Curriculum / Math / 7th Grade / Unit 1: Proportional Relationships / Lesson 3
Math
Unit 1
7th Grade
Lesson 3 of 18
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Determine the constant of proportionality in tables, and use it to find missing values.
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.
7.RP.A.2.B — Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
The foundational standards covered in this lesson
6.RP.A.2 — Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. Expectations for unit rates in this grade are limited to non-complex fractions. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."
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
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Randy is driving from New Jersey to Florida. Every time Randy stops for gas, he records the distance he traveled in miles and the total number of gallons of gas he used.
a. Assume that the number of miles driven is proportional to the number of gallons of gas used. Complete the table with the missing values.
b. Randy thinks that he could still fill out the table accurately even if the relationship between gallons of gas and miles was not proportional. Do you agree with Randy? Explain why or why not.
Grade 7 Mathematics > Module 1 > Topic A > Lesson 3 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Two water hoses are pouring water into two separate pools. Kareem measures the volume of the water in each pool after different amounts of time and records the information in the two tables below.
a. For each hose, is there a proportional relationship between the time a hose has been running and the volume of water in the pool? Explain your reasoning for each hose.
b. Based on your answer to part (a), can you determine the number of liters of water in either pool after 25 minutes?
A set of suggested resources or problem types that teachers can turn into a problem set
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In science class, you measure the mass and volume of different pieces of aluminum. You determine that there is a proportional relationship between mass and volume. The data on four samples of aluminum is shown in the table.
After you put your scale away, you realize that you forgot to find the mass of one more piece of aluminum. The volume of the piece of aluminum is 10 cm$${^3}$$. Can you determine the mass without taking your scale back out?
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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 2
Lesson 4
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
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
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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