Dilation Constructions Mini-Project

As you may know from wherever you are currently reading this, it's been quite a winter so far in the great Northeast. We've already used 2 snow days and have had a 2 hour delay for cold, along with a fair number of cancelled after school activity days. Not to mention we've had a ton of stomach bugs and the flu bouncing from student to student like a pinball game. Needless to say, the best laid plans of math teachers have gone astray once or twice.

Since we run on an A/B day schedule and almost all of our time lost has been on B days, one of my geometry with lab classes inevitably zoomed in front of the other. In an effort to get them back on track, I designed this mini-project for my class that was light years ahead. I liked that it was creative, gave them some choice, and had them really practice the skills of constructing a dilation. Understanding the construction so strongly ties to the conceptual understanding of both dilations and similarity, so I knew this wouldn't be time wasted. 

You don't need much for the project. To prep, I printed tons of tiny images of famous characters. I went cartoons, but you could have kids bring in their own or design their own "logo." I had students put a dot at the center of the top of a sheet of printer paper, then glue down the original. This would be our pre-image and our center. From there, we started constructing! Students identified significant points and then created a "connect the dots" to help them draw the dilated figure. Many experimented with scale factor, trying to find the one that would be the largest without falling off of the page. 

After completing their dilations, students wrote a reflection relating what they'd done that day to the Desmos activity (Working with Dilations) we'd been working on prior to the activity. They needed to discuss center, projection lines, scale factor, and ratios. I've seen this play out in a deeper understanding of dilations in the remainder of our unit and a stronger ability to work with centers off the origin and dilations off the coordinate plane in general. 

Here are a few of my favorites!