Curriculum / Math / 6th Grade / Unit 1: Understanding and Representing Ratios / Lesson 5
Math
Unit 1
6th Grade
Lesson 5 of 18
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Represent ratios using double number lines and identify equivalent ratios.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
5.NF.B.5 — Interpret multiplication as scaling (resizing), by:
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
A Puerto Rican restaurant specializes in making arroz con gandules, or rice with pigeon peas. Chicken broth and rice are two of the main ingredients used in this dish. For one batch, the restaurant uses a ratio of 3 cups of broth to 2 cups of rice.
a. How much broth and rice will the restaurant use to make 2 batches of this dish? To make 3 batches? Show your reasoning using a visual representation of your choice.
b. On a busy Saturday, the restaurant uses 36 cups of broth for arroz con gandules. How much rice does the restaurant use for this dish, and how many batches is this? Show your reasoning using a visual representation of your choice.
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Arianna is making origami swans for her friend's birthday party. She wants to make 9 swans, one for each party guest. If Arianna takes 15 minutes to make each swan, will she be able to make 9 swans in 2 hours? Explain.
Party Planning, accessed on July 18, 2017, 3:49 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.
To make green-colored water, Brian mixes drops of green food dye and cups of water in a ratio of 4:3.
a. Draw a double number line to represent the ratio of drops of green food dye to cups of water.
b. Use your double number line to find 2 equivalent ratios.
c. Brian’s friend, Evan, uses a ratio of 20 drops of green food dye to 15 cups of water. Will Evan’s water be the same color green as Brian’s? Explain your reasoning.
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15-20 minutes
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5-10 minutes
The ratio of boys to girls in a sixth-grade class is 3:5.
a. Draw a double number line to represent this ratio.
b. If there were 15 girls in the class, how many boys were in the class? Explain or show your reasoning.
c. Does the ratio of 18 boys to 30 girls represent an equivalent ratio to this sixth-grade class? Explain or show your reasoning.
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.
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Solve ratio problems using strategies including double number lines.
Topic A: Understanding & Describing Ratios
Define ratio and use ratio language to describe associations between two or more quantities.
Standards
6.RP.A.1
Represent ratios using discrete drawings. Understand that the order of numbers in a ratio matters.
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Topic B: Equivalent Ratios
Define and find equivalent ratios.
Reason with equivalent ratios and determine if two ratios are equivalent.
6.RP.A.3
Find equivalent ratios using ratios with “per 1” unit.
6.RP.A.36.RP.A.3.B
Compare situations using equivalent ratios and double number lines.
Use ratio reasoning to solve a three-act task.
Topic C: Representing Ratios in Tables
Represent ratios in tables.
6.RP.A.36.RP.A.3.A
Understand the structure of tables of equivalent ratios. Solve ratio problems using tables.
Solve ratio problems using tables, including those involving total amounts.
Compare ratios using tables.
6.RP.A.3.A
Solve ratio problems using different strategies.
6.RP.A.16.RP.A.36.RP.A.3.A
Topic D: Solving Part:Part:Whole Ratio Problems
Solve part:part ratio problems using tape diagrams.
6.RP.A.16.RP.A.3
Solve part:whole ratio problems using tape diagrams.
Solve more complex ratio problems using tape diagrams.
Solve ratio problems using a variety of strategies, including reasoning about diagrams, double number lines, tables, and tape diagrams. Summarize strategies for solving ratio problems.
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