Lesson 3Making Scaled Copies

Learning Goal

Let’s draw scaled copies.

Learning Targets

  • I can draw a scaled copy of a figure using a given scale factor.

  • I know what operation to use on the side lengths of a figure to produce a scaled copy.

Lesson Terms

  • corresponding
  • scale factor
  • scaled copy

Warm Up: More or Less?

Problem 1

For each problem, select the answer from the two choices.

  1. The value of is:

    1. More than 205

    2. Less than 205

  2. The value of is:

    1. More than 10

    2. Less than 10

  3. The value of is:

    1. More than 0.2

    2. Less than 0.2

Activity 1: Drawing Scaled Copies

Problem 1

Figure A is a quadrilateral with side lengths 2, 3, 3, and diagonal side up 3 over 1 units. Figure C is a 6 by 3 rectangle with a 2 by 4 rectangle appended to the left top 2 squares and a 1 by 2 rectangle appended to the top right square.

  1. Draw a scaled copy of either Figure A or B using a scale factor of 3.

    open applet in presentation mode

  2. Draw a scaled copy of either Figure C or D using a scale factor of .

    open applet in presentation mode
Print Version
Figure A is a quadrilateral with side lengths 2, 3, 3, and diagonal side up 3 over 1 units. Figure C is a 6 by 3 rectangle with a 2 by 4 rectangle appended to the left top 2 squares and a 1 by 2 rectangle appended to the top right square.

  1. Draw a scaled copy of either Figure A or B using a scale factor of 3.

    A blank grid

  2. Draw a scaled copy of either Figure C or D using a scale factor of .

    A blank grid

Activity 2: Which Operations? (Part 1)

Problem 1

Diego and Jada want to scale this polygon so the side that corresponds to 15 units in the original is 5 units in the scaled copy.

Original polygon is a rectangle of height 30 and length 36 with a rectangle of height 12 and length 15 removed from the bottom right corner.

Diego and Jada each use a different operation to find the new side lengths. Here are their finished drawings.

Diego's drawing has 6 side lengths of 26, 8, 5, 2, 11, and 20, but the sides do not connect to form a closed figure. Jada's drawing is a rectangle of height 10 and length 12 with a rectangle of height 4, length 5 removed from the bottom right corner.

  1. What operation do you think Diego used to calculate the lengths for his drawing?

  2. What operation do you think Jada used to calculate the lengths for her drawing?

  3. Did each method produce a scaled copy of the polygon? Explain your reasoning.

Activity 3: Which Operations? (Part 2)

Problem 1

Andre wants to make a scaled copy of Jada’s drawing so the side that corresponds to 4 units in Jada’s polygon is 8 units in his scaled copy.

A polygon with side lengths 12, 6, 5, 4, 7, and 10.

  1. Andre says “I wonder if I should add 4 units to the lengths of all of the segments?” What would you say in response to Andre? Explain or show your reasoning.

  2. Create the scaled copy that Andre wants. If you get stuck, consider using the edge of an index card or paper to measure the lengths needed to draw the copy.

Are you ready for more?

Problem 1

The side lengths of Triangle are all 5 more than the side lengths of Triangle . Can Triangle be a scaled copy of Triangle ? Explain your reasoning.

Lesson Summary

Creating a scaled copy involves multiplying the lengths in the original figure by a scale factor.

For example, to make a scaled copy of triangle where the base is 8 units, we would use a scale factor of 4. This means multiplying all the side lengths by 4, so in triangle , each side is 4 times as long as the corresponding side in triangle .

Triangle A, B, C has side lengths 2, 1, and 2.24. Triangle D, E, F has side lengths 8, 4, and 8.96.