Curriculum / Math / 6th Grade / Unit 1: Understanding and Representing Ratios / Lesson 8
Math
Unit 1
6th Grade
Lesson 8 of 18
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Compare situations using equivalent ratios and double number lines.
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 essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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.
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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.
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.
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?
A set of suggested resources or problem types that teachers can turn into a 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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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? Justify your answer.
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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Use ratio reasoning to solve a three-act task.
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.
Represent ratios using double number lines and identify equivalent ratios.
6.RP.A.3
Solve ratio problems using strategies including double number lines.
Find equivalent ratios using ratios with “per 1” unit.
6.RP.A.36.RP.A.3.B
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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