Understanding and Representing Ratios

Lesson 9

Math

Unit 1

6th Grade

Lesson 9 of 18

Objective


Use ratio reasoning to solve a three-act task.

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. Make observations and pose questions to an incomplete problem.
  2. Make an educational guess and pose a possible solution pathway.
  3. Make adjustments to a ratio in order to create equivalent ratios.

Tips for Teachers


  • Students have worked with three-act tasks in previous grades of the Fishtank math curriculum; however, as the first one in sixth grade, you may want to establish a culture or process in your classroom around how these are used.
  • Students engage in MP.1 in this three-act task as they analyze the information given to them and determine how they can use equivalent ratios to fix the mixup. They must map out their own strategy and check their answers, making adjustments as needed.
  • Students also discover how they can apply ratio reasoning to support them in understanding the math in the problem and determine a solution (MP.4).
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Anchor Problems


Problem 1

Act 1: Watch the prologue video to the "Nana's Paint Mixup" three-act task.

What do you notice? What do you wonder?

Guiding Questions

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References

101Questions Nana's Paint MixupPrologue and Act 1

Nana's Paint Mixup by Dan Meyer is made available on 101Questions under the CC BY 3.0 license. Accessed July 18, 2017, 4:33 p.m..

Problem 2

Act 2: How can we use equivalent ratios to fix this mix-up? 

Guiding Questions

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References

101Questions Nana's Paint Mixup

Nana's Paint Mixup by Dan Meyer is made available on 101Questions under the CC BY 3.0 license. Accessed July 18, 2017, 4:33 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

Act 3: Watch the video answer

Was your answer reasonable? Why or why not?

Guiding Questions

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References

101Questions Nana's Paint Mixup

Nana's Paint Mixup by Dan Meyer is made available on 101Questions under the CC BY 3.0 license. Accessed July 18, 2017, 4:33 p.m..

Problem 4

Sequel: How many other ways to fix the mix-up can you find?

Guiding Questions

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References

101Questions Nana's Paint Mixup

Nana's Paint Mixup by Dan Meyer is made available on 101Questions under the CC BY 3.0 license. Accessed July 18, 2017, 4:33 p.m..

Problem Set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?

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.

  • Opportunity to review concepts and skills from previous lessons
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Lesson 8

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Lesson 10

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

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