The Size of the Scale Factor

Aim: Soring out Objects Based on Scale Factor.

Here is a set of cards. On each card, Figure A is the original and Figure B is a scaled copy.

(1). Sort the cards based on their scale factors. Be prepared to explain your reasoning.

(2). 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?

(3). Examine cards 8 and 12 more closely. What do you notice about the figures? What do you notice about the scale factors?

Aim: Naming a Scale Factor.

What is the scale factor from the original triangle in the applet below to its copy? Explain or show your reasoning.

The scale factor from the original trapezoid to its copy is 2. Draw the scaled copy.

The scale factor from the original figure to its copy is ³⁄₂. Draw the original figure.

What is the scale factor from the original figure to the copy in the applet below? Explain how you know.

The scale factor from the original figure to its scaled copy is 3. Draw the scaled copy.

Aim: To investigate the relationship Between Scale Factor and Area of a Figure.

Use the slider below to explore the relationships between scale factor, perimeter, and area.

(1). As Square B doubles in size compared to Square A, what happens to Square B’s perimeter compared to Square A?

(2). As Square B doubles, triples, etc. in size compared to Square A, what happens to Square B’s area compared to Square A?

(3). If Square B is 5 times larger than Square A, explain how you could determine the Square B’s perimeter and area.

(4). What is the relationship between scale factor and perimeter?

(5). What is the relationship between scale factor and area?

Rectangles P, Q, R, and S are scaled copies of one another. Use the to answer All the challenge questions below.