# Zero-Knowledge Proofs

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## Graphing Inequalities

November 3, 2011 by John Scammell

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 $2x-y \le 7$

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 $y>x^2+3x-2$ , 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.

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Posted in Math 20-1 | Tagged Math 20-1 | 3 Comments

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1. Love this – I used something similar to this (because I went through so many GReader posts last night, I couldn’t remember it exactly). I had students choose a point in our grid (both x and y went from -6 to 6) and test it in the inequality to see if it worked. We plotted the ones that did and then I went through with them the process. The second and third times I did it with my students, I had them plot the points on their example paper before we actually graphed the inequality on the same grid. In my last class, right after I had students graph the line but before we shaded the half that worked, one of my students who normally struggled said “Oh, I get it!” even before we talked about how to determine which half to shade. That was really cool! Thanks for sharing!

2. Nice, simple method to help students understand what is usually just a procedure to them (1. Graph line (or parabola or …). 2. Dashed line if… solid line if…. 3. Test a coordinate point. 4. Shade appropriately.).

If we can get our students to understand the idea, I am confident they will have no trouble remembering the procedure, since they can just recreate it themselves.

3. [...] reading John Scammell’s recent post on linear inequalities, I realized that I had it backwards. I’d begin by graphing the line. I’d explain that a [...]

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