Lesson 8 | Percent and Scaling | 7th Grade Mathematics

Objective

Solve percent problems fluently, including percent increase and decrease.

Common Core Standards

Core Standards

The core standards covered in this lesson

7.EE.A.2 — Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

Expressions and Equations

7.EE.A.2 — Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

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.

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 what information is given in a percent problem and how it relates to the question at hand.
Determine what missing value is being solved for in a percent problem.
Use various strategies to solve percent problems.

Tips for Teachers

Suggestions for teachers to help them teach this lesson

This lesson brings together the concepts from the first seven lessons in the unit. Students must make sense of the quantities in each problem, how they are related, what they mean in context, etc., and then determine what strategy or approach they will use to solve (MP.1).

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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

Sarita is collecting signatures to put a question on her town’s voting ballot. She has three weeks to collect the signatures. At the end of each week, Sarita finds the total number of signatures she has collected.

a. At the end of week 1, Sarita has collected 528 signatures. This is 44% of the number of signatures she needs. How many signatures does Sarita need to collect?

b. At the end of week 2, Sarita has a new total of 704 signatures. By what percent did the number of Sarita’s signatures increase over the week?

c. At the end of week 3, her total number of signatures increased by 75%. Does Sarita have enough signatures? Justify your answer.

Guiding Questions

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Problem 2

Ben spends 25% more minutes getting to school than Kate. If $$b$$ represents Ben’s time to get to school in minutes, and $$k$$ represents Kate’s time to get to school in minutes, which equations model this situation? Select all that apply.

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Guiding Questions

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Problem Set

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

Fishtank Plus Content

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

Juniper Middle School serves students in 7th and 8th grades.

a. 55% of the students at Juniper are in the 8th grade. The remaining 117 students are in 7th grade. How many students attend Juniper Middle School?

b. In September, there was an average of 4.8 daily unexcused absences. In October, this daily average was 6. By what percent did the average daily unexcused absences change from September to October?

Student Response

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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 6 — Exercises, Problem Set; this problem set has a nice collection of problems spanning the previous lessons
EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic A > Lesson 6 — Sprint, “Percent More or Less”
Illustrative Mathematics The Price of Bread — This is a great challenge problem that connects to financial literacy; it looks at the rising cost of bread alongside the rising minimum wage.
Illustrative Mathematics Comparing Years — This problem includes some challenging numbers that may be supported with calculator use.

Lesson 7

Lesson 9

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

Expressions and Equations

Ratios and Proportional Relationships

Foundational Standards

Ratios and Proportional Relationships

Criteria for Success

Tips for Teachers

Anchor Problems

Problem 1

Guiding Questions

Problem 2

Guiding Questions

Problem Set

Target Task

Student Response

Additional Practice

Lesson Map

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