Objective
Solve ratio problems using tables, including those involving total amounts.
Common Core Standards
Core Standards
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.
Ratios and Proportional Relationships
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.A— Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
Ratios and Proportional Relationships
6.RP.A.3.A— Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
Foundational Standards
The foundational standards covered in this lesson
5.NF.B.3
Number and Operations—Fractions
5.NF.B.3— Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Criteria for Success
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Add a total column to tables of equivalent ratios when a total of like units is involved in the problem and is valuable to consider.
- Write ratios that represent part to total associations.
- Given a ratio of a:b, in like units, reason about the ratio of a units to total units, b units to total units, and the fractional amounts of the total that represent a and b. For example, “For every vote candidate A received, candidate C received nearly three votes,” meaning that candidate C received 3 out of every 4 votes, or$$\frac{3}{4}$$of all votes.”
Tips for Teachers
Suggestions for teachers to help them teach this lesson
In this lesson, students look at ratio problems that involve total amounts of the same unit and solve these by adding a total column to a table of equivalent ratios. In Lessons 15 and 16, students will look more closely at part-to-part and part-to-whole problems, and will learn how to use tape diagrams as a strategy to solve them.
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Anchor Problems
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Problem 1
Jessica gets her favorite shade of purple paint by mixing 2 cups of blue paint with 3 cups of red paint. How many cups of blue and red paint does Jessica need to make 20 cups of her favorite purple paint?
Complete the table of equivalent ratios below to answer the question.
| Blue paint (cups) | Red paint (cups) | Purple paint (cups) |
Guiding Questions
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References
Illustrative Mathematics Perfect Purple Paint 1
Perfect Purple Paint 1, accessed on July 19, 2017, 10:33 a.m., is licensed by Illustrative Mathematics under either theCC BY 4.0orCC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Modified by Fishtank Learning, Inc.
Problem 2
Michaela and Lucas both ran for class treasurer at their middle school. The ratio of votes for Michaela to votes for Lucas was 3:1.
Determine if each statement below is true or false.
a.For every 5 votes Lucas got, Michaela got 10 votes.
b.Michaela got 3 out of every 4 votes.
c.Lucas got 1 out of every 3 votes.
d.Lucas got$$\frac{1}{4}$$of all the votes.
e.Out of 32 votes, Michaela got 24.
Guiding Questions
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Problem Set
A set of suggested resources or problem types that teachers can turn into a problem set
Fishtank Plus Content
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
Target Task
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Josie is a new employee at Smoothie King. During training, she learns that to make the Classic King smoothie, she needs to blend a liquid strawberry mix and yogurt in a ratio of 2 cups of strawberry mix to 3 cups of yogurt. Josie gets a large order and needs to make 35 cups of the Classic King smoothie. How much of each ingredient does she need to use?
Complete the table below to support your answer.
Strawberry Mix (cups) | Yogurt (cups) | Smoothie (cups) |
Student Response
An example response to the Target Task at the level of detail expected of the students.
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Additional Practice
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.
- Include problems where students are given a ratio associating two quantities in the same unit and must reason about an equivalent ratio when given a total amount. Have students use tables of equivalent ratios with a total column as a strategy to solve.
- Illustrative Mathematics Mixing Concrete
- Illustrative Mathematics Voting for Two, Variation 2
- Illustrative Mathematics Voting for Two, Variation 1
Lesson 11
Lesson 13
