Curriculum / Math / 6th Grade / Unit 1: Understanding and Representing Ratios / Lesson 7
Math
Unit 1
6th Grade
Lesson 7 of 18
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Lesson Notes
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Find equivalent ratios using ratios with “per 1” unit.
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.
6.RP.A.3.B — Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?
The foundational standards covered in this lesson
5.NF.B.5 — Interpret multiplication as scaling (resizing), by:
5.NF.B.5.A — Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
5.NF.B.5.B — Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson includes informal understanding of unit rate, which will be studied more thoroughly in unit 2. In this lesson, students see the benefit of finding an equivalent ratio where one of the values in the ratio is 1 in order to find more equivalent ratios or to solve ratio problems. This is especially a useful strategy when a multiplicative relationship between the two ratios is not immediately apparent.
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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 grocery store, 1 pound of grapes costs $3.50. At this rate, how much would 3 pounds cost? 5 pounds?
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A turtle can swim 20 meters in 4 seconds. At this rate, how many meters can the turtle swim in 10 seconds?
Kiwis are on sale at the grocery store. You can buy 5 kiwis for $2. At this rate, how much would 72 kiwis cost?
Taivon is training for a running and biking race. The biking part of the race is longer than the running part, so while Taivon trains, he wants to bike more than he runs. He decides that for every 4 miles he runs, he wants to bike 16 miles. How far should Taivon bike if he runs 8 miles? What if he runs for 11 miles? What if he runs for 25 miles?
Grade 6 Mathematics > Module 1 > Topic A > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
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
A pizza has 8 slices and sells for $12. At this rate, how much would 15 slices cost?
Find the price for 1 piece of pizza in your solution.
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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Compare situations using equivalent ratios and 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.
Represent ratios using double number lines and identify equivalent ratios.
6.RP.A.3
Solve ratio problems using strategies including double number lines.
6.RP.A.36.RP.A.3.B
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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