Lesson 5

The Size of the Scale Factor

Lesson Narrative

In this lesson, students deepen their understanding of scale factors in two ways:

  1. They classify scale factors by size (less than 1, exactly 1, and greater than 1) and notice how each class of factors affects the scaled copies (MP8), and

  2. They see that the scale factor that takes an original figure to its copy and the one that takes the copy to the original are reciprocals (MP7). This means that the scaling process is reversible, and that if Figure B is a scaled copy of Figure A, then Figure A is also a scaled copy of Figure B.

Students also continue to apply scale factors and what they learned about corresponding distances and angles to draw scaled copies without a grid.

Two of the activities, Scaling a Puzzle, and Missing Figure, Factor, or Copy, are optional. In Scaling a Puzzle, students scale the 6 pieces of a puzzle individually and then assemble them to make a scaled copy of the puzzle. The individual pieces are rectangular with line segments partitioning them into regions. Students need to think strategically about which measurements to take in order to scale the pieces accurately. In Missing Figure, Factor, or Copy, students gain fluency dealing with the different aspects of scaled copies, supplying the missing information in each case.  


Learning Goals

Teacher Facing

  • Describe (orally and in writing) how scale factors of 1, less than 1, and greater than 1 affect the size of scaled copies.
  • Explain and show (orally and in writing) how to recreate the original figure given a scaled copy and its scale factor.
  • Recognize (orally and in writing) the relationship between a scale factor of a scaled copy to its original figure is the “reciprocal” of the scale factor of the original figure to its scaled copy.

Student Facing

Let’s look at the effects of different scale factors.

Required Preparation

Print and cut sets of slips for the sorting activity from the Scaled Copies Card Sort blackline master. Make enough copies so that each group of 3–4 students has a set. If possible, copy each complete set on a different color of paper, so that a stray slip can quickly be put back.

Print and cut puzzle pieces and blank squares for the Scaling a Puzzle activity from the Scaling a Puzzle blackline master. Make enough copies so that each group of 3 students has 1 original puzzle and 6 blank squares.

Make sure students have access to their geometry toolkits—especially rulers and protractors.

Learning Targets

Student Facing

  • I can describe the effect on a scaled copy when I use a scale factor that is greater than 1, less than 1, or equal to 1.
  • I can explain how the scale factor that takes Figure A to its copy Figure B is related to the scale factor that takes Figure B to Figure A.

CCSS Standards

Building On

Addressing

Building Towards

Glossary Entries

  • corresponding

    When part of an original figure matches up with part of a copy, we call them corresponding parts. These could be points, segments, angles, or distances.

    For example, point \(B\) in the first triangle corresponds to point \(E\) in the second triangle. Segment \(AC\) corresponds to segment \(DF\).

    2 triangles with corresponding parts
  • reciprocal

    Dividing 1 by a number gives the reciprocal of that number. For example, the reciprocal of 12 is \(\frac{1}{12}\), and the reciprocal of \(\frac25\) is \(\frac52\).

  • scale factor

    To create a scaled copy, we multiply all the lengths in the original figure by the same number. This number is called the scale factor.

    In this example, the scale factor is 1.5, because \(4 \boldcdot (1.5) = 6\), \(5 \boldcdot (1.5)=7.5\), and \(6 \boldcdot (1.5)=9\).

    2 triangles
  • scaled copy

    A scaled copy is a copy of a figure where every length in the original figure is multiplied by the same number.

    For example, triangle \(DEF\) is a scaled copy of triangle \(ABC\). Each side length on triangle \(ABC\) was multiplied by 1.5 to get the corresponding side length on triangle \(DEF\).

    2 triangles

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