Curriculum / Math / 6th Grade / Unit 1: Understanding and Representing Ratios / Lesson 17
Math
Unit 1
6th Grade
Lesson 17 of 18
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Solve more complex ratio problems using tape diagrams.
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
Students encounter more challenging real-world problems in this lesson providing them with the opportunity to apply their ratio reasoning and strategies to model and solve the problems (MP.4). Tape diagrams are an effective tool to use to solve these problems, however, students may also use other strategies of their choice.
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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 a concert, the ratio of the number of people who are local to people who are from out of town is 2:7. If there are 250 more people from out of town than people who are local, how many local people are at the concert?
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The Business Direct Hotel serves people who travel for business. On a Saturday night, not many people are traveling, so the ratio of the number of busy rooms to open rooms is 2:5. However, on Sunday night, a lot of people arrive for a conference. The ratio of the number of busy rooms to open rooms is 6:1.
If the Business Direct Hotel has 432 busy rooms on Sunday night, how many open rooms does it have on Saturday night?
Grade 6 Mathematics > Module 1 > Topic A > Lesson 6 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..
You made green paint by mixing yellow and blue paint in a ratio of 5 to 3. You then added an additional 14 liters of blue paint, and the amount of yellow paint and blue paint in the mixture was equal. How much green paint total was in the mixture at first, before adding the extra blue paint?
Draft 6-7 Progression on Ratios and Proportional Relationships, by the Common Core Standards Writing Team is made available by Institute for Mathematics and Education, University of Arizona. © 2007 The Arizona Board of Regents. All contents copyrighted. All rights reserved. Accessed Sept. 11, 2017, 10:53 a.m.. For updates and more information about the Progressions, see http://ime.math.arizona.edu/progressions.
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 tee-shirt store sells long sleeve (LS) and short sleeve (SS) tee-shirts. In the fall, they stock 4 LS tee-shirts for every 3 SS tee-shirts. In the spring, they stock only 2 LS tee-shirts for every 5 SS tee-shirts.
If the store stocks the same number of tee-shirts in the fall and in the spring, and there are 105 SS tee-shirts in the fall, how many SS tee-shirts does the store stock in the spring?
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 a variety of strategies, including reasoning about diagrams, double number lines, tables, and tape diagrams. Summarize strategies for solving ratio problems.
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
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.
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