Library

Unit 5 - Lesson 3 - Grade 8: Illustrative Mathematics

By Formative Library
Last updated 2 months ago
16 Questions
Note from the author:
Grade 8 Unit 5
Lesson 3: Equations for Functions
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 5
Lesson 3: Equations for Functions
CC BY 2021 Illustrative Mathematics®
Lesson: Equations for Functions

A Square’s Area (Warm Up)

1.

Fill in the table of input-output pairs for the given rule. Write an algebraic expression for the rule in the box in the diagram.

Diagrams, Equations, and Descriptions

Record your answers to these questions in the table provided.
2.

Match the description with its diagram.

The circumference, C, of a circle with radius, r.

3.

Match the description with its diagram.

The distance in miles, d, that you would travel in hours if you drive at 60 miles per hour.

4.

Match the description with its diagram.

The output when you triple the input and subtract 4.

5.

Match the description with its diagram.

The volume of a cube, v, given its edge length, s.

6.

Record your answers to these questions in the table provided.
  • Write an equation for each description that expresses the output as a function of the input.
  • Find the output when the input is 5 for each equation.
  • Name the independent and dependent variables of each equation.


Dimes and Quarters

Jada had some dimes and quarters that had a total value of $12.50. The relationship between the number of dimes, d, and the number of quarters, q, can be expressed by the equation 0.1d + 0.25q = 12.5
7.

If Jada has 4 quarters, how many dimes does she have?

8.

If Jada has 10 quarters, how many dimes does she have?

9.

Is the number of dimes a function of the number of quarters? If yes, write a rule (that starts with d =...) that you can use to determine the output, d, from a given input, q. If no, explain why not.


10.

If Jada has 25 dimes, how many quarters does she have?

11.

If Jada has 30 dimes, how many quarters does she have?

12.

Is the number of quarters a function of the number of dimes? If yes, write a rule (that starts with q =...) that you can use to determine the output, q, from a given input, d. If no, explain why not.


Cool Down: The Value of Some Quarters

The Value of Some Quarters

The value v of your quarters (in cents) is a function of n, the number of quarters you have.
13.

Draw an input-output diagram to represent this function.

14.

Write an equation that represents this function.

15.

Find the output when the input is 10.

16.

Identify the independent and dependent variables.