Sometimes I’ll put my kids on the spot at lunchtime or some such and give them a math problem like, “What’s 5000 plus 2000?” Usually, I’ll get a real answer. However, if the kids don’t want to be bothered, I’ll get something like, “Oh, 2 million. Mommy, leave me alone!”.
I can’t say that I was completely innocent of this as a child, and it was something that drove my mom up a wall. In an easy scenario like this, I would have been expected, of course, to have the right answer.
However, when it came to doing assignments, my mom was also really big on having us understand what was reasonable even before having the right answer. It drove her crazy to no end when people didn’t seem to understand this principle. For example, I remember being at a store in about 1985 and my mom picked out a bunch of corduroy pants for me and my sister that had previously been reduced by 20% and now were on sale for 40% off. When we got to the register, despite the fact that they had been in a bin that said “All corduroy pants 40% off”, they still rang up as 20% off because the prices hadn’t been updated in the system. My mom noticed this right away, and mentioned it to the cashier.
Now, the cashier was probably barely out of high school and seemed completely confused. After all, there was a discount being applied, so why was my mom complaining? I remember my mom trying to patiently explain to the cashier that because the discount was 40%, the total had to be closer to half off. (Still not understanding, a manager had to be called over, who, in turn tried to argue with my mom that the items – despite being in a display that clearly marked them as 40% off – were not actually 40% off, which prompted my mom to bring the whole sign over to the register to prove she was right.)
And, more math. When the manager finally agreed that these items should be 40% off, the first impulse was to just tack another 20% discount on the items. Of course, this will not get you a 40% discount, but rather 36% off the original price. Had the items originally rung up for 36% off rather than 40% off, even my mom may not have noticed because the total would have probably still been in the realm of “reasonable”. Instead, because my mom was so annoyed at their attitude and lack of math skills, she made them change the price back to the original on each item and then apply the full 40% discount. As a little kid, I just remember being impatient because we were probably standing at the register for 25 minutes!
But here’s the thing: If the pants had been full-price, the total would have come to something like $50. Half of that is $25. At 40% off, the total should be closer to $25 than to $50, which is the logic my mom was trying to use with the cashier, since 20% off only brings the total down to $40. The actual total should have been right around $30 and that was what my mom was expecting to pay. At an “additional 20% off”, the total would have been around $32, which, with the crazy sales tax of our state, probably wouldn’t have been noticed unless my mom went over the receipt later. What drove my mom nuts, though, is that the cashier seemed incapable of following the logic behind what was reasonable.
Understanding the principle of “reasonable” isn’t necessarily something that is taught in school, whether in math or in other subjects. However, it’s the first line of defense, say, in protecting one’s self from getting ripped off – an announced 30% increase in a monthly bill shouldn’t result in the amount being charged doubling. And so, it drove my mom absolutely crazy when she would ask us math questions and we’d come up with something way out there, because she expected that before we’d open our mouths to answer questions, we’d take a moment to think about whether the answer would make sense. In math, this is somewhat related to estimation skills, but the principle is more a function of logic, not just preventing an answer of 1,000,000 to “What is 5,000 plus 2,000?” but also things like the thought that George Washington was President when Jesus spent his time on earth! 🙂