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9-12 Integrated Math 3 Unit 6 Lesson 8

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 Integrated Math 2 •Integrated Math 3

Unit

Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7

Modeling Prompts

Lesson

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 •Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7

Modeling Prompts

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18
Lesson 19
Lesson 20

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Unit 6, Lesson 8

Rising and Falling

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Integrated Math 3

Practice

Problem 1
Student Task Statement

A fan blade spins counterclockwise once per second.

Which of these graphs best depicts the height, , of after seconds? The fan blades are 1 foot long, and the height is measured in feet from the center of the fan blades.

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Problem 2

Student Task Statement

Which situations are modeled accurately by a periodic function? Select all that apply.

the distance from the earth to the sun as a function of time
the vertical height of a point on a rotating wheel as a function of time
the area of a sheet of paper as a function of the number of times it is folded in half
the number of centimeters in inches
the height of a swinging pendulum as a function of time
the height of a ball tossed in the air as a function of time

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Problem 3

Student Task Statement

Here is the graph of a function for some values of .

Can you extend the graph to the whole plane so that the function is periodic? Explain your reasoning.
Can you extend the graph to the whole plane so that the function is not periodic? Explain your reasoning.

<p>Coordinate plane, x, negative 3 to 3 by 1, y, negative 0 to 5 by 1. A segment from 0 comma 1 to 1 comma 2.</p>

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Problem 4

Student Task Statement

Can a non-constant linear function be periodic? Explain your reasoning.
Can a quadratic function be periodic? Explain your reasoning.

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Problem 5

ForLesson 1: Moving in Circles

Student Task Statement

Do and lie on the same circle centered at ? Explain how you know.

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Problem 6

ForLesson 5: The Pythagorean Identity (Part 1)

Student Task Statement

The measure of angle is between 0 and radians. Which statements must be true of and ? Select all that apply.

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Problem 7

ForLesson 7: Finding Unknown Coordinates on a Circle

Student Task Statement

The center of a clock is the origin in a coordinate system. The hour hand is 4 units long. What are the coordinates of the end of the hour hand at:

3:00
8:00
11:00

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Problem 8

ForLesson 13: Transforming Parabolas

Student Task Statement

A parabola is transformed from to .

Write an equation for the parabola in vertex form.
What transformations were applied to the parabola?

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Lesson 8 Resources

Student Materials

If , then .

If , then .

.

The point lies on the unit circle.