Painted Cube (again!)

Today another group of grade 10s worked on the painted cube rich task (blogged earlier).

As always when doing this problem, something new shows up as students interpret it differently, or work to make connections to math that they know.

This group decided to represent the blocks as a fraction of the whole. This makes me see all kinds of connections to fractions and percents, or patterning about what happens to these fractions or percents as the cube’s side length increases.

Something I’d be curious to explore with a class is modelling the patterns you’d see in the fractions. This would be an interesting task for grade 11s and 12s I think, as an inquiry into the rational functions. There could be discussion about vertical asymptotes and end behaviours.

These functions could be graphed, and then the intersections between them could be calculated too.

We didn’t go down that road with these grade 10s because they were struggling a bit with the initial task and building general equations for a cube with side length x, and were not ready to push into new territory.

It’s so refreshing to see new ideas and approaches pop up with each new iteration of the task.

Good teamwork today!