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The Unit Rate as the Scale Factor

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Lesson Plans and Worksheets for Grade 7
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More Lessons for Grade 7
Common Core For Grade 7

Examples, solutions, and videos to help Grade 7 students learn to recognize the scale factor to be the constant of proportionality.

New York State Common Core Math Grade 7, Module 1, Lesson 17

Download the Worksheets for Grade 7, Module 1, lesson 17 (pdf)

Student Outcomes

Students recognize that the enlarged or reduced distances in a scale drawing are proportional to the corresponding distance in the original picture.

Students recognize the scale factor to be the constant of proportionality.

Given a picture or description of geometric figures, students make a scale drawing with a given scale factor.

Example 1: Rubin’s Icon

Rubin created a simple game on his computer and shared it with his friends to play. They were instantly hooked and the popularity of his game spread so quickly that Rubin wanted to create a distinctive icon, so players could easily identify his game. He drew a simple sketch. From the sketch, he created stickers to promote his game, but Rubin wasn’t quite sure if the stickers were proportional to his original sketch.

Steps to check for proportionality for scale drawing and original object/picture:

1. Measure lengths of scale drawing. Record on table.
2. Measure corresponding lengths on actual picture/drawing. Record on table.
3. Check for constant of proportionality.

Key Idea:

The scale factor can be calculated from the ratio of any length in the scale drawing to its corresponding length in the actual picture. The scale factor corresponds to the unit rate and the constant of proportionality.

Scaling by factors greater than 1, enlarge the segment, and scaling by factors less than 1, reduce the segment.

Example 2

Use a scale factor of 3 to create a scale drawing of the picture below.

Example 3

Your family recently had a family portrait taken. Your aunt asked you to take a picture of the portrait using your cell phone and send it to her. If the original portrait is 3 feet by 3 feet and the scale factor is 1/18 ' draw the scale drawing that would be the size of the portrait on your phone.

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