Curriculum  /  Math  /  7th Grade  /  Unit 5: Percent and Scaling  /  Lesson 13

Percent and Scaling

Lesson 13

Math

Unit 5

7th Grade

Lesson 13 of 19

Objective

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

Common Core Standards

Core Standards

  • 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.
  • 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

  • 5.NF.B.5
  • 5.NF.B.5.A
  • 5.NF.B.5.B
  • 7.RP.A.2

Criteria for Success

  1. Create a table of values with scale and actual measurements.
  2. Identify the constant of proportionality from a table of values, and connect it to scale factor.
  3. Define scale factor as the value that all sides of a figure are multiplied by to create a scale image.
  4. Find the scale factor between two scaled images.
  5. Use a given scale factor to draw a scale image.

Tips for Teachers

Students deepen their understanding of the connection between scale and proportionality in this lesson. They determine that in creating a scale image, they are creating a proportional relationship between the measurements of the two images. 

Lesson Materials

  • Graph Paper (2-3 sheets per student)
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Anchor Problems

25-30 minutes

Problem 1

Pentagon $${FGHIJ}$$ is a scale image of pentagon $${ABCDE}$$. 

a.   Complete the table below with the measurements of each pentagon. 

Original line segment Original length Corresponding line segment Scale length
$$AB$$   $$FG$$  
$$BC$$   $$GH$$  
$$CD$$   $$HI$$  
$$AE$$   $$FJ$$  

b.   Is there a proportional relationship between the side lengths of the original pentagon and the scaled pentagon? Explain using the measurements in the table.

c.   What is the constant of proportionality?

d.   What is the scale factor?

Guiding Questions

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Student Response

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Problem 2

Melissa orders business cards to promote her new website. She previews the cards online before placing her order. The scale image she sees online and the actual size of the cards are shown below. 

What scale factor was used to create the online image from the actual size of the business card? 

Guiding Questions

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Student Response

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Problem 3

For each situation described below, sketch and label the scale image using the scale factor.

a.   Your family recently had a family portrait taken. Your aunt asks you to take a picture of the portrait using your phone and send it to her. The original portrait is 3 feet by 3 feet and the scale factor from the original picture to the picture on your phone is $${1 \over18}$$. Draw the scale drawing, in inches, that would be the size of the portrait on your phone.

b.   Create a scale drawing of the arrow below using a scale factor of 150%. 

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 7 Mathematics > Module 1 > Topic D > Lesson 17 — Part a: Example 3

Grade 7 Mathematics > Module 1 > Topic D > Lesson 17 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Problem Set

15-20 minutes

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

Target Task

5-10 minutes

Right triangles $$A$$ and $$B$$ are scale copies.  


 

a.   What scale factor was applied to triangle $$A$$ that resulted in triangle $$B$$?

b.   Use the same scale factor on rectangle $$C$$, shown below, to draw rectangle $$D$$. Label the dimensions of rectangle $$D$$ in your drawing.

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.

Next

Use a scale to determine actual measurements.

Lesson 14
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Percent, Part, and Whole

Topic B: Percent Increase and Decrease

Topic C: Percent Applications

Topic D: Scale Drawings

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