Linear Relationships

Lesson 4

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Objective

Compare proportional relationships represented in different ways.

Common Core Standards

Core Standards

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  • 8.EE.B.5 — Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Foundational Standards

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  • 7.RP.A.2

Criteria for Success

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  1. Compare graphs of proportional relationships to other situations represented as tables, equations, and verbal descriptions.
  2. Determine the rate of change or unit rate in equations, tables, and verbal descriptions. 
  3. Solve problems using proportional reasoning.

Tips for Teachers

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Lessons 3 and 4 address comparing proportional relationships. In this lesson, students compare across multiple forms of proportional relationships as they consider various applications. 

Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Choose two Anchor Problems (all benefit from worked examples). Find more guidance on adapting our math curriculum for remote learning here.

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Anchor Problems

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Problem 1

At a factory, a machine fills jars with salsa. The manager of the factory is considering buying a new machine that will fill 78 jars of salsa every 3 minutes. To support his decision, he wants to compare the rate of the new machine to the rate of the old machine that is currently in the factory.

The graph below shows the number of jars of salsa filled over time with the old machine.

The manager is about to fill an order of 765 jars of salsa. How long would it take to fill this order on each machine? Should the manager consider replacing the old machine with the new one? Explain.

Guiding Questions

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Problem 2

Kristina and her sister, Tracee, are painting rooms in their house. The graph below represents the rate at which Kristina paints, and the table below shows how many square feet Tracee painted for given amounts of time. Both sisters paint at a constant pace.

Who paints at the faster rate? Justify your answer.

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References

EngageNY Mathematics Grade 8 Mathematics > Module 4 > Topic C > Lesson 22Example 4

Grade 8 Mathematics > Module 4 > Topic C > Lesson 22 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..

Modified by Fishtank Learning, Inc.

Problem 3

The corner market sells rice by the pound using the equation $${y=1.25x}$$, where $$y$$ represents the total cost for $$x$$ number of pounds. 

The local grocery store also sells rice by the pound. The relationship between cost and weight at the grocery story is shown in the graph below.


Which store offers a better deal on rice? Explain your answer. 

Guiding Questions

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Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

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A kitchen sink has a maximum water flow of 11 gallons in 5 minutes. The maximum water flow for a bathroom sink is shown below in the graph.

a.   Write an equation to represent the maximum water in gallons, y, from the kitchen sink after x minutes.

b.   Which sink, the kitchen or bathroom, has a greater maximum water flow? Justify your reasoning.

Mastery Response

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