Curriculum / Math / 7th Grade / Unit 1: Proportional Relationships / Lesson 8
Math
Unit 1
7th Grade
Lesson 8 of 18
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Compare proportional and non-proportional relationships.
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 is a good opportunity for students to construct arguments and defend their decisions around if a relationship is proportional or not. They may also work in pairs to listen to and critique the arguments of others (MP.3).
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Syrus is 12 years old and has a younger sister, Samira, who is 6 years old. Syrus says, “Our ages are in a proportional relationship because I am two times as old as my sister.”
Is Syrus correct? Justify your answer.
At the zoo, you can buy tickets to take a train ride between exhibits. Each ticket costs $0.50; however, there is a deal that if you buy 10 or more tickets, you only pay $4.00.
Is the cost of the tickets proportional to the number of tickets you buy? Create a table with some values and plot the points on a coordinate plane.
Four tables and four graphs are shown below. Which tables and graphs represent proportional relationships? Explain your reasoning for each one.
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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
Two ice cream shops are located across the street from one another on a busy street.
At which ice cream shop is the cost of the sundaes (including the toppings), proportional to the number of sundaes purchased? Justify your answer with tables, graphs, or an explanation.
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 7
Lesson 9
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
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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