Math 8 – We continued with painted cubes today and several groups were able to start making generalizations. It was so great to see. There were lots of wins today. One student was so happy once she started to see that the cubes with 1 face painted increased with squares. She saw that if there was a 9x9x9 cube, the # of cubes with one face painted would be 7×7, and there would be 6 faces like that. Huge high-five! Check out the whiteboard below.
Math 8 – Today the class started on the “Painted Cubes” problem. I figured this problem would be quite difficult for them, and I’m structuring the problem to focus on two things. First, I want students to use a problem solving strategy that helps them move from a specific case to a general case. Secondly, this problem is used to reinforce that squares, cubes, square roots and cube roots are not abstract ideas with weird symbols, but that they have physical meanings.
The students first have to understand what they know – the problem setup. Next, they have to be clear on what they’re looking for and what they want. To begin with this is the # of cubes that will have 3 faces painted, 2 faces painted, 1 face painted and 0 faces painted. What they’re doing today is solving a first specific example of this problem: a 3x3x3 cube. This is specialization. We’ll do a few more specializations, and then try a generalization.
In the top photo you can see a good example of the students checking their solution. They knew they needed 27 cubes in total, and the solution in the bottom right corner didn’t allow them to have a cube with 0 faces painted.
The other photos show how some groups are trying to specialize with a 4x4x4 cube, and how to record their information in a way that makes sense.