Lesson 5

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.  

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.