# Proportional Relationships

## Objective

Write equations for proportional relationships from word problems.

## Common Core Standards

### Core Standards

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

• 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.

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• 6.EE.B.7

• 6.EE.C.9

## Criteria for Success

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1. Recall that a ratio relationship $A:B$ has two unit rates, $A/B$ and $B/A$.
2. Find the constant of proportionality from a situation (not a table) by finding the value of $y/x$, where $y$ is the dependent variable and $x$ is the independent variable.
3. Write an equation using the constant of proportionality for a proportional relationship.
4. Use an equation to solve problems.
5. Decontextualize situations to represent them as equations and re-contextualize equations to explain their meanings as they relate to situations (MP.2).

## Tips for Teachers

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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 Problems 1 and 2 (benefit from worked examples). Find more guidance on adapting our math curriculum for remote learning here.

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## Anchor Problems

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### Problem 1

A repair technician replaces cracked screens on phones. He can replace 5 screens in 3 hours.

1. Write an equation you can use to determine how long it takes to replace any number of screens.
2. Write an equation you can use to determine how many screens can be replaced in a certain number of hours.
3. Use one of your equations to determine how long it would take to replace 30 screens.
4. Use one of your equations to determine how many screens could be replaced in 12 hours.

#### Guiding Questions

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### Problem 2

A train traveling from Boston to New York moves at a constant speed. The train covers 260 miles in 3.25 hours.

Write an equation that represents this relationship. Explain what your equation tells you about the train.

#### Guiding Questions

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### Problem 3

Deli turkey meat is on sale at two different grocery stores, as represented below.

Stop & Buy

$c=6.25p$, where $c$ represents cost in dollars and $p$ represents number of pounds of turkey

Roger's

 Amount (pounds) Cost () 3 19.50 4 26 6 39 7 45.50 What's the unit price of turkey per pound at each store? Which store has the better sale? #### Guiding Questions Create a free account or sign in to access the Guiding Questions for this Anchor Problem. ## Problem Set ? With Fishtank Plus, you can download a complete problem set and answer key for this lesson. Download Sample The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set. • Challenge: The average person uses about 90 gallons of water per day. At this rate, how long would it take a family of 4 to use enough water to fill an average-size swimming pool? An olympic-size swimming pool? ## Target Task ? The 7th graders at Wilson Middle School are taking a field trip to the science museum. So far, 12 students have turned in a total of81 to pay for their ticket.

1. Write an equation to represent the cost, $c$, for $t$ tickets.
2. If all 72 students turn in their ticket money, how much money will be collected?

### Mastery Response

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