As an introduction to graphing linear inequalities, I asked students to write down all of the questions about this picture.
- What is the solution?
- What do the shaded areas mean? Do their edges count for lines?
- y does one of the lines have no slope?
- Why is the line dotted?
- whats the intercepts?
I had already planned on teaching students about solid and dashed lines, which side to shade on, and what are the solutions of a linear inequality. Because students asked the questions, they had much more interest when we discussed these topics. They were also enthusiastic about coming up with the answers themselves. Students wanted to answer the questions their peers asked and they were pretty confident in justifying their answers. Letting students ask the questions always leads to higher engagement.