That is simultaneously a lot of unused and (now) unusable cardboard. I see this a lot, and it’s an issue I’ve been wanting to address for a while.
Here’s my plan. I wanted my students to arrive at the understanding that, when planned with purpose, you can get a lot out of a material (whether its cardboard, foam, etc.). If you cut out of the middle, you get far less. So I borrowed some math manipulatives from my sister-in-law and sketched out a quick activity;
How it works. I asked my students to pair up, then I gave them each an activity sheet and a tray of pre-sorted shapes. We talked about what a resource was and what it meant to be efficient. I showed them the piece of cardboard pictured above. Then I worked through this slide deck, challenging the students to fit shapes into various spaces.
The results. While working together to fit the shapes into the spaces, it was as close to 100% engagement as I’ve ever had. Kids loved it, and several exclaimed that they didn’t think that many shapes could fit into such a small space. Several kids even made the connection between lining up the end of the shapes with the edge of the box to maximize efficiency. It was awesome. We reflected how we might use this in our MYP Design practice, and before we knew it class was over.
Tips, tricks, and what I’d change. First, I’d rearrange the activity sheet so that the boxes with the cutouts were on top, since we’re doing those first. Second, I’d go over everything BEFORE handing out the plastic pieces. Total noob mistake right there. Third, I don’t know how to create this digitally because I needed the exact area the shapes would take up. Here’s a picture of a possible solution for the large box. If anyone knows how to make that box using Google Draw so that it prints out to be exactly 8cmx9cm on an A4 size paper, let me know. Finally, have an example to show the kids. I’ve been keeping that piece of cardboard just in case, and I’m really glad I did. I think having that piece of evidence really solidified their understanding of our problem.