveled review of the key skills of this unit provides students with the opportunity to assess their understanding and make a work plan based on this self-assessment.

Lesson Author

Hilary Yamtich

Oakland, CA

Grade Level

Eleventh grade

Twelfth grade

Subjects

Math

Graphing (Algebra)

Trigonometric functions

unit circle

modeling

Precalculus and Calculus

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 π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosines, and tangent for x, π + x, and 2π – 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.

Multiple Representations

40 minutes

The big idea of the Ferris Wheel Multiple Representations task is to ask students to look at the same problem in different ways and to make connections between all aspects of the problem that they have been studying. The idea is for students to find out all 4 key pieces of information about each Ferris wheel using each of the representations given. I tell students that this task will give them a chance to think about the big picture and to make as many connections as possible—if they understand this task, they will have a good understanding of the whole learning target.

As they work, I ask my students to make a graphic organizer of some kind that shows how to find the key information in each representation. There are rich opportunities here for precise mathematical communication (MP6) by asking them to make clear how they are finding their answers. It may help to provide them with some key vocabulary:

Amplitude
Center line
Frequency
Period
Horizontal shift
Vertical shift

As they attempt to explain their answers and their process, I circulate to help them figure out how to use these words to explain the connections they are making. Depending upon how the activity transpires, I may ask a few students to share their organizers/webs or to explain their connections to other groups of students or to the whole class.