A page with a cartoon figure was Xeroxed from S&S.
The activity consists of using two connected rubber bands, with the knot tracing the original figure and the pencil in the outer loop, to trace a copy of the figure scaled up by a factor of 2. [This is a physical model of the mathematical concept of dilation.]
Questions were asked about why the figure is scaled. [To see this it helps to look one segment at a time.] Also what would happen with other combinations of rubber bands, etc., to get other ratios than 2?
Practical note -- Use new rubber bands. A lot of ours were in pieces.
Students take points (3,4), (7, 6), (4, 11) from overhead. Plot these points on graph paper and draw a triangle ABC with these vertices.
Plot new triangle A'B'C' by changing (x,y) to (3x, 3y).
Check that this could have been drawn by the "rubber band" (dilation) method. [The center is (0,0). They can see this by drawing lines AA', BB', CC'.]
After checking this out, they are asked to do the same for the following rules:
(x,y) -> (2x+1, 2y-1)
(x,y) -> (2x, 3x)
(x,y) -> (-x, -y)
Many of the group got through one of these additional rules. Time ran out for most before getting to the other rules. This kind of transformation appears again in Inv 2 and the homework.