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

Proportional Relationships

Lesson 1

Math

Unit 1

7th Grade

Lesson 1 of 18

Objective

Solve ratio and rate problems using double number lines, tables, and unit rate.

Common Core Standards

Core Standards

  • 7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.
  • 7.RP.A.2 — Recognize and represent proportional relationships between quantities.

Foundational Standards

  • 6.RP.A.1
  • 6.RP.A.2
  • 6.RP.A.3

Criteria for Success

  1. Understand the concept of equivalent ratios in real-world context. 
  2. Define equivalent ratios: The ratio of $${A:B }$$ is equivalent to $${c \times A:c \times B}$$ for a non-zero number $$c$$.
  3. Identify the unit rate for a ratio $${a:b}$$ as $$a/b$$ or $$b/a$$.
  4. Know that equivalent ratios have the same unit rate, and that the unit rate represents the multiplicative factor across columns in a table of equivalent ratios. 

Tips for Teachers

  • This lesson approaches standards 7.RP.1 and 7.RP.2 by reviewing concepts and skills from 6th grade standards in the Ratios and Proportions domain. These standards are foundational to this 7th grade unit, and will support students in later lessons. 
  • In terms of pacing, this lesson may be skipped or extended an additional day, depending on the needs of your students.
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Anchor Problems

25-30 minutes

Problem 1

Luiz is making brigadeiros, Brazilian chocolate truffles, for his sister's high school graduation party. He uses a ratio of 3 ounces of sweetened condensed milk for every 2 ounces of cocoa powder. For this recipe, he measures 18 ounces of sweetened condensed milk and pours it into a bowl.

a.   How many ounces of cocoa powder should Luiz add to the bowl?

b.   Luiz's friend Paulo wants to help make the brigadeiros. Paulo says he uses a recipe that calls for 9 parts sweetened condensed milk to 4 parts cocoa powder. Will Paulo's recipe taste the same as Luiz's? Explain why or why not.

Guiding Questions

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Student Response

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Problem 2

Terrance bikes 3.6 miles to school in 18 minutes. Jacqueline bikes 5.4 miles to school in 30 minutes. Assuming each student rode at a constant speed, who is traveling at a faster speed? 

Guiding Questions

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Student Response

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Problem 3

At the corner market, you can buy jasmine rice by the pound. The table below shows some weights and their corresponding costs.

jasmine rice (lbs.) cost ($)
2 11
10 55
13 ?
? 88

a.   How much does 13 pounds of jasmine rice cost?

b.   How many pounds of jasmine rice can you buy with $88?

Guiding Questions

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Student Response

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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 distance and time traveled for 4 toy cars is shown in the table below.

Car Time (seconds) Distance (meters)
A 4 10
B 6 12
C 9 22.5
D 16 42

Which two cars are traveling at the same constant speed? Show or explain how you determined your answer.

Student Response

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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.

  • Include problems that incorporate a review of 6th grade ratio and rate concepts, using double number lines and tables, and finding unit rate

Next

Represent proportional relationships in tables, and define the constant of proportionality.

Lesson 2
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Lesson Map

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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

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