Curriculum / Math / 6th Grade / Unit 1: Understanding and Representing Ratios / Lesson 4
Math
Unit 1
6th Grade
Lesson 4 of 18
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Reason with equivalent ratios and determine if two ratios are equivalent.
The core standards covered in this lesson
6.RP.A.1 — Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, "The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak." "For every vote candidate A received, candidate C received nearly three votes."
The foundational standards covered in this lesson
5.NF.B.5 — Interpret multiplication as scaling (resizing), by:
5.NF.B.5.A — Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.B.5.B — Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This is the second of two lessons that introduce equivalent ratios. Students should continue to understand the definition of equivalent ratios and use it in context to determine and/or find equivalent ratios. Diagrams can be used to support understanding where applicable, but students should also see the multiplicative relationship between two ratios, as described in the definition.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
In a marching band there are 24 trombones and 15 snare drums.
Heather says, “The ratio of trombones to snare drums is 24:15.” Audrey says, “No, the ratio of trombones to snare drums is 8:5.” Who is right and why?
Equivalent Ratios 2, accessed on July 18, 2017, 3:35 p.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.
You are making a mixed bag of walnuts and cashews. The ratio of the number of walnuts to the number of cashews you want to use is 5:6. You have 54 cashews to include in the mix. How many walnuts should you add? Justify your answer by showing that the new ratio you created of the number of walnuts to cashews is equivalent to 5:6.
Grade 6 Mathematics > Module 1 > Topic A > Lesson 4 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..
Which of the ratios in the list below are equivalent to the ratio 12:8? Explain or show how you know each ratio is equivalent.
a. 8:12
b. 3:2
c. 2:3
d. 24:16
e. 6:4
f. 6:2
g. 15:10
h. 20:16
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A store sells water bottles in large and small sizes. There are 24 large water bottles and 18 small water bottles on display in the store. The manager of the store wants there to be 3 large water bottles on display for every 2 small water bottles. Should the manager make any changes to the current display? Explain.
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Lesson 3
Lesson 5
Topic A: Understanding & Describing Ratios
Define ratio and use ratio language to describe associations between two or more quantities.
6.RP.A.1
Represent ratios using discrete drawings. Understand that the order of numbers in a ratio matters.
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Topic B: Equivalent Ratios
Define and find equivalent ratios.
Represent ratios using double number lines and identify equivalent ratios.
6.RP.A.3
Solve ratio problems using strategies including double number lines.
Find equivalent ratios using ratios with “per 1” unit.
6.RP.A.3 6.RP.A.3.B
Compare situations using equivalent ratios and double number lines.
Use ratio reasoning to solve a three-act task.
Topic C: Representing Ratios in Tables
Represent ratios in tables.
6.RP.A.3 6.RP.A.3.A
Understand the structure of tables of equivalent ratios. Solve ratio problems using tables.
Solve ratio problems using tables, including those involving total amounts.
Compare ratios using tables.
6.RP.A.3.A
Solve ratio problems using different strategies.
6.RP.A.1 6.RP.A.3 6.RP.A.3.A
Topic D: Solving Part:Part:Whole Ratio Problems
Solve part:part ratio problems using tape diagrams.
6.RP.A.1 6.RP.A.3
Solve part:whole ratio problems using tape diagrams.
Solve more complex ratio problems using tape diagrams.
Solve ratio problems using a variety of strategies, including reasoning about diagrams, double number lines, tables, and tape diagrams. Summarize strategies for solving ratio problems.
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