Math  /  7th Grade  /  Unit 5: Percent and Scaling

Percent and Scaling

Students expand on and apply their understanding of percentages by studying percent increase and decrease, percent applications such as tax and simple interest, and scaled geometric drawings.

Math

Unit 5

7th Grade

Unit Summary

Please Note: In October 2025, this unit and its lesson plans received a round of enhancements. Teachers should pay close attention as they intellectually prepare to account for the updated pacing and content. 

In Unit 5, 7th grade students build on their understanding of ratios and proportions from Unit 1 to solve various real-world applications involving percentages and scale drawings. They begin the unit by studying the relationship between percents, parts, and wholes using familiar strategies from 6th grade as well as new strategies from this year, such as proportions. Students then investigate how percentages can be used to represent increases and decreases in quantities. They use visual diagrams to model these situations and to understand how 100% and 20% of a value is the same as 120% of that value MP.2 Reason abstractly and quantitatively. . Students continue to build fluency with percent problems as they solve real-world problems including calculating purchase totals with discounts and tax. Lastly, students study scale drawings and learn how a scale can be used to create scale copies of real-life measurements such as maps or floor plans. They apply proportional reasoning and strategically use tools to recreate scale drawings or find actual measurements from scale drawings MP.5 Use appropriate tools strategically. . Throughout this unit, students use skills and understandings they have already built to make sense of and reason through new types of problems MP.1 Make sense of problems and persevere in solving them. , including continuing to work with a range of rational numbers.

In 6th grade, students learned several strategies to solve ratio and rate problems, including setting up tables, drawing tape diagrams, creating double number lines, and writing equations. They also defined percent as a rate per 100 and solved percent problems to find the wholes, parts, or percents. These standards are foundational to this 7th grade unit, and the first four lessons in this unit incorporate a review of these concepts and skills.

In 8th grade, students will refine their understanding of scale and scale drawings when they study dilations in their transformations unit. They will define similar figures and use dilations and other transformations to prove that two images are similar or scale drawings of one another.

Pacing: 23 instructional days (19 lessons, 3 flex days, 1 assessment day)

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Assessment

The following assessments accompany Unit 5.

Pre-Unit

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

Mid-Unit

Have students complete the Mid-Unit Assessment.

Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Expanded Assessment Package

Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

Unit Prep

Intellectual Prep

Unit Launch

Before you teach this unit, unpack the standards, big ideas, and connections to prior and future content through our guided intellectual preparation process. Each Unit Launch includes a series of short videos, targeted readings, and opportunities for action planning to ensure you're prepared to support every student.

Internalization of Standards via the Post-Unit Assessment

  • Take the Post-Unit Assessment. Annotate for:
    • Standards that each question aligns to
    • Strategies and representations used in daily lessons
    • Relationship to Essential Questions of unit
    • Lesson(s) that Assessment points to

Internalization of Trajectory of Unit

  • Read and annotate the Unit Summary.
  • Notice the progression of concepts through the unit using the Lesson Map.
  • Do all Target Tasks. Annotate the Target Tasks for: 
    • Essential Understandings
    • Connection to Post-Unit Assessment questions
  • Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

Unit-Specific Intellectual Prep

Essential Understandings

  • Percentages can be used to understand the relationship between parts of quantities and the whole quantity. Percentages can also be used to understand how quantities change in relation to their starting values. As a result, we can use percentages to model many real-world applications such as price changes and simple interest. 
  • Scale drawings represent proportional relationships between two figures using a constant ratio called the scale factor. 
  • Scales, such as “1 inch represents 10 miles,” enable us to model and work with large or small measurements. These ratios can be used to create and interpret maps, floor plans, and other designs.

Materials

To see all the materials needed for this course, view our 7th Grade Course Material Overview.

Vocabulary and Models

Unit Vocabulary

corresponding

discount

markup/markdown

measurement error

percent error

percent increase/percent decrease

scale image/drawing

scale factor

simple interest

tax

tip

Foundational Vocabulary

commission

percent

percentages

scale

To see all the vocabulary for Unit 5, view our 7th Grade Vocabulary Glossary.

Access foundational vocabulary for Unit 5 in the same 7th Grade Vocabulary Glossary.

Models

Model Example
table

280 students attend a carnival, representing 80% of the school.

Table showing relationships between amounts, percentages, and operations (÷4, ×5).
tape diagram

280 students attend a carnival, representing 80% of the school.

Rectangular model showing 70 repeated 4 times, representing 80% of a total of 280.
double number line

280 students attend a carnival, representing 80% of the school.

Double number line showing 280 and 80% corresponding to 0 and 100%.
proportion

 280 students attend a carnival, representing 80% of the school.

$$\frac{280}{x}=\frac{80}{100}$$

$$x=350$$
percent equation

280 students attend a carnival, representing 80% of the school. 

$$280=0.80x$$

$$x=280/0.80$$

$$x=350$$

Lesson Map

Topic A: Percent, Part, and Whole

Topic B: Percent Increase and Decrease

Topic C: Percent Applications

Topic D: Scale Drawings

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

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.EE.B.3 — Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Geometry

  • 7.G.A.1 — Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

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.

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

Geometry

  • 6.G.A.1

Number and Operations—Fractions

  • 5.NF.B.5
  • 5.NF.B.5.A
  • 5.NF.B.5.B

Ratios and Proportional Relationships

  • 6.RP.A.3
  • 6.RP.A.3.C
  • 7.RP.A.2

Future Standards

Geometry

  • 8.G.A.2
  • 8.G.A.4

Standards for Mathematical Practice

  • CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

  • CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

  • CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

  • CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

  • CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

  • CCSS.MATH.PRACTICE.MP6 — Attend to precision.

  • CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

  • CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.

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