Curriculum / Math / 6th Grade / Unit 1: Understanding and Representing Ratios / Lesson 15
Math
Unit 1
6th Grade
Lesson 15 of 18
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Solve part:part ratio problems using tape diagrams.
The core standards covered in this lesson
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."
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.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Shanni and Mel are using ribbon to decorate a project in their art class. The ratio of the length of Shanni’s ribbon to the length of Mel’s ribbon is 7:3.
a. Name two possible lengths of Shanni’s and Mel’s ribbons.
b. Draw a tape diagram to represent the ratio of ribbon length.
c. If each block in the tape diagram represented 1 inch, what are the lengths of the ribbons?
d. What if each block in the tape diagram represented 2 yards, what are the lengths of the ribbons?
e. Could Shanni’s ribbon be 21 inches and Mel’s ribbon be 9 yards? Why or why not?
Grade 6 Mathematics > Module 1 > Topic A > Lesson 3 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..
Mason and Laney ran laps to train for the long-distance running team. The ratio of the number of laps Mason ran to the number of laps Laney ran was 2 to 3.
a. If Mason ran 4 miles, how far did Laney run?
b. If Laney ran 930 meters, how far did Mason run?
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Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
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Your school's office manager surveyed the entire sixth grade to find out what transportation students use to get to school. She determined that the ratio of students who took the bus to students who walked to school to students who got a ride was 5:3:2.
If 27 students walked to school, how many students are in the sixth grade? Draw a tape diagram and use it to show your answer.
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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.
Lesson 14
Lesson 16
Topic A: Understanding & Describing Ratios
Define ratio and use ratio language to describe associations between two or more quantities.
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.3 6.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.3 6.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.1 6.RP.A.3 6.RP.A.3.A
Topic D: Solving Part:Part:Whole Ratio Problems
6.RP.A.1 6.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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