Unit Rates and Percent

Lesson 1

Math

Unit 2

6th Grade

Lesson 1 of 14

Objective


Investigate and use rate in real-world situations.

Common Core Standards


Core Standards

  • 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.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?

Criteria for Success


  1. Recall strategies for solving problems where ratios are present.
  2. Determine that finding a rate or an amount “per 1 unit” is an efficient strategy for solving ratio and rate problems.

Tips for Teachers


  • This lesson is meant to introduce students to the concept of rate through real-world applications and why it can be very useful to consider when solving problems. Students previewed this concept in Unit 1, Lesson 7, when they used an amount “per 1 unit” to find equivalent ratios. Students may solve these problems using a variety of strategies from Unit 1, however, throughout the lesson, guide students towards understanding why using a rate (defined informally) is beneficial and efficient. Rate will be further defined and honed in the lessons that follow.

Lesson Materials

  • Calculators (1 per student) — It is recommended that students use calculators in this lesson since some of the problems involve decimals. Students have experience with calculating with decimals from fifth grade, but they will study them more in depth and with fluency in Unit 3. Calculators will ensure the focus of the lesson is on the concepts and reasoning, rather than calculations (MP.5).
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Anchor Problems


Problem 1

Chichén Itzá was a Mayan city in what is now Mexico. The picture below shows El Castillo, also known as the pyramid of Kukulcán, which is a pyramid located in the ruins of Chichén Itzá.

The temple at the top of the pyramid is approximately 24 meters above the ground, and there are 91 steps leading up to the temple. 

How high above the ground would you be if you were standing on the 50th step? The 33rd step? The 80th step?

Guiding Questions

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References

Illustrative Mathematics Climbing the Steps of El Castillo

Climbing the Steps of El Castillo, accessed on July 25, 2017, 1:46 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

On your way home from school, you stop at the corner store and pick up some eggs and apple juice. However, you don’t need as many eggs or juice cans as come in the package. The cashier lets you buy only part of the package and pay only for what you buy. About how much is your total bill? (Note, the prices shown are for a 6-pack of juice and a dozen eggs, respectively.)

        

Guiding Questions

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References

Dan Meyer Partial Product

Partial Product by Dan Meyer is made available at dy/dan under the CC BY 4.0 license. Accessed July 25, 2017, 1:44 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

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Target Task


Watermelon is on sale for $4 per pound.

a.   How much would 5 pounds cost? 7.5 pounds? 12.8 pounds?

b.   Why do you think grocery stores show the price per 1 pound? How is it useful or efficient when determining the cost of differently sized watermelons?

Student Response

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Lesson 2

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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