9/12/17 EDIT: I haven’t taught Geometry since the Fall 2015 semester and this is still one of my favorite activities from the last three years. I also enjoy Classifying Solutions to Systems of Equations and Maximizing Profits: Selling Boomerangs.
Any time I talk about MAPs on here it’s almost always going to be referencing the The Mathematics Assessment Project. I love this resource. Some of the tasks and lessons have worked better than others – sometimes I have poor classroom management, my students aren’t engaged, or the concepts are too abstract for them – but I try to do at least one a month with one of my classes. This MAP was the best one we’ve done yet.
We had been talking about nets, surface area, and volume for 4 days. During those days the students did problems involving surface area and volume of prisms, cylinders, cones, pyramids, and spheres, as well as compound solids. They were cruising right along using their formula sheet and were mostly able to figure out when to use trig ratios or the Pythagorean Theorem to help them complete their calculations. The next day life became a little more difficult for them:
What are similar solids and how do we know that they are similar?
We have already learned about similar triangles and polygons, so we only spent half a class period discussing what similar solids were and how we can check their scale factors (or ratios or whatever it is that you call them) to see whether or not solids are similar.
But then we started to get more abstract. What if I double a rectangular prism’s length? What happens to the surface area and volume? Is this going to be true for ANY rectangular prism whose length gets doubled? It was like the world was ending! After I encouraged them to draw some pictures and try to come up with a statement as a group, the ball got rolling.
The MAP lesson that we did is titled Evaluating Statements About Enlargements. A brief overview of the MAP (the MAP itself has very explicit instructions, including questions/prompts for teachers to ask whole group and small group):
- Students were in groups of 3-4. You are supposed to group them based on their responses to the pre-assessment, and I do that to an extent.
- After some whole group discussion about the previously mentioned questions, each group received a piece of butcher paper, glue stick, and statement cards.
- As a group, the students had to determine which of the statements were always true, and which of the statements were false. They had to provide either a pictoral or written explanation on their butcher paper for each choice once they agreed as a group.
- If they believed a statement was false, they were challenged to alter it to create a true statement.
After all of the groups worked on this, we did a gallery walk where students made comments and asked questions. I need to get better at helping my students be a productive part of the feedback process! Then we reviewed the statements together as a class and worked through any misconceptions that still existed.
From the beginning of the MAP, students were engaged. There were drawings. There were calculations. There were arguments. It was great! Most of my students were not at a point where they could extrapolate using their own words to the idea of a:b, a^2:b^2, and a^3:b^3 but I didn’t mind that. We discussed that together as a class at the end and I think they understood well enough to remember it, or at least well enough to take the time to figure out these types of problems every time.