I put together this three-act activity two years ago, and decided to include it in the playlist for this year’s Math 9 course. The students got right to work in figuring out the total mass of the three bricks together.
This time, I circulated the actual bricks among the students as they worked. I opted not to do this two years ago because I wanted to force them to use the dimensions in the image above to find their answers. The result was that some students chose to make the measurements themselves rather than use the image. This yielded some great interactions between students asking if the bricks were proportional to each other, and those assuming they were proportional. There were some excellent examples of strong explanations involving proportional reasoning among the student work, as well as typical examples of misconceptions, such as the mass being proportional to the scale factor between the sides.
I also did something new with this modeling task and asked students to predict their uncertainty. Often times, students see that they were close to the actual answer revealed in the third act (but not exactly equal), and subsequently classify their answers as wrong. The uncertainties allow more flexibility in this regard. It also revealed some misunderstanding of the relationship between uncertainty and reporting answers that wasn’t unexpected: one student gave 16.895 grams, with an uncertainty of plus or minus 0.1 grams. This is a frequent issue in science classes, but not something I’ve addressed with mathematics students in the past.