Changing Scales

Examples, videos, and solutions to help Grade 7 students when given Drawing 1 and Drawing 2 (a scale model of Drawing 1 with scale factor), they understand that Drawing 1 is also a scale model of Drawing 2 and compute the scale factor.

New York State Common Core Math Grade 7, Module 4, Lesson 13

Worksheets for Grade 7

Lesson 13 Student Outcomes

• Given Drawing 1 and Drawing 2 (a scale model of Drawing 1 with scale factor), students understand that Drawing 1 is also a scale model of Drawing 2 and compute the scale factor.
• Given three drawings that are scale drawings of each other and two scale factors, students compute the other related scale factor.

Lesson 13 Summary

To compute the scale factor from one drawing to another, use the representation:
Quantity = percent × whole
where the whole is the length in the actual or original drawing and the quantity is the length in the scale drawing.
If the lengths of the sides are not provided but two scale factors are provided, use the same relationship but use the scale factors as the whole and quantity instead of the given measurements.

Lesson 13 Classwork

A scale drawing is a reduction of the actual drawing when the corresponding lengths of the scale drawing are smaller than the lengths in the actual drawing and when the scale factor is less than 100%.
A scale drawing is an enlargement of the actual drawing when the corresponding lengths of the scale drawing are larger than the lengths in the actual drawing and when the scale factor is greater than 100%.

Opening Exercise
Describe Scale Factor, using percentages, the difference between a reduction and an enlargement. Use the two drawings below to complete the chart. Calculate the first row (Drawing 1 to Drawing 2) only.
Compare Drawing 2 to Drawing 1. Using the completed work in the first row, make a conjecture (statement) about what the second row of the chart will be. Justify your conjecture without computing the second row.
Compute the second row of the chart. Was your conjecture proven true? Explain how you know.

Example 1
The scale factor from Drawing 1 to Drawing 2 is 60%. Find the scale factor from Drawing 2 to Drawing 1. Explain your reasoning.

Example 2
A regular octagon is an eight-sided polygon with side lengths that are all equal. All three octagons are scale drawings of each other. Use the chart and the side lengths to compute each scale factor as a percent. How can we check our answers?

Example 3
The scale factor from Drawing 1 to Drawing 2 is 112% and the scale factor from Drawing 1 to Drawing 3 is 84%. Drawing 2 is also a scale drawing of Drawing 3. Is Drawing 2 a reduction or an enlargement of Drawing 3? Justify your answer using the scale factor. The drawing is not necessarily drawn to scale.
Explain how you could use the scale factors from Drawing 1 to Drawing 2 (112%) and from Drawing 2 to Drawing 3 (75%) to show that the scale factor from Drawing 1 to Drawing 3 is 84%.

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