Vertical Dilation

My algebra 2 students are learning about various function transformations and I was trying to think of a way to make this topic a little more engaging.  My students are all wild about silly bands (I'm not sure why... They're still pretty excited about the fact that the silly bands always maintain their shape no matter how stretched they become) so I thought it would be pretty fun to see if we could explore vertical dilation through silly bands.  This led to kind of a neat little warm up, but I think it was maybe a little more prep than the educational content was worth.

I cut out squares of cardboard and taped graph paper to them.  Then I let the students choose their own silly bands out of a selection:

The students had a lot of fun picking out their silly bands at least.  The robot shaped ones were the most popular.

I then had them put their silly bands against the graph paper and draw a coordinate axis.  They were told to plot at least 10 points that their silly bands went through.  I asked them to double all their y-values and plot the points on their cardboard graph paper with thumb tacks.  They then tried to stretch their silly bands over the tacks to see how the shapes of their rubber bands changed:

This was a cup cake shaped silly band.

It was a nice visual because in the past, I've had students get confused because a parabola that's been stretched vertically by a factor of 2 looks skinnier, so students thought that it must have been multiplied by 1/2 instead of 2.  This activity I think showed them that multiplying by a number bigger than 1 made the object taller and skinnier, while a multiplication by 1/2 would make it shorter and fatter.

It was kind of anti-climactic however when we just launched right into normal classwork after this activity.  I would love to find a way to pull this idea into a larger lesson plan rather than just a warm up problem.