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Luke_A_Somers comments on Advice for a smart 8-year-old bored with school - Less Wrong
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I think that 7+7+7 is short enough, with enough general arithmetic skills. Probably the best drill for that is keeping a running total at a external pace; that will take a long time to get boring if the total is something you care about.
If 7+7+7 requires paper and 'carry the one' twice, then the problem isn't with multiplication, the problem is with addition. At the very least, everyone should be able to find the difference between two numbers when the difference is four digits or less, in their head, in the time it takes to receive change. People good at math should be able to add small amounts so that the change contains fewer coins.
That particular practical requirement doesn't require being able to multiply 7 by 3.
There's a large gap between 'fast enough to be a decent substitute for a LUT' and 'needs paper'. There's no doubt that one needs to be ABLE to add 7+7+7, but I don't think that each repetition on the path to memorizing 3*7=21 needs to involve it.
Does it take longer to ad 7+7+7 than to say "Seven times three is twenty-one" and "three times seven is twenty-one"?
if you have to memorize 3x7 and 7x3 separately, you're doing it wrong
Really? Which one is in the standard form? How long does it take to convert the other into standard form, as opposed to doing the multiplication?