Last year when students took a math assessment, many could not visualize the volume problems they had to solve. Because of this I ordered a collection of cubes to better the lessons this year.
Yesterday I taught the lesson twice. During the lesson we explored the properties of cubes and rectangular prisms. Students built structures that matched drawings and we focused on the cubes you could see and then the cubes you could not see. Later, working with partners, they made as many different rectangular prisms as they could with 36 cubic units.
The first two times went well, but I clearly had to give the directions a bit better and partner the students with greater care. The third time around, I heeded those lessons and the activity went much better. In fact a good question arose which was how many different cubes can we make with these blocks and what are the dimensions of the cubes we can make. Of course once students started exploring this, they would quickly realize that the dimensions of a cube are equal and the bases are square numbers. We may do that exploration at another time.
Our next exploration will involve order of operations. A fun way to do this would be to give students sticky notes with each operation and four different numbers. Then students could arrange the sticky notes in many different ways to come up with expressions that equal more or less. We may do this. The satisfaction of a good lesson is great, and with regard to the two trial lessons yesterday, those events match a quote I heard that columnist Susan Wagner noted, a quote from her husband's family that bumps become boosts (or you can learn from your mistakes). Onward.