Curriculum / Math / 8th Grade / Unit 5: Linear Relationships / Lesson 3
Math
Unit 5
8th Grade
Lesson 3 of 15
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Compare proportional relationships represented as graphs.
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
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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
The graphs below show the cost $$y$$ of buying $${{x }}$$ pounds of fruit. One graph shows the cost of buying $${{x }}$$ pounds of peaches, and the other shows the cost of buying $$x$$ pounds of plums.
a. Which kind of fruit costs more per pound? Explain.
b. Bananas cost less per pound than peaches or plums. Draw a line alongside the other graphs that might represent the cost, $$y$$, of buying $$x$$ pounds of bananas.
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Peaches and Plums, accessed on Feb. 23, 2018, 11:12 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.
Kell works at an after-school program at an elementary school. The table below shows how much money he earned every day last week.
Mariko has a job mowing lawns that pays $7 per hour.
a. Draw a graph for each person's situation, where $$y$$ represents the amount of money each person earns for working $$x$$ hours. Your graph should have 2 lines drawn in it.
b. Who makes more money for working 10 hours?
c. How can you see who makes more per hour by just looking at the graphs? Explain.
d. Use your graphs to determine who makes more for 2 hours of work and approximately how much more.
Who Has the Best Job?, accessed on Feb. 23, 2018, 11:14 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.
The graph below shows the relationship between the distance biked and the time spent biking for two different bikers in a road race.
Which of the following accurately compares the speed of the two bikers?
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
The graphs below show the distance two cars have traveled along the freeway over a period of several seconds. Car A is traveling 30 meters per second.
Which equation from those shown below is the best choice for describing the distance traveled by car B after $$x$$ seconds? Explain.
Comparing Speeds in Graphs and Equations, accessed on Feb. 23, 2018, 11:19 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.
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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Compare proportional relationships represented in different ways.
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.
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Topic B: Slope and Graphing Linear Equations
Graph a linear equation using a table of values.
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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