# Proportional Relationships

## Objective

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

## Common Core Standards

### Core Standards

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• 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.

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• 6.RP.A.2

• 6.RP.A.3

## Criteria for Success

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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

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• 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.
• Tools that may be useful for this lesson: calculators

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### 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.

1. 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
1. If the relationship between gallons of gas and miles was not proportional, could you still complete the table? Explain why or why not.

#### 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. Alex 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

1. 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.
2. Based on your answer to part (a), can you determine the number of liters of water in either pool after 25 minutes?

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own 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.

 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?

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