Understanding and Representing Ratios

Lesson 8

Math

Unit 1

6th Grade

Lesson 8 of 18

Objective


Compare situations using equivalent ratios and double number lines.

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.

Criteria for Success


  1. Use strategies to reason about two situations involving ratios.
  2. Look for common values in double number lines in order to reason about two situations (MP.7).
  3. Compare situations by rewriting ratios so that one pair of corresponding values are the same and reasoning about the other pair of values.

Tips for Teachers


In the next unit, students will study unit rate and use it to compare situations. In this lesson, students reason about two situations by applying equivalent ratios on double number lines. By writing ratios where one of the pairs of corresponding values are the same, they are able to reason about the situation by looking at the other pair of values. For example, if one person is moving 5 feet in 2 seconds and another person is moving 5 feet in 3 seconds, you can reason that the first person is moving faster. In Lesson 13, students will revisit this topic but use tables to compare ratios.

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Anchor Problems


Problem 1

At the store, you see oranges on sale at 1 pound for $3. At a different store, your brother sees oranges on sale at 3 pounds for $8. 

Do the oranges cost the same at both stores? Which store offers the better deal? Justify your answer.

Guiding Questions

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Problem 2

Callie biked 12 miles in 3 hours. Carter biked 10 miles in 2 hours.

Represent each person's trip with a double number line. Explain how you can see that they are not going the same speed.

Guiding Questions

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References

Illustrative Mathematics Constant Speed

Constant Speed, accessed on July 18, 2017, 4:20 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.

Modified by Fishtank Learning, Inc.

Problem 3

Density is the relationship between the mass of an object and its volume, or amount of space it takes up. A scientist finds a rock and determines its mass to be 18 grams and its volume to be 4 cm$$^{3}$$. Another rock is found with a mass of 63 grams and a volume of 14 cm$$^{3}$$

Draw two double number lines to compare the two rocks. Do the rocks have equivalent ratios of mass and volume? Do they have the same density?

Guiding Questions

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Problem Set

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Target Task


Samira is applying for an internship at the county clerk’s office. The application says that candidates must be able to type 150 words in 5 minutes. Samira knows that she can type 120 words in 3 minutes. Does Samira meet the expectation for the application? 

Draw a double number line and use it to justify 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 examples where students compare two different situations using double number lines, equivalent ratios, “for every 1,” or other strategies that they have learned so far. Situations could include:
    • Comparing speeds of people, animals, vehicles, etc.
    • Comparing prices of foods, tickets, etc.
    • Comparing flavors in recipes or shade of colors 
    • Comparing density ratios of mass and volume
  • Inside Mathematics Performance Assessment Tasks Grades 3-High School Snail Pace
  • MARS Formative Assessment Lessons for Grade 6 Using Proportional ReasoningUse the Mixing Drinks task and optional matching cards to order the given ratios by level of orange taste. This is also available on Illustrative Mathematics under “Fizzy Juice."
  • SERP Poster Problems The Intensity of Chocolate MilkThis lesson goes into topics that have not been covered yet; however, the video of the two different chocolate milks is a good application to use for this lesson.
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Lesson 7

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Lesson 9

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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