One of my favorite such examples is when the Scarecrow inaccurately recites the Pythagorean Theorem once a brain is decreed upon him (note also how Scarecrow magically moves from the middle of the characters to the far right of the frame after confronting the Wizard). His mishap is recreated by a glasses-wearing Homer Simpson who makes the same mistake, but is corrected by a gentleman in the bathroom stall behind him.
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I paraphrase what the Scarecrow said when first meeting Dorothy (pictured at left): "We can go both ways." The same can be said of absolute values, in that they measure the same distance from a central reference point; in the general case, a number's distance from zero.
In introducing the concept of absolute value this year in Algebra 2, I emphasized greatly the importance of that feature, that absolute value equations would measure the same distance from a central reference point. Refer to the example here:
Solve the equation | x - 2 | = 3. Check your solutions in the original equation.
They started talking, but only focusing on using that distance in the positive direction, citing 5 as the only solution. This diagram helped them clarify that -1 is also 3 units away from 2. We substituted each value back into the original equation to check our work and conclude that each apparent solution was indeed a valid solution (a great time to introduce the idea of extraneous solutions and emphasize how our conclusion would have differed if we were discussing money, volume, unit sales, and other applications.
I then decided to give an open-ended task to end class that day. I asked students to find something in real life around them that involved the same distance away from a central point. The example I gave was that I parked my car that morning so it was the same distance away from the striped lines on each side of my parking spot, making sure to point out how disappointed I would be if all students returned the next day having simply taken a photo of their car in the parking lot. They came through with some great examples, as shown in the slide show below.
I aim to do more of these sort of open-ended, scavenger hunt-like examples where students find examples of math around them. I'll call it "Have My Stu's Do A 101Q" to give proper credit to Dan Meyer's 101qs.com website for posting examples of photos meant to drive student curiosity. I might even be able to coerce some of them into posting to Twitter with a class-named hashtag. Only time will tell. Like the Scarecrow said, it "could go both ways."