Curriculum  /  Math  /  6th Grade  /  Unit 1: Understanding and Representing Ratios  /  Lesson 11

Understanding and Representing Ratios

Lesson 11

Math

Unit 1

6th Grade

Lesson 11 of 18

Objective

Understand the structure of tables of equivalent ratios. Solve ratio problems using tables.

Common Core Standards

Core Standards

  • 6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • 6.RP.A.3.A — Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Foundational Standards

  • 5.NF.B.5
  • 5.NF.B.5.A
  • 5.NF.B.5.B
  • 5.OA.B.3

Criteria for Success

  1. Identify the relationship between rows in a table of equivalent ratios, and use it to solve ratio problems.
  2. Identify the relationship across rows in a table of equivalent ratios and, use it to solve ratio problems. 
  3. Efficiently use a table of equivalent ratios as a tool to solve ratio problems, especially where an intermediary equivalent ratio is helpful.

Tips for Teachers

Students analyze the structure of tables of equivalent ratios to understand how they can use them in multiple ways to represent ratios and solve ratio problems (MP.7).

Fishtank Plus

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

Anchor Problems

25-30 minutes

Problem 1

The table below represents the ratio of pints of blue paint to pints of yellow paint to make a shade of green paint. Use the table to answer the questions that follow. 

Blue paint (pints) Yellow paint (pints)
3 12
6 24
7 ?
12 48
21 84
? 120

a.   Show that the ratio 3:12 is equivalent to the ratio of 6:24.

b.   Explain how you can use the relationship between rows to find the number of pints of blue paint to mix with 120 pints of yellow paint.

c.   Explain how you can use the relationship across each row to find the number of pints of yellow paint to mix with 7 pints of blue paint.

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

Gianna is paid $90 for 5 hours of work. Use and complete the table of equivalent ratios shown below to answer the following questions.

Hours worked $ earned
5 90
8  
  60
   
   

a.   At this rate, how much would Gianna make for 8 hours of work?

b.   At this rate, how long would Gianna have to work to make $60? 

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.

References

Illustrative Mathematics Gianna’s Job

Gianna’s Job, accessed on July 19, 2017, 10:23 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

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

Steven waters the outdoor plants for his apartment complex. He determines that 75 gallons of water flows out of the hose in the 15 minutes he spends watering the plants. To cut down on water usage, he wants to reduce the time he spends watering the plants to 9 minutes. Steven wants to know how many gallons of water he’ll use in 9 minutes. To answer his question, he creates the following table of equivalent ratios.

Water (gallons) Time (minutes)
75 15
15 3
45 9

a.   Explain how Steven used the table to answer his question. What is his answer?

b.   Show a different way that Steven could have completed a table of equivalent ratios to answer his question.

Water (gallons) Time (minutes)
   
   
   

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.

  • Include problems similar to Lesson 7, where a multiplier is not easily seen to find a missing value and it would be efficient to find an equivalent ratio as an intermediary step. Have students use tables to organize their work.
  • Give examples of tables of equivalent ratios and ask students to describe/show the relationships they see in the tables. 
  • Include examples where tables of equivalent ratios are shown horizontally to familiarize students with another orientation. 

Next

Solve ratio problems using tables, including those involving total amounts.

Lesson 12
icon/arrow/right/large

Lesson Map

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

Topic A: Understanding & Describing Ratios

Topic B: Equivalent Ratios

Topic C: Representing Ratios in Tables

Topic D: Solving Part:Part:Whole Ratio Problems

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