Question

activity 3 scaling a puzzle your teacher will give you 2 pieces of a 6 - piece puzzle. a. if you drew scaled copies of your puzzle pieces using a scale factor of 1/2, would they be larger or smaller than the original pieces? how do you know? b. create a scaled copy of each puzzle piece on a blank square, with a scale factor of 1/2. c. when everyone in your group is finished, put all 6 of the original puzzle pieces together like this: a 2x3 grid with numbers 1 - 6 in the squares 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? d. revise any of the scaled copies that may have been drawn incorrectly. e. 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?

Explanation:

Step1: Understand scale - factor concept

A scale factor of $\frac{1}{2}$ means the new size is half of the original.

Step2: Answer part a

The scaled - copies would be smaller. Since the scale factor $\frac{1}{2}<1$, each dimension of the new pieces is half of the original dimensions.

Step3: Answer part b

To create a scaled copy with a scale factor of $\frac{1}{2}$, measure each side length of the original puzzle piece and divide it by 2, then draw the new piece with the calculated side - lengths.

Step4: Answer part c

If the scaled puzzle seems off, possible reasons could be inaccurate measurement while scaling (e.g., incorrect division by 2 when measuring side - lengths), or errors in drawing the scaled shapes.

Step5: Answer part d

Check the side - lengths of the incorrectly drawn scaled copies against the correct scaled measurements (half of the original side - lengths) and redraw them accurately.

Step6: Answer part e

Since the scale factor from the scaled copy to the original is 2 (the reciprocal of $\frac{1}{2}$), measure each side length of the scaled piece and multiply it by 2 to get the side - lengths of the original piece, then draw the original piece with the calculated side - lengths.

Answer:

a. The scaled copies would be smaller because the scale factor $\frac{1}{2}<1$.
b. Measure each side of the original piece and divide by 2 to draw the scaled copy.
c. Possible reasons for off - parts are inaccurate measurement or drawing errors.
d. Check side - lengths against the correct scaled measurements (half of original) and redraw.
e. Multiply each side length of the scaled piece by 2 to recreate the lost original piece.