Curriculum / Math / 6th Grade / Unit 1: Understanding and Representing Ratios / Lesson 16
Math
Unit 1
6th Grade
Lesson 16 of 18
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Solve part:whole 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.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Review and recall from Lesson 12 how students used tables of equivalent ratios to solve problems involving a total or whole amount. Introduce tape diagrams as another method to solve these problems.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Sammy and David were selling water bottles to raise money for new soccer uniforms. Sammy sold 5 water bottles for every 3 water bottles David sold. Together they sold 160 water bottles. How many did each person sell? Draw a tape diagram and use it to show your answer.
Grade 6 Mathematics > Module 1 > Topic A > Lesson 5 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..
The ratio of the number of boys to the number of girls at school is 4:5. There are 270 students at this school. For each of the following statements, explain whether the statement is true or false and why:
a. The number of boys at school is $$\frac{4}{5}$$ the number of girls.
b. $$\frac{4}{5}$$ of the students in the school are boys.
c. There are exactly 30 more girls than boys.
d. There are exactly 30 boys at the school.
e. $$\frac{5}{9}$$ of the students in the school are girls.
Evaluating Ratio Statements, accessed on July 19, 2017, 11:42 a.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.
A set of suggested resources or problem types that teachers can turn into a problem set
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
In a jigsaw puzzle, there are edge or corner pieces that have at least one straight edge, as well as inside pieces that have no straight edges. The ratio of edge/corner pieces to inside pieces is 3 to 5. If the puzzle has 96 pieces, how many are inside pieces?
An example response to the Target Task at the level of detail expected of the students.
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 15
Lesson 17
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
Solve part:part ratio problems using tape diagrams.
6.RP.A.1 6.RP.A.3
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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