This week your student will learn about scaling shapes. An image is a scaled copy of the original if the shape is stretched in a way that does not distort it. For example, here is an original picture and five copies. Pictures C and D are scaled copies of the original, but pictures A, B, and E are not.

In each scaled copy, the sides are a certain number of times as long as the corresponding sides in the original. We call this number the scale factor. The size of the scale factor affects the size of the copy. A scale factor greater than 1 makes a copy that is larger than the original. A scale factor less than 1 makes a copy that is smaller.

Here is a task to try with your student:

1. For each copy, tell whether it is a scaled copy of the original triangle. If so, what is the scale factor?
2. Draw another scaled copy of the original triangle using a different scale factor.

Solution:

1. 1. Copy 1 is a scaled copy of the original triangle. The scale factor is 2, because each side in Copy 1 is twice as long as the corresponding side in the original triangle. , ,
   2. Copy 2 is a scaled copy of the original triangle. The scale factor is or 0.5, because each side in Copy 2 is half as long as the corresponding side in the original triangle.  , ,
   3. Copy 3 is not a scaled copy of the original triangle. The shape has been distorted. The angles are different sizes and there is not one number that we can multiply by each side length of the original triangle to get the corresponding side length in Copy 3.
2. Answers vary. Sample response: A right triangle with side lengths of 12, 15, and 19.2 units would be a scaled copy of the original triangle using a scale factor of 3.