Proportional Relationships

Lesson 6

Math

Unit 1

7th Grade

Lesson 6 of 18

Objective


Represent proportional relationships in graphs.

Common Core Standards


Core Standards

  • 7.RP.A.2 — Recognize and represent proportional relationships between quantities.
  • 7.RP.A.2.A — Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
  • 7.RP.A.2.D — Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Foundational Standards

  • 6.RP.A.3.A

Criteria for Success


  1. Graph a proportional relationship in a coordinate plane using a table of values.
  2. Identify key features of the graph of a proportional relationship: a straight line that passes through the origin.
  3. Understand the graph of a proportional relationship to represent the set of equivalent ratios of the two quantities, represented as coordinate points.
  4. Interpret the coordinate point $$(x,y)$$ as it relates to the context of the situation.

Tips for Teachers


  • Lessons 6 and 7 focus on representing proportional relationships in the coordinate plane. Students may need to review concepts and skills around the coordinate plane in order to fully access this lesson.

Lesson Materials

  • Graph Paper (2-3 sheets per student)
  • Ruler (1 per student)
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Anchor Problems


Problem 1

An amusement park sells tickets that can be used to go on rides and play games. The cost of the tickets is proportional to the number of tickets purchased. The table below shows how many tickets can be purchased for different amounts of money.

# of Tickets Cost ($)
2 3
4 6
6 9
8 12
10 15

Graph the relationship in a coordinate plane. What features do you notice about the graph of a proportional relationship?

Guiding Questions

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Problem 2

When Lili’s grandmother uses her rice cooker to make sushi rice, she uses a specific ratio of water to uncooked rice. The graph below shows this relationship.

a.   Record the coordinate points from the graph. What do these ordered pairs represent?

b.   What is the ratio of water to uncooked rice that Lili’s grandmother uses?

c.   If Lili added 6 cups of water to 5 cups of uncooked rice, did she use her grandmother’s ratio? Explain how you know by looking at the graph.

d.   What does the point (0, 0) represent in this situation? Why does it make sense that it is included on the graph?

Guiding Questions

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Problem Set

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Target Task


The graph below shows the relationship between the cost of gasoline and the number of gallons of gasoline purchased at a gas station.

a.   Is the cost of gasoline proportional to the amount of gasoline purchased? Explain how you know using the graph.

b.   How many gallons of gasoline can you purchase with $15?

c.   How much can you expect to pay for 3 gallons of gasoline?

d.   What are the coordinates of point P, shown in the graph? Describe what point P means in context of the situation.

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 review problems of prior skills such as graphing coordinate points in the coordinate plane, determining and setting up appropriate scale intervals, naming coordinate points in the coordinate plane, distinguishing between points on the $$x$$-axis and those on the $$y$$-axis, etc.
  • Include problems where students are given a table of values and are asked to represent the relationship in a graph.
  • Include problems where students are given a graph of a proportional relationship and must write a table of values to accompany it. 
  • Include problems where students interpret coordinate points $$(x,y)$$ from both graphs and tables
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Lesson 5

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Lesson 7

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

Topic B: Non-Proportional Relationships

Topic C: Connecting Everything Together

Topic D: Solving Ratio & Rate Problems with Fractions

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