Unit 2, Lesson 1
Projecting and Scaling
Grade 8
1.2
Activity
Sorting Rectangles
Rectangles are made by cutting an
An image of an 8 point 5 by 11 inch rectangle. A dashed line divides the entire rectangle in half and one rectangle is labeled B. A dashed line divides the other half of B and one rectangle is labeled C. A dashed line divides the other half of C and one rectangle is labeled D. A dashed line divides the other half of D and both rectangles are labeled E.
- Some of the rectangles are scaled copies of Rectangle A (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) A 11 - Some of the rectangles are not scaled copies of Rectangle A (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?
- Look at the measurements for the rectangles that are not scaled copies of the full sheet. What do you notice?
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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? What do you notice?
1.3
Activity
Scaled Rectangles
Here is a picture of Rectangle R, which has been evenly divided into smaller rectangles. Two of the smaller rectangles are labeled B and C.
- Is B a scaled copy of R? If so, what is the scale factor?
- Is C a scaled copy of B? If so, what is the scale factor?
- Is C a scaled copy of R? If so, what is the scale factor?
Student Lesson Summary
In this diagram, the larger rectangle is a scaled copy of the smaller one, and the scale factor is
A small rectangle inside a larger rectangle with same lower left point and a dashed diagonal line from that lower left point through both upper points. The small rectangle has length 4 and height 2. The large rectangle has length 6 and height 3.
None
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