Comment by eszed

Comment by eszed 2 days ago

Calculating 8x12 in my head relies on a trick / technique - they call it "chunking", I believe, in the Common Core maths curriculum that US parents get so angry about - that (I'm also in my 40s) was never demonstrated in schools when we were kids. (They tried to make me memorize the 12x table, which I couldn't, so I calculated it my way instead; took a little longer, but not so much that anyone caught on that I wasn't doing what the teacher said.) I'd like to think I was smart enough to work it out for myself, but I suspect my dad showed it to me.

I'll show it to you, but first: are you able to add 80 + 16 in your head? (There's another trick to learn for that.)

neom 2 days ago

96, easy. Lets go, real time math tutoring in the hackernews comments, 2025 baby! :D

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jacobolus 15 hours ago

There are lots of good ways to break down this multiplication problem:
8 × 12 = 8 × (10 + 2) = 8 × 10 + 8 × 2 = 80 + 16 = 96
8 × 12 = (10 − 2) × 12 = 10 × 12 − 2 × 12 = 120 − 24 = 96
8 × 12 = (10 − 2) × (10 + 2) = 10 × 10 − 2 × 2 = 100 − 4 = 96
8 × 12 = (5 + 3) × 12 = 5 × 12 + 3 × 12 = 60 + 36 = 96
8 × 12 = 4 × 24 = 2 × 48 = 96
8 × 12 = 2³ × (2² × 3) = 2⁵ × 3 = 32 × 3 = 96
etc.

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eszed 2 days ago

:-)
12 is made up of a 10 and a 2.
What's 8 x 10? 80.
What's 8 x 2? 16.
Add 'em up? 96, baby!
They teach you to do math on paper from right to left (ones column -> tens column, etc), I find chunking works best if you approach from left to right. Like, multiply the hundreds, then the tens (and add the extra digit to the hundreds-total you already derived), then the ones place (ditto).
It's limited by your short-term memory. I can do a single-digit times anything up to maybe five digits. Two-digits by two digits, mostly. Three-digits times three digits I don't have the working memory for.

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- neom 2 days ago
  
  Seems my math teachers in school...er..didn't. That makes sense, I know how to write math out on paper and solve it, but then my instinct has always been to reach for that method mentally, so I literally draw a pen and paper in my imagination, and look at it and do the math and it takes way too long so I just give up, this seems like I can just learn more rules and then apply them, as long as I have the rules.
  Thank you kindly for taking the time to teach me this! This thread has been one of the most useful things in a long ass time that's for sure. If I can ever be helpful to you, email is in the bio. :)
  
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  eszed 2 days ago
  
  My pleasure! I'm no one's idea of a mathematician, but I enjoy employing arithmetic tricks and shortcuts like this one.
  A few years ago I had an in-depth conversation with a (then) sixth-grader of my acquaintance, and came away impressed with the "Common Core" way of teaching maths. His parents were frustrated with it, because it didn't match the paper-based methods of calculation they (and you and I) had been taught, but he'd learned a bunch of these sorts of tricks, and from them had derived a good (probably, if I'm honest, better than mine) intuition for arithmetic relationships.
  
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