Curriculum / Math / 7th Grade / Unit 1: Proportional Relationships / Lesson 7
Math
Unit 1
7th Grade
Lesson 7 of 18
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Interpret proportional relationships represented in graphs.
The core standards covered in this lesson
7.RP.A.2 — Recognize and represent proportional relationships between quantities.
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
Students reason abstractly as they represent proportional situations using tables and graphs, and interpret the information to identify the constant of proportionality and write an equation. Given a graph of a proportional relationship, students re-contextualize information represented in coordinate points to explain what $$ (0, 0)$$ and $$ (0, r)$$ mean in context of the problem (MP.2).
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
In a video game, for every 3 coins you collect, you earn 4 points.
a. Create a table of values to represent the relationship.
b. Graph the relationship.
c. Determine the equation that represents the relationship.
Three toy cars race down a straight path. The distance each car traveled, in meters, over time, measured in seconds, is shown in the graph below.
a. At what speed is each car traveling? Where can you see each speed in the graph?
b. Explain the significance of the coordinate point $$(1, r)$$. What do you think the “$$r$$” represents?
The graph below shows the number of gallons of gasoline used by a car over a given number of miles.
a. Explain what each point A, B, and C means in the context of the situation.
b. Plot the point that represents the unit rate. Explain how you determined your answer, and what it means in context of the situation.
c. Does this car get more or less miles per gallon of gasoline than a car that gets 30 miles per gallon?
A set of suggested resources or problem types that teachers can turn into a problem set
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
A souvenir shop sells magnets, 2 for $3. The graph below shows the proportional relationship.
Which statements below are true? For each false statement, correct it so that the statement reads true.
An example response to the Target Task at the level of detail expected of the students.
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.
Lesson 6
Lesson 8
Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs
Solve ratio and rate problems using double number lines, tables, and unit rate.
7.RP.A.1 7.RP.A.2
Represent proportional relationships in tables, and define the constant of proportionality.
7.RP.A.2 7.RP.A.2.B
Determine the constant of proportionality in tables, and use it to find missing values.
7.RP.A.2.A 7.RP.A.2.B
Write equations for proportional relationships presented in tables.
7.RP.A.2.B 7.RP.A.2.C
Write equations for proportional relationships from word problems.
7.RP.A.2 7.RP.A.2.C
Represent proportional relationships in graphs.
7.RP.A.2 7.RP.A.2.A 7.RP.A.2.D
7.RP.A.2 7.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.2 7.RP.A.2.A 7.RP.A.2.B 7.RP.A.2.C 7.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.1 7.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.1 7.RP.A.2 7.RP.A.3
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