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Memorizing multiplication tables is over rated. Seeing connections between those early multiples up to 12 is more interesting. Can be helpful I suppose in facto
by somethingroma 8y ago
Memorizing multiplication tables is over rated. Seeing connections between those early multiples up to 12 is more interesting. Can be helpful I suppose in factorization.
Maybe I just don't trust my memory (as in how am I sure that 7*8 is 56) and why I despise rote memorization and rather retain memory from use and practice.
Regardless a good example of something to remember in math is the quadratic formula
Still enjoyable to derive and 'see' why it works but also just used so much. That said, I wouldn't encourage memorizing it without first understanding it.
- PascLeRasc 8y agoThe best is the 9's table, how all the digits add up to 9. My mom's an elementary teacher and there's always a few third graders who figure that out on their own and love it.
- sdenton4 8y agoI was legit angry that I didn't learn about the divisibility checks for 3 and 11 until college...
- somethingroma 8y agoAdditionally 9 * n = [n-1, 10-n] for n = 2-11; where n-1 is the digit in the 10's place and 10-n in the single place. This just an aesthetic curiosity. I know the pattern continues for larger n I've just never bothered to generalize it. Also never compared it to other bases.
- Koshkin 8y ago> [n-1, 10-n] for n = 2-11 I think the usual 10 * n - n makes more sense and is much easier to remember.
- sdenton4 8y agoIt's not an aesthetic curiosity at all! 10 is equal to 1 mod 9... So suppose X is written in base 10 (a0 * 10^0 + a1 * 10^1 + a2 * 10^3 +...) and you want to find X mod 9. Then all of the 10^k's are just 1 (mod 9), so you just get the sum of the digits. So if X is divisible by 9, then the sum of the digits (mod 9) is zero. Same works for 3 (x is div by 3 iff the sum of the digits id divisible by 3). And 11 gets an /alternating/ sum of the digits, since 10 is -1 mod 11...
- aj7 8y agoNo. If you can’t multiply in your head, you are crippled in any quantitative reasoning. You have interjected too many steps in estimating, calculating, judging, etc. This is not to say there aren’t useful, non-quantitative pursuits.
- somethingroma 8y agoI don't understand what you're saying or objecting to. Incase this is what you mean: remembering the multiplication table is the antithesis of multiplying in ones head.
- Koshkin 8y ago> remembering the multiplication table is the antithesis of multiplying in ones head But it's not! Because in order to be able to multiply numbers in your head efficiently you must remember the multiplication table.
- somethingroma 8y agoNo. By definition remembering an answer is not the same as doing. Additionally my experience tells me otherwise.
- brianpgordon 8y agoI'm sorry but this seems patently wrong to me. There's only so much working stack space in your brain. If you're constantly having to think through multiple steps to multiply single digits then you're going to be at a serious disadvantage when you need to solve a bigger problem that involves more work than just single-digit multiplication.
- deleted 8y ago[deleted]
- aj7 8y agoNo remembering the table is the ROM-table part. You need the algorithm part too.