rho: As a result of an IRC conversation

ρ (

rho) wrote,
@ 2009-11-25 08:23:00

As a result of an IRC conversation

Poll #1776 forty-six twenty-nines are one thousand three hundred and thirty four!
Open to: All, detailed results viewable to: All, participants: 48

When you learned the times tables in school, what number did you learn up to?

View Answers

9
3 (6.2%)

10
10 (20.8%)

11
1 (2.1%)

12
30 (62.5%)

something else (please comment)
4 (8.3%)

In IRC, I commented that 8 times 12 was part of the time tables, and someone else was surprised by this, having only learned up to the 9s (and then sort of tacked on the 10s and 11s since they were simple). This is weird for me, since I see the 12s as pretty vital. We have a special word for twelve of something ("a dozen") and even a special word twelve twelves ("a gross"). There are 12 inches in a foot. Lots of things come in 12s. 12 is a useful number since it's divisible by 2, 3, 4, and 6. It's also an even fraction of 60 (seconds in a minute) and 360 (degrees in a circle), so being able to work with 12s helps you work with those things too. In short, familiarity with the twelve times table is important for a lot of mental arithmetic, and it surprised me to find someone who didn't learn it with the rest of the times tables.

I'm curious whether the school of the person in question was anomalous, or whether it's an America/Britain thing, or whether it's due to the age difference. Hence why I'm asking.

(As an aside, if you've ever wondered why there are 60 seconds in a minute or 360 degrees in a circle, I'm now going to tell you. In fact, I'm going to tell you even if you've never wondered. The ancient Sumerians and Babylonians used to use a base 60 number system (as opposed to the base 10 system we use today). One of the big advantages of base 60 was how it made a lot of arithmetic easier. 60 divides evenly by 2, 3, 4, 5 and 6, so with a base 60 system, you'd wind up with a lot of calculations that were trivial (sort of like how multiplication by 5 is in a base 10 system). Naturally, they chose to use 60 when they created units of time, and we've been using their system ever since.

360 degrees is similar, except the explanation there also comes from astronomy. The Babylonian astronomers were pretty smart cookies, and they noticed how things move about in the sky over the year. They also knew that a year was 365 days, so that if they made their circle be divided up into 360 degrees (six sixties), not only would this give them nice, simple arithmetic to do but it would also mean that movement across the sky happened by very close to 1 degree every day. Handy!)

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damned_colonial
2009-11-25 09:58 am UTC (link)

Tables up to 12x12 at my school in Victoria, Australia in the early 80s. I am a big fan of 12s for everyday use, eg. when deciding how many stitches to cast on for a knitting project, exactly because of its divisibility by just about anything. I grew up learning metric measurements at school, but learnt imperial informally from family as we were not far past the time when Australia converted and my grandparents etc. never learnt metric.

(Reply to this)

	synecdochic 2009-11-25 10:35 am UTC (link)
	I was taught up to the 12s. I learned up to the 8s or so, and everything past what I can count on my fingers is a little fuzzy, but that's my dyscalculia and not anything having to deal with what I was taught. (Reply to this)

	yvi 2009-11-25 11:33 am UTC (link)
	Germany here and the year we did that, we only did stuff up to the number 100, so 11 and 12 were out for that. (Reply to this)

	anotherdream 2009-11-25 12:00 pm UTC (link)
	Finland here, and we only did up to 10. Which is logical, since we are metric-only, everything is in tens. (Reply to this) (Thread)

	rho 2009-11-25 12:04 pm UTC (link)
	You don't have 12 months in a year or 12 hours in a half-day, then? :p (Reply to this) (Thread from start)(Parent)(Thread)

	anotherdream 2009-11-25 12:06 pm UTC (link)
	Bah. :p Obviously, we do. But I guess we're sort of taught to regard those as special cases. Everything works in tens, but there are these few tiny exceptions. (Can't say I've ever needed to know the times tables for 11 and 12.) (Reply to this) (Thread from start)(Parent)(Thread)

rho
2009-11-25 12:11 pm UTC (link)

Awww, and there was me thinking that you crazy Finns had gone and invented decimalised time but not told anyone else about it.

And like a lot of arithmetic, it's not something that anyone really needs to know, but it is something that you can make good use of if you do know it. Like most things, it's easier to spot when you can use it when you know it than when you don't.

