Lesson 3 | Percent and Scaling | 7th Grade Mathematics

Objective

Find the whole given a part and percent.

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 whole when given the part and percent using multiple strategies including tables, equations, and proportions.
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

At the Kennedy Middle School, 280 students attended the end-of-year carnival, representing 80% of the students in the school.

a. Draw a visual representation of the problem.

b. Determine how many students are at the Kennedy Middle School. 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

At Shoe Line, there are 132 boots, which make up 24% of the shoes in the store. At Shoe Warehouse, there are 120 boots, which make up 15% of the shoes in the store.

Which store has more shoes? Justify your answer.

Guiding Questions

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Problem 3

A new company selling sports equipment sold 2,835 helmets in their second year of operation. This is 225% of the number of helmets they sold in their first year.

How many helmets did the company sell in their first year?

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

At the Blackstone High school, 86 seniors submitted college applications for early decision. This represented approximately 34% of the senior class.

The Truman High School, across town from the Blackstone High School, has 266 seniors.

Which high school has the larger senior class? Justify your answer.

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 4, Problem Set 1c, 1d, 3, 9
EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic A > Lesson 3 — Sprint, “Part, Whole, or Percent” - Located at the end of the lesson
Illustrative Mathematics Shirt Sale

Lesson 2

Lesson 4

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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