# More Inequality Explorations

Over a year ago I hit upon a simple idea related to linear inequality explorations: mapping locations. In this version, with limited iPads at my disposal, I put a list of predetermined locations on the board "demonstrate west of Toyota Center" for example. This year, in my crazy Algebra II experiment, we entered graphing with knowledge of more than just linear functions. In fact, at this point, the idea of quadratic or absolute value inequality was no big deal to any of the students.

Anyway, while discussing the idea of single condition inequalities of all types I retreated back to this mapping activity as a way to discuss multiple conditions in a realer sense. What does it mean to be a valid point within an inequality?  Multiple inequalities?

I pulled up my (not actual) house in Google Maps and discussed how I would describe the location of a Halloween party they weren't invited to:

It wasn't hard to grasp the idea that discussing the house this way helped narrow down its location. Given a driver with decent knowledge of the city, this might be enough to place the address.

Idea in hand, I passed out iPads, styluses (stylii?) and gave them their instructions:

• Given six locations: your house, your middle school, our high school, the US Capitol, Empire State Building, and free choice
• Locate four of these items on a Map
• Screenshot the map
• Find two ways to describe the location

I gave a brief tutorial on Google Drive export, but since they had to submit four items, they got it down after a bit.

Results were pretty good. This took 40 minutes or so of class time. I used to jump off on their task for the next day.

### The Extension

The next class day we explored multiple inequality conditions created by all sorts of functions. I prepared and array of points and had them test where they were valid. There were a set of 5 condition groups they tested.

Going further, later they were given other conditions and we created sketches of the entire solution region and attempted to describe the domain and range of them.

The most enlightening thing for me about this task is that it would be much more cumbersome without a modern graphing utility. The plots could be done by hand or with a TI, yes. But what is my goal here? To be able to discuss the nature of meeting a condition, or watch kids struggle to even get there because they took 20 minutes to make one pair of graphs?

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