# Linear Inequality Exploration

We aren't quite to this topic yet, but it will come up soon enough. I thought I'd share an interesting exploration activity for Linear Inequalities. Well, specifically the graphs of the linear inequalities. Simple linear graphs are something they see in Algebra I and they maybe get to the inequality version in Algebra I, but you never know. Last year while teaching this I had a kid ask the dreaded "when would we use this?" and I was able to come up with something related to optimized profit regions or something. It wasn't bad, but I think this will help too. This is a rough outline. There will probably be discussion questions related to this as well or something for them to follow along with. My Algebra numbers are low enough that I can manage 2-3 kids per iPad easily.

Needed items: iPads, Maps app (built-in), SketchBook Express (free)

Intro: Presented with a landmark, describe where I live, in whatever method seems right to you.

Step 2: Represent what it means to live "east of Blalock":

Step 3: Narrow the area a little more. Would it help to use another reference street? Does "north of Long Point" help?

Step 4: Could we refine this more? Could "south of Campbell" help also? How many iterations would it take to get an accurate idea of where I live?

After modeling this, assign locations for the students to find, have them represent the location of their landmark using a graph AND include a description that someone could use to narrow down the search area.

Going further questions:

• Is two streets enough to figure out where someone lives? Is three streets too much to remember? What about four?
• How would this apply to search and rescue?
• Why am I designating the streets with dashed lines instead of solid lines?
• How could we represent "east of Blalock" as an inequality? Should we consider "east" as greater than or less than?
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