(Reply to this) (Thread from start)(Parent)(Thread)

	crschmidt.net 2009-11-25 02:28 pm UTC (link)
	I think that was the Swiss! Internet Time, Baby. (http://www.swatch.com/zz_en/internettime/itime_howitworks.html) (Yet another projected with Nicholas Negroponte at the beginning, and nothing but pain and suffering at the end.) (Reply to this) (Thread from start)(Parent)

	sarianna 2009-11-25 12:39 pm UTC (link)
	See, I remember in grade 3 learning up through nines before Christmas break, and then going on to twelves. But I suspect my elementary school was rather math-focused as a result. (Reply to this)

	pne 2009-11-25 01:15 pm UTC (link)
	We did up to 12×12 - International School, mix of US and UK influence in education. (Probably more UK, though? Hard to tell.) I think I did this in 3rd grade, where I had an American teacher, but I don't know who set the syllabus. I recall hearing from someone who learned an asymmetric times table, up to either 10×20 or 12×20. (Reply to this)

lizw
2009-11-25 02:23 pm UTC (link)

I learned in Germany, where we were taught the tables up to 10. When I became aware that my parents had learned up to 12 in Scotland, I assumed the difference was to do with metrication, as

anotherdream suggests. I think my kids have also only learned up to 10, which fits with that idea, since they're taught in metric by default. I can in fact multiply by 12 without having to break it down into the component operations, but that's just because I've picked it up as I went along. I suppose the fact that it's come up often enough to sink in like that is significant, but I can't say I've ever felt at a disadvantage.

(Reply to this)

	crschmidt.net 2009-11-25 02:29 pm UTC (link)
	Taught up to 10s, learned up to 12s. (Reply to this)

	cheyinka 2009-11-25 02:45 pm UTC (link)
	I was raised in the US and was taught them up to ten. Many of my school notebooks (not anything official - the ones I was bought to write in) had in the back the times tables up to twelve, though, so I taught myself those, and then made a good effort at memorizing the thirteens, too. (Reply to this)

recessional
2009-11-25 03:08 pm UTC (link)

Canada, and technically we were taught up to 12. I say "technically" because a) I don't think anyone learned it, and b) because we always STARTED at 1 or 2, by the time we got to 12 within the school year, it was pressing up against dismissal time and we sort of grazed it, stuck it on a couple of Mad Minutes and called it a day.

I think largely because even though there are a few base-twelve things, it genuinely isn't used that much: while yes, there are 24 hours in a day, we then stick that under a single-unit name of "one day", and likewise with months; Canada doesn't actually use "dozen" all that much beyond one dozen eggs, and there you run out of 12s that even might show up in ordinary use for us.

Which is not to say we actually use the 8-times more often, but those were on the WAY to 10 and 11, you see, and not as hard as 12.

(Reply to this)

	branchandroot 2009-11-25 04:00 pm UTC (link)
	US school. I suppose, technically, we were taught up to tens, but ten was never actually /covered/ because it was so simple. So, effectively, we were taught up to the nines. (Reply to this)

	red 2009-11-25 04:14 pm UTC (link)
	We were taught up to 12s, but I struggled at the 6s due to the dyscalculia. Getting the certificate for the 6s was a happy moment for me. XD (Reply to this)

niqaeli
2009-11-25 05:32 pm UTC (link)

I was taught through 12x12. But I can't remember how much that was school vs. how much that was my parents; my father drilled them with me. American here, though.

Actually the biggest damned thing I wish anyone had ever taught me in school is how to do tipping math in your head. I wanted to head-desk so much as soon as I realised that I didn't need to be trying to figure out 15% straight up -- just move the bloody decimal point to get 10%, halve that, and add the two up. (Or actually these days I just multiply by two and tip 20%). I mean, this method won't work for people who can't hold numbers in their head and do arithmetic but it really boggles me that I didn't get taught it. I was 17 before I figured it out on my own!

