Curriculum  /  Math  /  6th Grade  /  Unit 1: Understanding and Representing Ratios  /  Lesson 10

Understanding and Representing Ratios

Lesson 10

Math

Unit 1

6th Grade

Lesson 10 of 18

Objective

Represent ratios in 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. Understand how tables of equivalent ratios are similar to and different from other ratio representations (diagrams, double number lines).
  2. Create tables for ratios and include equivalent ratios.
  3. Identify equivalent ratios in tables.
  4. Fill in missing values in tables of equivalent ratios.
  5. Understand the multiplicative relationship between rows of equivalent ratios in a table.
  6. Decontextualize a problem to represent in a table and recontextualize a table to understand a situation (MP.2).

Tips for Teachers

Lessons 10 and 11 introduce students to using tables to represent equivalent ratios and solve problems. Students began this unit using discrete diagrams and pictures as representations. They then progressed to using double number lines, which allowed them to model with greater values. While tables provide greater flexibility than diagrams and double number lines, they are more abstract and can be difficult to interpret. If students struggle with understanding the relationships seen in tables, spiral back to double number lines and diagrams and make the connection between how ratios are seen in all three representations. 

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Anchor Problems

25-30 minutes

Problem 1

To make paper mâché paste, the art teacher mixes water and flour. For every 2 cups of water, she needs to mix in 3 cups of flour to make one batch of the paste. She wants to know how many cups of water she should use for 3 batches of the paste.

a.   Draw a diagram to determine how much water the teacher needs for 3 batches of the paste.

b.   Draw a double number line to represent the ratio, and use it to help the teacher answer her question.

c.   The art teacher has been asked to make paste for two middle schools. She determines that she will need to use about 120 cups of flour to have enough paste for both schools. How many cups of water will she need?

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 6 Mathematics > Module 1 > Topic B > Lesson 9 — Example 1

Grade 6 Mathematics > Module 1 > Topic B > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 2

The diagram below shows the relationship between orange juice and soda water in an orange soda. 

a.   Name two similarities between the double number line and the table.

b.   Name two differences between the double number line and the table.

c.   How much soda water would you need to mix with 44 liters of orange juice? Which representation did you use?

Guiding Questions

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Student Response

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References

Open Up Resources Grade 6 Unit 2 Lesson 11 — Activity 11.2: A Huge Amount of Sparkling Orange Juice

Grade 6 Unit 2 Lesson 11 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed Jan. 18, 2019, 11:30 a.m..

Modified by Fishtank Learning, Inc.

Problem 3

A cleaning solution can be made by mixing bleach and water. The ratio table below has some missing information. Fill in the blanks.

Bleach (tablespoons) Water (gallons)
3 4
6  
  20
9  
  2
90  
  32

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

A florist shop is preparing bundles of flowers to sell over the weekend. In a bundle of flowers, the shop uses 3 roses for every 4 carnations. Create a table of equivalent ratios to represent the relationship between roses and carnations in the bundles of flowers.

   
   
   
   
   
   
   

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 where students represent ratios in double number lines and tables to see the connection between the two representations.
  • Include problems where students complete a table with missing information; include tables with rows “out of order.”
  • Include error analysis problems where students determine errors made in tables of equivalent ratios.

Next

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

Lesson 11
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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

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