To review linear functions in my Algebra class, I presented this pattern from Visual Patterns:
I asked students how we could represent this pattern and what questions we could ask about it. Most determined that we should represent the pattern with a table, graph, and equation (rule).
A student asked, “Should we write a rule for the number of green hexagons or the total number of hexagons in the figure?”
I could have answered with one or the other (or both). I could have let them choose. But here was an opportunity for an extension. I wrote on the board, “What changes in our representations if we use the number of total hexagons rather than just the green hexagons?”
Lots of good discussion ensued. Misconceptions about the effects of change in slope versus change in y-intercept were addressed. It was much more productive than if I had just answered the question as asked. Student questions can be great jumping off points for further investigations. Harness the brain power that’s in the room and use it to everyone’s advantage.