Unit Rates and Percent

Lesson 2

Math

Unit 2

6th Grade

Lesson 2 of 14

Objective


Define rate and unit rate, and find rates from situations involving ratios. 

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. Define and understand a rate, associated with a ratio a:b, as a/b units of the first quantity per 1 unit of the second quantity. For example, if a person walks 6 miles in 2 hours, the person is traveling at a rate of 3 miles per hour. 
  2. Define and understand a unit rate as the numerical part of a rate. For example, in the rate of 3 miles per hour, the 3 represents the unit rate. 
  3. Identify the two unit rates for a ratio a:b as a/b and b/a.
  4. Know that equivalent ratios have the same unit rates, and that the unit rate represents the multiplicative factor across columns in a ratio table.

Tips for Teachers


Lesson Materials

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


Problem 1

Hugh drove on the highway at a constant rate. He traveled 204 miles in 3 hours. How far did Hugh travel in 1 hour? At what rate was he traveling? 

Guiding Questions

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Problem 2

Hippos sometimes get to eat pumpkins as a special treat.

a.   If 3 hippos eat 5 pumpkins, how many pumpkins per hippo is that?

b.   If there are 9 hippos, how many pumpkins do you need?

c.   If 3 hippos eat 5 pumpkins, how many hippos per pumpkin is that?

d.   If you have 30 pumpkins, how many hippos can you feed?

Guiding Questions

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References

Illustrative Mathematics Hippos Love Pumpkins

Hippos Love Pumpkins, accessed on July 25, 2017, 1:30 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

A florist sells a bundle of 12 sunflowers for $9. You can also buy single sunflowers at the same rate. Fill in the table below.

Number of sunflowers Cost ($) Unit rate ($ per sunflower)
2    
4    
6    
8    
10    
12    

Do equivalent ratios have the same unit rate? Explain how you know.

Guiding Questions

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Problem Set

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Target Task


A candy store sells small pieces of candy, 12 pieces for $4.

a.   How many pieces can you buy per dollar?

b.   What is the cost per piece of candy?

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.

  • Include problems where students are given a ratio of two quantities and determine a rate (or both rates). For example, 3 pounds of long-grain rice costs $13.50. What is the rate in dollars per pound? What is the rate in pounds per dollar? 
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Lesson 1

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Lesson 3

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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