The radical as a chuppah

Have I mentioned that I have my own unorthodox ways of describing math processes? I refer to the ubiquitous unwritten one in algebra as sneaky one or as his evil twin negative sneaky one (who often trips up students). I tell my students (in a Catholic school) that the absolute value sign works a lot like going into a confessional. If you have sinned (a negative), you leave forgiven ( a positive). If you had no sin (a positive), you still leave forgiven (a positive). Of course, this follows after the discussion of the true meaning of the absolute value being the distance a number is from zero (and distance is always positive as we don't say, "I drove 140 miles to Chicago and -140 miles back giving me a total distance of zero miles round trip.") Some students need an image to help them to remember what is going on with the math symbols. Sometimes a wacky (to them) story helps.

When studying square roots, the radical is the name of the square root sign which unfortunately looks too much like one of the division signs. The number under the radical is called the radicand. When you want an exact answer (not a decimal approximation) with a simplified radical expression, some students have a difficult time looking for perfect squares to pull out. The students already know how to find the prime factors of numbers using factor trees so this an opportunity to use this method to find the roots. Using a factor tree we get √ 8 = √ 2*2*2.

This is where the chuppah comes in. In the Jewish faith, a couple gets married under a canopy known as a chuppah. In Christianity and Judaism, we both draw from the biblical ideal of marriage being two people coming together to become one. I point out that we have a couple of 2s under the chuppah (the radical looks like a canopy) so one 2 comes out. The other 2 is "left at the altar" or is still waiting for his/her match. Therefore we are left with 2√2. For √72 = √3*2*3*2*2 √we see two couples 3*3 and 2*2 with one extra 2. In this case the 3 and the 2 come out married (as one number each) and the other 2 is left behind with the answer being 3*2√2 = 6√2. One girl in the class was especially taken with the word chuppah announcing it like "Opa" at a Greek restaurant each time she did a problem. Another girl was saying under her breath, "You circle the couples, and one comes out."

Mixed metaphors, stretched analogies, and cross-cultural fusions in a math classroom? Welcome to my world.