### Classwork: Module 1 Lesson 9

```Materials Needed for this Lesson
Student packet with Class Notes, Exit Ticket
and Problem Set
Representing Proportional Relationships with
Equations
Objective:
Use the constant of proportionality to represent proportional relationships by
equations in real world context as they relate the equations to a corresponding
ratio table and/or graphical representation.
Classwork:
9
Module 1 Lesson
Take out Lesson 9 -- Classwork - sp. 33
Classwork:
9
Module 1 Lesson
Define the variables:
Does it matter which variable is the independent or dependent?
What is the constant of proportionality?
What does the constant of proportionality mean in the context of the problem?
On sp. 33 complete question 'a.'
a. Write an equation that you could use to find out how long it will take him to build any number
of birdhouses.
Classwork:
9
Module 1 Lesson
Discussion:
9
Module 1 Lesson
While you may work for a fractional part of an hour, a customer
will not want to buy a partially built birdhouse.
Discuss with a partner situations where a fractional answer is
appropriate, while in other situations integers must be rounded
to whole numbers.
Be prepared to share out.
Classwork:
9
Module 1 Lesson
Take out Lesson 9 -- Classwork - sp. 34
Classwork:
9
Module 1 Lesson
Select any two pairs of numbers from either Al's Produce stand or Barbara's Produce stand to
calculate the constant of proportionality.
When completing example 2, use the following questions to assist in your thinking:
Which makes more sense: to use a unit rate of "ears of corn per dollar" or of "dollars/cents per ear of corn"?
Based on the previous question, which would be the independent variable?
Which would be the dependent variable and why?
How do you write an equation for a proportional relationship?
Discussion:
9
Module 1 Lesson
Which makes more sense: to use a unit rate of "ears of corn per dollar" or of "dollars/cents per ear of corn"?
Based on the previous question, which would be the independent variable?
Which would be the dependent variable and why?
What numbers did you use to determine your unit rate or constant of proportionality? How do these values
compare for Al's and for Barbara's?
How do you write an equation for a proportional relationship?
What is the equation for Al's Produce stand?
What is the equation for Barbara's Produce stand?
Closing:
Module 1 Lesson 9
What type of relationship can be modeled using an equation in the form y = kx, and what do
you need to know to write an equation in this form?
Give an example of a real-world relationship that can be modeled using this type of equation
and explain why.
How do you determine which value is x (indpendent) and which value is y (dependent)?
Give an example of a real-world relationship that cannot be modeled using this type of
equation and explain why.
Exit Ticket:
Module 1 Lesson 9
Problem Set:
Module 1 Lesson 9
Problem Set Directions: Print each question on a sheet of paper. Post the questions around the room. Have students work in
groups of four and progress from problem to problem. Give students a student record sheet as a place to record their solutions.
Use a timer to help students pace the activity and stay on task from one problem to the next. Students within a group should
discuss the problem and its solution and agree on the solutions as they move from problem to problem.
Take out Problem Set- sp. 35-36
Continued...
Problem Set:
Module 1 Lesson 9
The following pages have each problem set question on their own page to facilitate in a class discussion and allow for students to
come to the smartboard and explain their thinking.
Continued...
Problem Set:
Module 1 Lesson 9
Continued...
Problem Set:
Module 1 Lesson 9
Continued...
Problem Set:
Module 1 Lesson 9
Continued...
```