Last week, I mentioned to a group of teachers that I had never come up with a good way to teach kids where to shade when graphing an inequality. Vicky from one of our local high schools shared her method with me. It’s pretty nice.
Vicky gives her students an inequality like
She asks them to each find two coordinates that satisfy the inequality, and then plot them on a giant grid at the front of the room. When 30 kids come up and plot points, it will look something like this.
From this graph, it becomes pretty obvious that there is a line involved, and which side of the line we should shade. It also becomes obvious that one kid made a mistake.
We could extend this method to quadratic inequalities. If the students were given the inequality , we could ask students to find ordered pairs that satisfy the inequality, and plot them on a grid at the front. It might look like this.
Students could then have conversations about which of the shading should include the boundary, and which should not, and how to deal with that.