Fishtank Learning

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

Objective

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

Anchor Problems - Problem 1

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

Grid showing two pentagons, ABCDE and FGHIJ, with FGHIJ a scaled version of 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

What happened to the image of Pentagon $$ABCDE$$? Did it get bigger or smaller?
If you know that the smaller pentagon is a scale image of the larger, then what else do you know?
Recall how to find the constant of proportionality from a table.
How does the constant of proportionality relate to what happened between the two images?
A scale factor is a value that all sides of a figure are multiplied by to create a scale image. What connection do you see between scale factor and the constant of proportionality?

Notes

Use this Anchor Problem to guide students toward defining scale factor and understanding that it represents the same value as the constant of proportionality.

Anchor Problems - 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.

Online scale image and actual size of Melissa

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

Guiding Questions

Will your scale factor be less than 1 or greater than 1? Why?
If you were looking for the scale factor from the online image to the actual image, would your scale factor be less than 1 or greater than 1? Why?
What are the corresponding lengths in these images?
What percent of the actual length does the scaled length represent?

Notes

If students are stuck, suggest they create a table as in Anchor Problem 1 to identify the scale factor.

Anchor Problems - 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%.

Grid with two arrows, one larger than the other, for scaling demonstration.

Problem Set

View Problem Set

Target Task

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

Two right triangles labeled A and B, with corresponding sides in proportion.

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.

Rectangle with dimensions 5 and 8.2, labeled as C.