Lesson 2 | Percent and Scaling | 7th Grade Mathematics

Objective

Find percent of a number when given percent and the whole.

Common Core Standards

Core Standards

The core standards covered in this lesson

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.

Ratios and Proportional Relationships

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.

7.NS.A.3 — Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

The Number System

7.NS.A.3 — Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

Foundational Standards

The foundational standards covered in this lesson

6.RP.A.3.C

Ratios and Proportional Relationships

6.RP.A.3.C — Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

Criteria for Success

The essential concepts students need to demonstrate or understand to achieve the lesson objective

Identify values that represent part, percent, and whole in a percent situation.
Represent percent situations using visual diagrams such as tape diagrams or double number lines.
Find a percent of a quantity using multiple strategies including tables, equations, and proportions.
Solve percent problems efficiently.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

The next three lessons, Lessons 2–4, are approaching 7.RP.3 and review solving percent problems finding part, percent, and whole. This lesson focuses on finding the part of a number when given the percent and the whole. Students recall strategies from sixth grade, such as tables, double number lines, and equations, while also using proportions, a new strategy learned in Unit 1 of seventh grade. These lessons may be combined or stretched as needed to meet the needs of your students.
In order to provide opportunities for students to engage with standard 7.NS.3, calculators are not recommended to be used for every problem. In the interest of pacing, calculators may be used selectively. Students should use estimation and benchmark percentages to estimate answers and use as a check for reasonableness of the calculated answers (MP.5).

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Anchor Problems

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

Problem 1

In a school election, 60 students voted for the next student body president. Aliyah won 45% of the votes.

a. Draw a visual representation of the problem. For example, you could draw a tape diagram or a double number line.

b. Determine how many votes Aliyah won. Use any strategy, for example, creating a table, writing an equation, or setting up a proportion.

c. Find a peer who used a different strategy to solve than you did. Compare and discuss your strategies and solutions.

Guiding Questions

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Problem 2

According to the U.S. Environmental Protection Agency, in 2013, people in the United States produced about 254 million tons of trash. Approximately 34.3% of this trash was recycled or composted.

About how many million tons of trash were recycled or composted in 2013?

Guiding Questions

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References

U.S. Environmental Protection Agency Municipal Solid Waste

Municipal Solid Waste is made available by the U.S. Environmental Protection Agency. Accessed Dec. 18, 2017, 6:21 p.m..

Problem 3

The chart below shows the number of students in each grade at a middle school.

Grade	# of students
6th	94
7th	103
8th	93

Approximately 52% of students in the school participate in an after school activity. How many students participate in an after school activity?

Guiding Questions

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Problem Set

A set of suggested resources or problem types that teachers can turn into a problem set

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

Target Task

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Trevor received a $75 gift card to a local music shop for his birthday. After making a purchase at the shop, he has 16% left on the gift card.

How much money is left on the gift card?

Student Response

An example response to the Target Task at the level of detail expected of the students.

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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.

Include reasoning problems such as “Sam has 50% of a muffin and his brother Joe has 50% of a muffin. Sam has more muffin than Joe does. How is this possible?” or “Sam has 25% of a cookie and Joe has 50% of a cookie. Give a possible weight of each cookie if Sam has more cookie (in weight) than his brother does.”

MARS Summative Assessment Tasks for Middle School Ice Cream
Open Up Resources Grade 6 Unit 3 Practice Problems — Lesson 15
Common Core Sheets Finding Percents — These problems are all without context but can be used to write situations with context.
EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic A > Lesson 2 — Opening Exercise, Examples 1–3, Exercises 1–2, Problem Set 1a, 1b, 2, 4, 7, 8

Lesson 1

Lesson 3

Lesson Map

Topic A: Percent, Part, and Whole

Define percent and convert between fractions, decimals, and percentages. Solve percent problems mentally with benchmark percentages.

7.RP.A.3

Find percent of a number when given percent and the whole.

7.NS.A.3 7.RP.A.3

Find the whole given a part and percent.

7.NS.A.3 7.RP.A.3

Find the percent given a part and the whole.

7.NS.A.3 7.RP.A.3

Topic B: Percent Increase and Decrease

Find a new amount given the original and a percent increase or decrease.

7.EE.A.2 7.RP.A.3

Find the original amount given a new amount after a given percent increase or decrease.

7.EE.A.2 7.RP.A.3

Find the percent of increase or decrease given the original and new amounts.

7.RP.A.3

Solve percent problems fluently, including percent increase and decrease.

7.EE.A.2 7.RP.A.3

Topic C: Percent Applications

Solve percent applications involving discount, tax, and tip.

7.EE.B.3 7.RP.A.3

Solve percent applications involving simple interest, commissions, and other fees.

7.EE.B.3 7.RP.A.3

Solve percent applications involving measurement and percent error.

7.EE.B.3 7.RP.A.3

Topic D: Scale Drawings

Define and identify scale images.

7.G.A.1

Define and determine scale factor between two scale images. Use scale factor to draw scale images.

7.G.A.1 7.RP.A.3

Use a scale to determine actual measurements.

7.G.A.1 7.RP.A.3

Use scales in maps to find actual distances between locations.

7.G.A.1 7.RP.A.3

Use scales in floor plans to find actual measurements and dimensions.

7.G.A.1 7.RP.A.3

Compute actual areas from scale drawings.

7.G.A.1 7.RP.A.3

Draw scale drawings at different scales.

7.G.A.1 7.RP.A.3

Create a scale floor plan (optional).

7.G.A.1 7.RP.A.3

Percent and Scaling

Objective

Common Core Standards

Core Standards

Ratios and Proportional Relationships

The Number System

Foundational Standards

Ratios and Proportional Relationships

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

References

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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