Curriculum / Math / 7th Grade / Unit 1: Proportional Relationships / Lesson 6
Math
Unit 1
7th Grade
Lesson 6 of 18
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Lesson Notes
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Represent proportional relationships in graphs.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
6.RP.A.3.A — Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
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
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.
Graph the relationship in a coordinate plane. What features do you notice about the graph of a proportional relationship?
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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?
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15-20 minutes
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A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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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Interpret proportional relationships represented in graphs.
Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs
Solve ratio and rate problems using double number lines, tables, and unit rate.
Standards
7.RP.A.17.RP.A.2
Represent proportional relationships in tables, and define the constant of proportionality.
7.RP.A.27.RP.A.2.B
Determine the constant of proportionality in tables, and use it to find missing values.
7.RP.A.2.A7.RP.A.2.B
Write equations for proportional relationships presented in tables.
7.RP.A.2.B7.RP.A.2.C
Write equations for proportional relationships from word problems.
7.RP.A.27.RP.A.2.C
7.RP.A.27.RP.A.2.A7.RP.A.2.D
7.RP.A.27.RP.A.2.D
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Topic B: Non-Proportional Relationships
Compare proportional and non-proportional relationships.
7.RP.A.2.A
Determine if relationships are proportional or non-proportional.
Topic C: Connecting Everything Together
Make connections between the four representations of proportional relationships (Part 1).
7.RP.A.27.RP.A.2.A7.RP.A.2.B7.RP.A.2.C7.RP.A.2.D
Make connections between the four representations of proportional relationships (Part 2).
Use different strategies to represent and recognize proportional relationships.
Topic D: Solving Ratio & Rate Problems with Fractions
Find the unit rate of ratios involving fractions.
7.RP.A.1
Find the unit rate and use it to solve problems.
7.RP.A.17.RP.A.3
Solve ratio and rate problems by setting up a proportion.
Solve ratio and rate problems by setting up a proportion, including part-part-whole problems.
Solve multi-step ratio and rate problems using proportional reasoning, including fractional price increase and decrease, commissions, and fees.
7.RP.A.3
Use proportional reasoning to solve real-world, multi-step problems.
7.RP.A.17.RP.A.27.RP.A.3
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