Curriculum  /  Math  /  7th Grade  /  Unit 1: Proportional Relationships  /  Lesson 5

Proportional Relationships

Lesson 5

Math

Unit 1

7th Grade

Lesson 5 of 18

Objective

Write equations for proportional relationships from word problems.

Common Core Standards

Core Standards

  • 7.RP.A.2 — Recognize and represent proportional relationships between quantities.
  • 7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Foundational Standards

  • 6.EE.B.7
  • 6.EE.C.9

Criteria for Success

  1. Recall that a ratio relationship $$A:B$$ has two unit rates, $$A/B$$ and $$B/A$$.
  2. Find the constant of proportionality from a situation (not a table) by finding the value of $$y/x$$, where $$y$$ is the dependent variable and $$x$$ is the independent variable. 
  3. Write an equation using the constant of proportionality for a proportional relationship.
  4. Use an equation to solve problems.
  5. Decontextualize situations to represent them as equations and re-contextualize equations to explain their meanings as they relate to situations (MP.2).

Tips for Teachers

Lesson Materials

  • Calculators (1 per student)
Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems

25-30 minutes

Problem 1

A repair technician replaces cracked screens on phones. He can replace 5 screens in 3 hours. 

a.   Write an equation you can use to determine how long it takes to replace any number of screens.

b.   Write an equation you can use to determine how many screens can be replaced in a certain number of hours.

c.   Use one of your equations to determine how long it would take to replace 30 screens.

d.   Use one of your equations to determine how many screens could be replaced in 12 hours.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 2

A train traveling from Boston to New York moves at a constant speed. The train covers 260 miles in 3.25 hours. 

Write an equation that represents this relationship. Explain what your equation tells you about the train.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem 3

Deli turkey meat is on sale at two different grocery stores, as represented below.

Stop & Buy

$$c=6.25p$$, where $$c$$ represents cost in dollars and $$p$$ represents number of pounds of turkey

Roger's

Amount

(pounds)

Cost

($)
3 19.50
4 26.00
6 39.00
7 45.50

 

What is the unit price of turkey per pound at each store? Which store has the better sale?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

The 7th graders at Wilson Middle School are taking a field trip to the science museum. So far, 12 students have turned in a total of $81 to pay for their ticket.

a.   Write an equation to represent the cost, $$c$$, for $$t$$ tickets.

b.   If all 72 students turn in their ticket money, how much money will be collected?

Student Response

Upgrade to Fishtank Plus to view Sample Response.

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Challenge: The average person uses about 90 gallons of water per day. At this rate, how long would it take a family of 4 to use enough water to fill an average-size swimming pool? An olympic-size swimming pool?

Next

Represent proportional relationships in graphs.

Lesson 6
icon/arrow/right/large

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

Topic B: Non-Proportional Relationships

Topic C: Connecting Everything Together

Topic D: Solving Ratio & Rate Problems with Fractions

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

We Handle Materials So You Can Focus on Students

We Handle Materials So You Can Focus on Students

We've got you covered with rigorous, relevant, and adaptable math lesson plans for free