When my son did math team as a sophomore in HS, someone came up with the idea of getting t-shirts that said "The Answer Is Seven" because it came up enough to be a good guess. I agreed, and told him why this is, about which he cared not a whit. He is more geeky/Aspie than I am in many ways, but in math, and specifically what is a fair answer on a competitive math problem, I chase even relatives away. I told him the second possibility was -1, because they are testing whether you kept track of the signs, or Did you keep track of the signs even when we threw a bunch of them into the problem? In one way this is not good teaching, because reality does not favor that rule over a dozen others. On the other hand, it is one of the things you are most likely to screw up, even in real life, so teaching you to be more alert for that one is good. I told him that if there was a circle in the problem somewhere, the answer was going to be 2π, especially if revolutions were going to be involved.
When my wife told me today that worldwide, people's favorite number is seven (second place is 3), my first thought was "Gee, there are more autistic people in the world than I thought." It's sort of the first really cool prime number. But it is considered the Lucky Number in our society, probably from English or Northern European roots, so there's that.
It's going to be a low number, less than ten, because most people don't think of high numbers day-to-day, and those that are willing to think out there are going to wash out between them whether it's 103, 104, or 105. Some numbers will be disproportionately popular in their region, but still not get up over the rise of the first ten. 17 is going to be big among math-y people, as are 111 and 1001. And those are all very cool numbers, I agree, for reasons not immediately apparent.
But answers on a team math test to be answered on the spot, even if quick written computation is allowed, are going to be designed to not reward "mere" calculation. We want to see more than just arithmetic, Caleb. We all like arithmetic, but we want to see you do MATH. Yet they also want to see you struggle for it just a bit. Low multiples of 2 and 3 are likely to be too easy at a glance, as are 5 , 10, and 11. 12's not bad, but 13 is getting to be a tougher compute in your head. It's good because you won't intuit 13's in numbers over 80, certainly 100, but we are starting to get into the territory of rewarding mere computational skill again. It's okay to favor the arithmetic nerds a bit, but frankly, they've got a leg up to begin with.
7 is the sweet spot, a prime porridge that is neither too hot nor too cold.
You can just feel it.
4 comments:
Now that you know that, you can figure out without watching the Mind Your Decisions (love that site) explanation of why everyone got a similar problem wrong on the 1982 SAT - the correct answer was not offered in the choices.
https://www.youtube.com/watch?v=kN3AOMrnEUs
For Plato, the best number was 5,040. That says something about the significance of having a ratio-based math instead of a decimal math.
Heh. I would have gotten the SAT question “right,” because the intuitive way to do it for me was:
C=2piR
C(large)=3(2)piR
Cancel out pi, since both have it.
Cancel our R, since both have it.
Cancel out 2, since both have it.
Therefore, 3.
Only on empirical examination do I see that is wrong.
Yeah, I had similar thoughts. You have to pick something, and you can knock out the others. I don't know what I would have thought at the time. Would I have even considered that they made a mistake? I might have. When we got new math books in sixth grade I pointed out to the teacher that one of the answers in the answer key at the back of the book was wrong. I still remember that it was 216 vs 108, but I don't remember which direction it went. They had either added in a factor of two or left one out.
But I was paranoid when it came to the SAT's because I knew I hadn't done much work in half my classes in highschool - my typical report card was 3A's and 2D's - and that test was my ticket, and I was good at them. I was sure that they were aware of "that kid in NH" and a dozen or two others across the country and were specifically trying to trick us personally. It might have been a crisis, but fortunately I also knew that if you can't get something quickly, then cut your losses and move on.
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