Lesson 5The Size of the Scale Factor
Learning Goal
Let’s look at the effects of different scale factors.
Learning Targets
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.
Lesson Terms
- corresponding
- reciprocal
- scale factor
- scaled copy
Warm Up: Number Talk: Missing Factor
Problem 1
Solve each equation mentally.
Activity 1: Scaled Copies Card Sort
Problem 1
Your teacher will give you a set of cards. On each card, Figure A is the original and Figure B is a scaled copy.
Sort the cards based on their scale factors. Be prepared to explain your reasoning.
Examine cards 10 and 13 more closely. What do you notice about the shapes and sizes of the figures? What do you notice about the scale factors?
Examine cards 8 and 12 more closely. What do you notice about the figures? What do you notice about the scale factors?
Are you ready for more?
Problem 1
Triangle
How many times bigger are the side lengths of Triangle
when compared with Triangle ? Imagine you scale Triangle
by a scale factor of to get Triangle . How many times bigger will the side lengths of Triangle be when compared with Triangle ? Triangle
has been scaled once. Triangle has been scaled twice. Imagine you scale triangle times to get Triangle , always using a scale factor of . How many times bigger will the side lengths of Triangle be when compared with Triangle ?
Activity 2: Scaling a Puzzle
Problem 1
Your teacher will give you 2 pieces of a 6-piece puzzle.
If you drew scaled copies of your puzzle pieces using a scale factor of
, would they be larger or smaller than the original pieces? How do you know? Create a scaled copy of each puzzle piece on a blank square, with a scale factor of
. When everyone in your group is finished, put all 6 of the original puzzle pieces together like this:
Next, put all 6 of your scaled copies together. Compare your scaled puzzle with the original puzzle. Which parts seem to be scaled correctly and which seem off? What might have caused those parts to be off?
Revise any of the scaled copies that may have been drawn incorrectly.
If you were to lose one of the pieces of the original puzzle, but still had the scaled copy, how could you recreate the lost piece?
Activity 3: Missing Figure, Factor, or Copy
Problem 1
What is the scale factor from the original triangle to its copy? Explain or show your reasoning.
Problem 2
The scale factor from the original trapezoid to its copy is 2. Draw the scaled copy.
Problem 3
The scale factor from the original figure to its copy is
Problem 4
What is the scale factor from the original figure to the copy? Explain how you know.
Problem 5
The scale factor from the original figure to its scaled copy is 3. Draw the scaled copy.
Lesson Summary
The size of the scale factor affects the size of the copy. When a figure is scaled by a scale factor greater than 1, the copy is larger than the original. When the scale factor is less than 1, the copy is smaller. When the scale factor is exactly 1, the copy is the same size as the original.
Triangle
This means that triangles
In other words, if we scale Figure A using a scale factor of 4 to create Figure B, we can scale Figure B using the reciprocal scale factor,