Unit Rates and Percent

Lesson 3

Math

Unit 2

6th Grade

Lesson 3 of 14

Objective


Find unit rates and use them to solve problems.

Common Core Standards


Core Standards

  • 6.RP.A.2 — Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. Expectations for unit rates in this grade are limited to non-complex fractions. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."
  • 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?

Foundational Standards

  • 5.NF.B.3
  • 6.RP.A.1

Criteria for Success


  1. Identify the two unit rates for a ratio a:b as a/b and b/a.
  2. Determine which unit rate is best to use to solve problems, depending on the information given and the question being asked. 
  3. Multiply by the unit rate in order to solve problems.

Tips for Teachers


Lesson Materials

  • Calculators (1 per student) — See note from lesson 1.
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Anchor Problems


Problem 1

The grocery store sells beans in bulk. The grocer's sign above the beans says, “5 pounds for $4.”

At this store, you can buy any number of pounds of beans at this same rate, and all prices include tax.

  • Alberto said, “The ratio of the number of dollars to the number of pounds is 4:5. That's $0.80 per pound.”
  • Beth said, "The sign says the ratio of the number of pounds to the number of dollars is 5:4. That's 1.25 pounds per dollar."

Are Alberto and Beth both correct? Explain.

Guiding Questions

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References

Illustrative Mathematics Price per Pound and Pounds per Dollar

Price per Pound and Pounds per Dollar, accessed on July 25, 2017, 1:24 p.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.

Modified by Fishtank Learning, Inc.

Problem 2

Claude and Dora go shopping at the same grocery store as Alberto and Beth. 

  • Claude needs two pounds of beans to make soup. Show Claude how much money he will need.
  • Dora has $10 and wants to stock up on beans. Show Dora how many pounds of beans she can buy.

Whose rate of change, Alberto’s or Beth’s, do you prefer to use to solve Claude’s problem? Dora’s problem? Explain.

Guiding Questions

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References

Illustrative Mathematics Price per Pound and Pounds per Dollar

Price per Pound and Pounds per Dollar, accessed on July 25, 2017, 1:24 p.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.

Modified by Fishtank Learning, Inc.

Problem 3

Sanyukta can type 2 pages in 8 minutes. 

a.   What are two rates associated with this ratio?

b.   Sanyukta has a deadline in 22 minutes, at which point she needs to be done typing an article. What is the greatest number of pages that Sanyukta can type before her deadline?

c.   Sanyukta has to type a 9-page article. How much time will it take her?

Guiding Questions

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Problem 4

Solve each problem involving distance, speed, and time.

a.   Melanie drives at a constant speed of 35 miles per hour. How far does she travel in 2 hours?

b.   Nathan drives at a constant speed of 40 miles per hour. How long it take him to travel 60 miles?

c.   Oscar drives at a constant speed of 50 miles per hour. How far does he travel in 90 minutes?

d.   Penelope travels 14 miles in 30 minutes. At what constant speed is she driving?

Guiding Questions

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Problem Set

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Target Task


You are shoveling snow from the sidewalks around your neighborhood after a big snowstorm. You work at a steady rate, shoveling 10 feet of sidewalk in 40 minutes.

a.   At this rate, how long will it take you to shovel 75 feet of sidewalk?

b.   At this rate, how many feet of sidewalk will you have shoveled after 2 hours?

Student Response

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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.

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Lesson 2

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Lesson 4

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Defining Rate & Solving Rate Problems

Topic B: Measurement Unit Conversions

Topic C: Percent

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