Proportional Relationships

Objective

Find the unit rate and use it to solve problems.

Common Core Standards

Core Standards

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• 7.RP.A.1 — Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.

• 7.RP.A.3 — Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

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• 6.RP.A.2

• 6.RP.A.3.B

• 6.NS.A.1

Criteria for Success

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1. Identify the appropriate unit rate for a ratio $a:b$, either $a/b$ or $b/a$, that will be most helpful to solve a problem.
2. Use the unit rate to solve problems.
3. Organize information and map out a solution process for a multi-step problem (MP.1).

Tips for Teachers

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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) and Anchor Problem 2 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

Fishtank Plus

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Anchor Problems

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Problem 1

A small pool is leaking water from a hole. After ${2{1 \over2}}$ minutes, ${3{1\over2}}$ liters of water have leaked out.

1. At this rate, how many liters will have leaked out after 10 minutes?
2. If the pool has 42 liters of water in it, after how many minutes will it be empty?

Problem 2

You have decided to remodel your bathroom and install a tile floor. The bathroom is in the shape of a rectangle, and the floor measures 14 feet, 8 inches long by 5 feet, 6 inches wide. The tiles you want to use cost $5 each, and each tile covers ${4{2\over3}}$ square feet. If you have$100 to spend, do you have enough money to complete the project?

References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic C > Lesson 12Example 1

Grade 7 Mathematics > Module 1 > Topic C > Lesson 12 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 3

Pieces of large rectangular fabric, measuring ${31{1\over5}}$ square inches, are cut into smaller rectangular pieces of size ${2{3\over5}}$ square inches. How many smaller pieces of fabric can be cut from 4 large pieces of fabric?

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.

• Challenge: Sound travels at a rate of $761\frac{1}{5}$ mph. If lightening strikes $3\frac{1}{2}$ miles from where you are, how long will be it before you hear its sound (thunder)?

At a candy store, you can buy pre-filled bags of candy that weigh $2\frac{1}{4}$ pounds for $8.10$. At this same rate, how much would a $4$ pound bag of candy cost?