Understanding and Representing Ratios

Lesson 2

Math

Unit 1

6th Grade

Lesson 2 of 18

Objective


Represent ratios using discrete drawings. Understand that the order of numbers in a ratio matters.

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."

Criteria for Success


  1. Represent ratios with discrete drawings that show the association between the two quantities.
  2. Use drawings of ratios as a tool to better understand how two quantities are associated with each other (MP.1).
  3. Understand that the order of the values in a ratio relates directly to the order of the objects described. 
  4. Describe ratios using precise language, paying attention to the order of the values and their corresponding units (MP.6).

Tips for Teachers


  • Throughout this unit, students will learn and use several representations for ratios in a natural progression. In this lesson, they learn to draw discrete diagrams. These diagrams are introduced as an early representation because they are the least abstract compared to tables and equations, which they will learn later. In diagrams, each object is represented individually, and the associations can be seen by counting. 
  • When drawing diagrams, students do not need to draw the actual item described but rather a simple symbol that can represent the quantity at hand. For example, students can use a box to represent a cup of liquid that is labeled as such.
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Anchor Problems

25-30 minutes


Problem 1

In a recipe for oatmeal raisin cookies, the ratio of teaspoons of cinnamon to cups of raisins is 4:8. 

Draw a diagram to represent the quantities, and write two other ratio statements for the situation.

Guiding Questions

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Student Response

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Problem 2

Maria is mixing lemon juice with water to make lemonade, but she can’t remember the ratio of the two ingredients. She writes down four ratios:

  1. The ratio of cups of lemon juice to cups of water is 5:1.
  2. The ratio of cups of water to cups of lemon juice is 5:1.
  3. The ratio of cups of lemon juice to cups of water is 1:5.
  4. The ratio of cups of water to cups of lemon juice is 1:5.

Draw a diagram to represent each ratio. If Maria used the ratios described, which lemonades would taste the same? Which ones would taste differently? Which ratio(s) should she use to make her lemonade?

Guiding Questions

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Student Response

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Problem 3

Students in art class are drawing flowers and making connections to ratios they are learning about in math class.

Terry describes his flower and says, “The ratio of petals to leaves to stems is 2:6:1.”

Draw a picture of what Terry’s flower could look like based on the ratio he described. Does Terry’s ratio seem accurate? If not, then describe any changes Terry might make.

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


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

Target Task

5-10 minutes


A recipe calls for 2 cups of tomato sauce and 3 tablespoons of oil. We can say that the ratio of cups of tomato sauce to tablespoons of oil in the recipe is 2:3, or we can say the ratio of tablespoons of oil to cups of tomato sauce is 3:2.

For each of the following situations, draw a picture and name two ratios that represent the situation.

a.   To make papier-mâché paste, mix 2 parts of water with 1 part of flour.

b.   A farm is selling 3 pounds of peaches for $5.

c.   A person walks 6 miles in 2 hours.

Student Response

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References

Illustrative Mathematics Representing a Context with a Ratio

Representing a Context with a Ratio, accessed on July 18, 2017, 2:59 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.

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 error analysis problems where the order of the values in a ratio is incorrect and students must critique a response.

Next

Define and find equivalent ratios.

Lesson 3
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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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