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Comment by MikeSchurman | Hacker News Reader

I don't know what the answer is, but we're currently going through this with our kids, but the opposite. There is now a push to not memorize the multiplication table, but treat multiplication as repeated addition. So to get 6 * 7 you do 6+6+6+6+6+6+6 or 7+7+7+7+7+7 (I forget which is 'correct' as it's been a few years). That's good because it gives understanding, but when you're trying to multiply 2 4 digit numbers, it's really useful to have your tables memorized! We're now going into a new school and their biggest advice to new students is to memorize their multiplication tables, as they'll have trouble otherwise. Maybe they should do understanding followed by memorization?*

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I picked up this trick intuitively as a very young kid, perhaps 7-8

I break multiplication and division up into chunks of 1's, 5's, and 10's so that it's mostly just adding a zero to the end, or doing that and then cutting it in half.

I never learned multiplication tables, long division, lattice multiplication or anything else. just did this in my head.

So say you want to find 86 * 32

86 * 10 = 860

860 * 3 = (2400 + 180 = 2580)

2580 + (86 * 2) = 2752

It starts to break down for bigger numbers depending on how "uneven" they are but it's been pretty useful in general

Multiplication tables memorized in school usually stop at 12x12. They're super useful for doing the exact thing you demonstrated, in your head, very fast, using some tricks to turn the problem into smaller problems (with memorized answers, so they're solved almost instantly).

Memorizing that multiplication table was a more valuable use of time than the vast majority of time I spent learning mathematics. It's useful daily. Can't say that for much else.

How do you know that 800 × 3 = 2400 if you haven't learned multiplication tables?

Addition

(8+8+8)*100

8 x 3 = 24

8 x 300 = 2400

Add two zeros

I meant, how do you know 8 × 3 without a multiplication table?

Ah I see what you mean In my head, I do this:

8 + 8 = 16

16 + 8 = 24

> I forget which is 'correct' as it's been a few years

God I hope they're not teaching one of them is correct and one of them is incorrect.

Unfortunately it is according to some of the common core grading rubrics (in the US).

5 x 3 can be understood as five groups of three items, or three groups of five items, and students at a particular grade level are "encouraged" to use one interpretation over the other to the point of taking off points when they naturally use the commutative property (and or choose to chunk differently). I forgot what it was exactly but I read about a parent (rightfully) complaining about this.

I don't think this is anywhere in the common core standards, but probably the teacher/school was using some pre-packaged rubric and the teacher didn't bother to override using better judgment.

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