Percent and Scaling

Lesson 17

Math

Unit 5

7th Grade

Lesson 17 of 19

Objective


Compute actual areas from scale drawings.

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

  • 6.G.A.1
  • 7.RP.A.2

Criteria for Success


  1. Determine how many copies of an original image will fit into a scaled copy of the original. 
  2. Understand that an image scaled by a scale factor $$n$$, has an area scaled by a scale factor $$n^2$$
  3. Find the actual area from scale drawings in two different ways. 

Tips for Teachers


In this lesson, students explore what happens to area when a scale factor is applied. In previous lessons leading up to this, students found lengths and other linear measurements from scale drawings. When it comes to scaling area, a common misunderstanding is to approach it the same way as scaling a linear measurement. Students must carefully attend to the meaning of scale factor and the units involved in order to understand that area is scaled by the square of the scale factor of the image (MP.2). If students struggle, bring them back to the concepts and visual supports in Anchor Problem 1.

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Anchor Problems


Problem 1

In the grid below, draw a scale image of the rectangle using a scale factor of 2. Then complete the table and answer the question.

Image Length Width Area # of original rectangles in image
Original        
Scale image        

When the scale factor is 2, how much is the area scaled by?

Guiding Questions

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Problem 2

In the grid below, repeat the activity from Anchor Problem 1, now using a scale factor of 3.

Image Length Width Area # of original rectangles in image
Original        
Scale image        

a.   When the scale factor is 3, how much is the area scaled by?

b.   If the scale factor of an image is $$n$$, how much is the area of the image scaled by?

Guiding Questions

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Problem 3

A triangular plot of land is represented by the scale drawing below. Two students are determining the actual area of the plot of land from the scale drawing. 


Cherita says, “I can use the scale to find the actual dimensions of the plot of land and then use those to find the area.”

Davis says, “I can find the area of the scale drawing first and then apply the scale factor for the area to find the actual area of the plot of land.” 

Whose strategy will correctly find the area of the plot of land? Will Cherita and Davis get the same answer? Try out each student’s strategy. 

Guiding Questions

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Problem 4

What percent of the area of the large square is the area of the small square?

Guiding Questions

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References

EngageNY Mathematics Grade 7 Mathematics > Module 4 > Topic C > Lesson 15Example 1

Grade 7 Mathematics > Module 4 > Topic C > Lesson 15 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

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

Target Task


You and your brother are debating whose room is bigger. To compare, you each draw a picture of your room. Use the drawings below to determine who has the bigger room. Justify your answer.

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.

  • Include error analysis questions that address common misconceptions.
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Lesson 16

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Lesson 18

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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