Lesson 1Projecting and Scaling
Learning Goal
Let’s explore scaling.
Learning Targets
I can decide if one rectangle is a dilation of another rectangle.
I know how to use a center and a scale factor to describe a dilation.
Lesson Terms
- scale factor
Warm Up: Number Talk: Remembering Fraction Division
Problem 1
Find each quotient. Write your answer as a fraction or a mixed number.
Activity 1: Sorting Rectangles
Problem 1
Rectangles were made by cutting an
Some of the rectangles are scaled copies of the full sheet of paper (Rectangle
). Record the measurements of those rectangles in this table. rectangle
length of short side (inches)
length of long side (inches)
Some of the rectangles are not scaled copies of the full sheet of paper. Record the measurements of those rectangles in this table.
rectangle
length of short side (inches)
length of long side (inches)
Look at the measurements for the rectangles that are scaled copies of the full sheet of paper. What do you notice about the measurements of these rectangles? Look at the measurements for the rectangles that are not scaled copies of the full sheet. What do you notice about these measurements?
Stack the rectangles that are scaled copies of the full sheet so that they all line up at a corner, as shown in the diagram. Do the same with the other set of rectangles. On each stack, draw a line from the bottom left corner to the top right corner of the biggest rectangle. What do you notice?
Stack all of the rectangles from largest to smallest so that they all line up at a corner. Compare the lines that you drew. Can you tell, from the drawn lines, which set each rectangle came from?
Are you ready for more?
Problem 1
In many countries, the standard paper size is not 8.5 inches by 11 inches (called “letter” size), but instead 210 millimeters by 297 millimeters (called “A4” size). Are these two rectangle sizes scaled copies of one another?
Activity 2: Scaled Rectangles
Problem 1
Here is a picture of Rectangle
Is
a scaled copy of ? If so, what is the scale factor? Is
a scaled copy of ? If so, what is the scale factor? Is
a scaled copy of ? If so, what is the scale factor?
Lesson Summary
Scaled copies of rectangles have an interesting property. Can you see what it is?
Here, the larger rectangle is a scaled copy of the smaller one (with a scale factor of