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I do try to lead my kids to notice that the distance formula = the pythagorean theorem = the formula for a circle. I also point out the relationships between distance on a number line, distance int he cartesian plane and distance in 3 space. In and of itself, it is a useless formula. When you help uncover connections then some math can stick.

I also totally endorse the banning of FOIL. I simply refer to it as that four letter F word that I will not use.

]]>On a personal note, I remember the day I was taught the distance formula: we were not shown its derivation, but the teacher was going slow enough for me to figure out I could draw the triangle and Pythagorean-it before she finished giving us notes. But, when she did give us the formula, it was somehow different from the one I created (probably subtracted x2 from x1, while I did it the other way), and I didn’t recognize until much later that they were equivalent, so I resigned myself to memorizing another math fact and stopped exploring on my own.

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