Proportional Relationships

Lesson 3

Math

Unit 1

7th Grade

Lesson 3 of 18

Objective


Determine the constant of proportionality in tables, and use it to find missing values.

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 6.RP.A.2
  • 6.RP.A.3

Criteria for Success


  1. Determine if a relationship shown in a table is proportional by testing if there is a constant number that is multiplied by the first quantity to get the second quantity. 
  2. Determine the constant of proportionality from a table. 
  3. Use unit rate and constant of proportionality to solve problems. 
  4. Understand that if a relationship is not proportional, then one cannot determine missing values.

Tips for Teachers


  • Students continue analyzing tables as a way to understand and quantify a proportional relationship between two units (MP.2). 
  • Students will spend more time comparing proportional and non-proportional relationships in Lessons 9 and 10. They are introduced to the comparison in this lesson in order to help solidify the role of the constant of proportionality between the two quantities, especially as presented in a table.

Lesson Materials

  • Calculators (1 per student)
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Anchor Problems

25-30 minutes


Problem 1

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.

Gallons of gas used 2 4     8 10  12 
Miles driven 54    189 216    

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.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic A > Lesson 3Exercise 4

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..

Problem 2

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.

Hose A
Time (min) Volume (liters)
2 36.7
3 55.05
5 91.75
8 146.8
Hose B
Time (min) Volume (liters)
2 42.8
4 85.6
7 126
10 165

 

 

 

 

 

 

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?

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


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.

Volume (cm$$^3$$) Mass (g)
4 10.8
7 18.9
12 32.4
18 48.6

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?

Student Response

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Additional Practice


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.

Next

Write equations for proportional relationships presented in tables.

Lesson 4
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Representing Proportional Relationships in Tables, Equations, and Graphs

Topic B: Non-Proportional Relationships

Topic C: Connecting Everything Together

Topic D: Solving Ratio & Rate Problems with Fractions

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