Understanding and Representing Ratios

Lesson 7

Math

Unit 1

6th Grade

Lesson 7 of 18

Objective


Find equivalent ratios using ratios with “per 1” unit.

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.B — Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?

Foundational Standards

  • 5.NF.B.5
  • 5.NF.B.5.A
  • 5.NF.B.5.B

Criteria for Success


  1. Find an equivalent ratio where one of the values in the ratio is 1.
  2. Use a ratio with “per 1 unit” in order to find more equivalent ratios or to solve ratio problems. 
  3. Choose an efficient strategy to solve a ratio problem (MP.5).

Tips for Teachers


This lesson includes informal understanding of unit rate, which will be studied more thoroughly in unit 2. In this lesson, students see the benefit of finding an equivalent ratio where one of the values in the ratio is 1 in order to find more equivalent ratios or to solve ratio problems. This is especially a useful strategy when a multiplicative relationship between the two ratios is not immediately apparent.

Lesson Materials

  • Calculators (1 per student) — This lesson involves calculations with decimals. Students have worked with decimals in 5th grade, however, in order to keep the emphasis on the ratio reasoning, it is recommended to give students calculators to support their computations throughout this lesson (MP.5).
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Anchor Problems


Problem 1

At the grocery store, 1 pound of grapes costs $3.50. At this rate, how much would 3 pounds cost? 5 pounds?

Guiding Questions

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Problem 2

A turtle can swim 20 meters in 4 seconds. At this rate, how many meters can the turtle swim in 10 seconds?

Guiding Questions

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Problem 3

Kiwis are on sale at the grocery store. You can buy 5 kiwis for $2. At this rate, how much would 72 kiwis cost?

Guiding Questions

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Problem 4

Taivon is training for a running and biking race. The biking part of the race is longer than the running part, so while Taivon trains, he wants to bike more than he runs. He decides that for every 4 miles he runs, he wants to bike 16 miles. How far should Taivon bike if he runs 8 miles? What if he runs for 11 miles? What if he runs for 25 miles?

Guiding Questions

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References

EngageNY Mathematics Grade 6 Mathematics > Module 1 > Topic A > Lesson 8Exercise 3

Grade 6 Mathematics > Module 1 > Topic A > Lesson 8 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 Set

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Target Task


A pizza has 8 slices and sells for $12. At this rate, how much would 15 slices cost? 

Find the price for 1 piece of pizza in your solution.

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 examples of ratio problems where it is efficient to find the ratio “for every 1 something” in order to find further equivalent ratios. Examples could include items and their costs, distance traveled and time, mixing liquids, etc.
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Lesson 6

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Lesson 8

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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