Curriculum / Math / 7th Grade / Unit 1: Proportional Relationships / Lesson 9
Math
Unit 1
7th Grade
Lesson 9 of 18
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Determine if relationships are proportional or non-proportional.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
6.RP.A.3 — Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This Lesson extends on Lesson 8 by having students make the determination if a relationship is proportional or non-proportional, and to justify their reasoning. They utilize their knowledge of tables, graphs, and equations to support their justifications.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Is the perimeter of a square proportional to the side length of a square? Is the area of a square proportional to the side length of a square?
Justify your answer to each question using tables, graphs, and/or equations.
At Sunny’s Market, soda water costs $2.55 for 3 liters.
Which stores below sell soda water at a price that is proportional to the price at Sunny’s Market?
Ahmed hiked at a constant speed for 6 hours and covered 21 miles. This is represented in the coordinate plane below.
Which coordinate points, when graphed on the plane above, would be in a proportional relationship to Ahmed’s hike? Select all that apply.
A. (0, 3.5)
B. (1, 3.5)
C. (2, 7)
D. (3, 14)
E. (4, 15)
F. (5, 17.5)
G. (8, 28)
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
Is the perimeter of an equilateral triangle proportional to the side length of the triangle? For any regular polygon, is the perimeter of the polygon proportional to the side length of the polygon? Explain your reasoning.
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 8
Lesson 10
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
Interpret proportional relationships represented in graphs.
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
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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