Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 4
Math
Unit 5
8th Grade
Lesson 4 of 15
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Lesson Notes
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Compare proportional relationships represented in different ways.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
Lessons 3 and 4 address comparing proportional relationships. In this lesson, students compare across multiple forms of proportional relationships as they consider various applications.Â
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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.
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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.
Tracee's Painting
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..
The corner market sells rice by the pound using the equation $${y=1.25x}$$, where $$y$$ represents the total cost for $$x$$ 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.
A set of suggested resources or problem types that teachers can turn into a problem set
15-20 minutes
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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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Graph a linear equation using a table of values.
Topic A: Comparing Proportional Relationships
Review representations of proportional relationships.
Standards
8.EE.B.5
Graph proportional relationships and interpret slope as the unit rate.
Compare proportional relationships represented as graphs.
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Topic B: Slope and Graphing Linear Equations
8.F.B.4
Define slope and determine slope from graphs.
8.EE.B.6
Determine slope from coordinate points. Find slope of horizontal and vertical lines.
8.EE.B.68.F.B.4
Graph linear equations using slope-intercept form $${y = mx + b}$$.
8.EE.B.68.F.A.3
Write equations into slope-intercept form in order to graph. Graph vertical and horizontal lines.
Topic C: Writing Linear Equations
Write linear equations from graphs in the coordinate plane.
Write linear equations using slope and a given point on the line.
Write linear equations using two given points on the line.
Write linear equations for parallel and perpendicular lines.
Compare linear functions represented in different ways.
8.F.A.28.F.B.4
Model real-world situations with linear relationships.
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