# Proportional Relationships

## Objective

Use different strategies to represent and recognize proportional relationships.

## Common Core Standards

### Core Standards

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• 7.RP.A.2 — Recognize and represent proportional relationships between quantities.

• 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.

• 7.RP.A.2.C — Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

• 7.RP.A.2.D — Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

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• 6.RP.A.3

## Criteria for Success

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1. Analyze proportional relationships
2. Use proportional reasoning to solve real-world problems involving proportional relationships (MP.4).

## Tips for Teachers

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This is a flex lesson that can be used in a variety of ways, depending on the individual class. There are no anchor problems, as teachers can determine what specific concepts are best to look at with the whole class. The Problem Set Guidance is a collection of problems that may be used for this day.

## 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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Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired 152 km with 95 miles. If $k$ represents the number of kilometers and $m$ represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why.

• Oscar wrote the equation $k = 1.6m$, and he said that the unit rate ${{1.6 \over1}}$ represents kilometers per mile.
• Maria wrote the equation $k = 0.625m$, and she said that the unit rate 0.625 represents kilometers per mile.

Sketch a graph that represents the correct proportional relationship between kilometers and miles.

#### References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic B > Lesson 9Exit Ticket

Grade 7 Mathematics > Module 1 > Topic B > Lesson 9 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..

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