Lesson 4 | Percent and Scaling | 7th Grade Mathematics

Objective

Find the percent given a part 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.
Determine what percent a part is of the whole.
Solve percent problems efficiently.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

Lessons 2–4 are approaching 7.RP.3 and review solving percent problems finding part, percent, and whole using strategies from 6th grade or using proportions learned earlier in the year. 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 30-minute television show, 12 minutes of the airtime are spent on commercials.

a. Draw a visual representation of the problem.

b. Determine what percent of the television show’s airtime is spent on commercials. Choose any strategy.

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

Cole and Jamie are raising money for the annual Walk for Hunger in their city. They each have a goal to raise $250. So far, Cole has raised $150 and Jamie has raised $180.

a. What percent of their goal did each boy raise so far?

b. What is the amount that Cole raised as a percent of the amount Jamie raised?

c. What is the amount Jamie raised as a percent of the amount Cole raised?

Guiding Questions

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Problem 3

At a middle school, 480 students in sixth through eighth grade responded to a survey that asked them what their favorite season was. The circle graph below shows some of the data from the survey.

Student Survey “Favorite Season”

a. How many students chose spring as their favorite season?

b. What percent of students chose summer as their favorite season?

c. In just the sixth-grade class, 28 students chose winter as their favorite season. This was 20% of the sixth grade. How many students are in the sixth grade at this school?

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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Target Task

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

You bought a winter coat for $34.10. The original price was $62.

What percent of the coat's original price did you pay?

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.

EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic A > Lesson 2 — Example 5, Problem Set 1e, 1f, 5, 6, 10
EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic A > Lesson 3 — Examples and Problem Set; note, there are some problems in the problem set that include some increase/decrease. Use these as challenge problems or do not include them in the problem set.
Kuta Software Free Pre-Algebra Worksheets Percent Problems, Straightforward
Illustrative Mathematics Exam Scores
Andrew Stadel's 3-Act Math Tasks iPad Usage

Lesson 3

Lesson 5

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

Problem 3

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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