Understanding and Representing Ratios

Lesson 1

Math

Unit 1

6th Grade

Lesson 1 of 18

Objective


Define ratio and use ratio language to describe associations between two or more quantities.

Common Core Standards


Core Standards

  • 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."

Foundational Standards

  • 4.MD.A.1
  • 4.OA.A.2

Criteria for Success


  1. Define and understand a ratio as a set of numbers that associates two or more quantities.
  2. Use ratio language and notation to compare quantities, including
  • The ratio of __ to __ is __ to __.
  • The ratio of __ to __ is __:__.
  • For every __ __, there are __ __.
  • There are __ __ for every __ __.
  1. Write different ratios for the same situation.

Tips for Teachers


  • The first two lessons in this unit introduce students to the concept of ratios and the language used to describe them. In this lesson students are introduced to different sentence starters that can describe ratios in different ways. They will continue to use and internalize this language throughout the unit.
  • In this first lesson, the focus is on students describing ratios when given objects, diagrams, or a situation. In the next lesson, students will begin to explore how to represent ratios using diagrams.

Lesson Materials

Fishtank Plus

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Anchor Problems


Problem 1

You have the following collection of shapes:

These shapes can be sorted into different groups. For example, you can make a group of squares and a group of circles. We can use ratios to describe how these groups are related; for example, the ratio of squares to circles is 4 to 10, or 4:10.

Sort the shapes into as many different groups as you can think of. For each one, describe the association between the groups using a ratio. 

Guiding Questions

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Problem 2

Some teachers and students are playing games during recess.

  • 16 students play basketball
  • 6 teachers play basketball
  • 8 students jump rope
  • 2 teachers jump rope

After recess, Mr. Hill shares this information with his class. He asks his students to compare the students and teachers playing different games.

Mika said: “Eight more students played basketball than jumped rope.”

Chaska said: “For every student who jumped rope, two students played basketball.”

Mr. Hill said, “Mika compared the students by looking at the difference, and Chaska compared the students using a ratio."

a.   Compare the number of teachers who played basketball and jumped rope using the difference. Write your answer as a sentence as Mika did.

b.   Compare the number of teachers who played basketball and jumped rope using a ratio. Write your answer as a sentence as Chaska did.

c.   Compare the number of students who played basketball to the number of teachers who played basketball using a ratio. Write your answer in two different ways.

Guiding Questions

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References

Illustrative Mathematics Games at Recess

Games at Recess, accessed on July 18, 2017, 1:23 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

Abigail mixed 2 cups of white paint with 6 tablespoons (T) of blue paint.

Write at least four ratio statements to describe the situation. Can you write more than four?

Guiding Questions

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References

Illustrative Mathematics Many Ways to Say It

Many Ways to Say It, accessed on July 18, 2017, 1:55 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.

Student Response

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Problem Set


The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

  • Include a partner activity where each student draws shapes or writes a situation, similar to Anchor Problem 1 or the Target Task, swaps with their partner, and then writes as many ratios for the situation as they can think of. Swap back with partner to read ratios and discuss any discrepancies.

Target Task


Different types of sports balls are shown below.

Write 4 ratio statements to compare the different types of sports balls in the collection.

Student Response

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Lesson 2

Lesson Map

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Topic A: Understanding & Describing Ratios

Topic B: Equivalent Ratios

Topic C: Representing Ratios in Tables

Topic D: Solving Part:Part:Whole Ratio Problems