Of course that is rather an American thing to want taught, I suppose... *wry*

(Reply to this) (Thread)

gramina
2009-11-25 06:02 pm UTC (link)

:D My dad taught me how to do that -- ! Not for tipping, but because we got an employee discount at the bookstore my mom worked at. The amount of the discount changed over the years, but taking 10% and then some fraction of that and adding them together (12%, 15%, 20%) was *so much easier.*

I do a lot of my math-in-my-head on the same principle, really -- addition, even. (take it apart to something easy, then put it back together. 43% of something is (4x10%)+(3x1%), which is all shifting decimal places; 987 + 2034 is 2000 + 900 (2900) plus 87+34, which is the same as 90+31 (move three over from the 34 to keep the numbers easy) and then 2900 + 90 +31 is the same as 2900 + 100 + 21 is 2900 +121 is 3000+21 is 3021. It's not necessarily faster than paper, but it's about *as* fast and if I don't have paper...)

I'm also very glad to have read about a finger-counting system a while ago called Chisenbop. The version I use starts with the little finger instead of the forefinger, but it's the same basic idea as in the link. When I can't hold a number in my head, Chisenbop helps me hold it in my hands :-) (and sometimes my toes.... if I need hundreds!) It's particularly convenient for me for subtracting, since I have more trouble with subtracting in my head than I do with adding.

(Reply to this) (Thread from start)(Parent)

phoenixsong
2009-11-25 06:09 pm UTC (link)

All the folders I bought for school had times tables to 12x12 in them, but I don't think my school (US, western NY state) actually formally taught to the table. We learned how to multiply, yes, and a couple teachers were kind enough to point out things like the easy way to figure out multiplication by 9s, but I have no memory of specifically learning it as a table.

Then again, I don't remember my school formally teaching us english measurement conversions, either.

(Reply to this)

gramina
2009-11-25 06:11 pm UTC (link)

I think we were taught up to nines, but I'm not sure; it might have been twelves. Elevens are almost as easy as tens -- 11x=10x+x -- and I sort of remember learning 12x12=144, but I'm not entirely sure I didn't learn that from reading The Fellowship of the Ring, which is definitely where I learned that a dozen dozen is a gross.

I had a great deal of *trouble* with the nines, until I finally abandoned memorizing most of them (though 9x9=81 charmed me because 8+1 is nine :) ) and just went with 9x=10x-x, which I could do in my head.

(Reply to this) (Thread)

	binary 2009-11-25 06:36 pm UTC (link)
	though 9x9=81 charmed me because 8+1 is nine :) Oh! My mom taught me the 9s using that principle... since all the 9*x results would add up to 9 (81, 72, 63, 54, 45, etc.). (Reply to this) (Thread from start)(Parent)

	conuly 2009-11-25 07:02 pm UTC (link)
	EVERY number divisible by 9 adds up to 9. And every number divisible by 3 adds up to 3, 6, or 9. (Reply to this) (Thread from start)(Parent)

	binary 2009-11-25 06:34 pm UTC (link)
	US here. I'm not really sure what the schools taught... I think probably up to 10. My parents tried to teach me up to 12, but I only really learned up to 11. (Reply to this)

conuly
2009-11-25 07:01 pm UTC (link)

I didn't learn the times tables in school, I learned them the hard way - by adding up numbers until the multiplication started to stick!

They taught up until 12 x 12, but I don't think they really tested past 10 x 10. After that, the focus was on multiple-digit multiplication, and when do 12 and 11 really come up? It's useful to have them memorized when converting from feet to inches, or from cartons to eggs, but you could do it just the same doing it the long way like you would for 21 x 21.

(Reply to this) (Thread)

	pthalo 2009-11-26 04:10 am UTC (link)
	for 2121 wouldn't you just do 2022=440 + 1? (Reply to this) (Thread from start)(Parent)

rainbow
2009-11-25 08:03 pm UTC (link)

12s in the SF Bay Area in the late 60s/early 70s. (although I didn't really learn them until 6th grade, when my teacher caught on that I was counting anything above 5s and didn't let me have free reading time until i memorised them. it took me 2 whole days of losing reading time; i was reading at college level and didn't want to lose any more reading time than i had to...)

i *did* learn 12x12 when i was 7 and asked my grandmother. i think that might have been part of what confused my teachers; that and counting quickly when i had to do anything with 6-9s.

(Reply to this) (Thread)

rho
2009-11-26 03:53 am UTC (link)

I used to work things out quickly rather than memorising them as well. Sometimes just by repeated addition and sometimes by repeated multiplication by a smaller factor. Or by adding and subtracting from one of the square numbers, which I did know. My teachers never did catch on to this, so it wasn't until years later when I finally memorised things, just as a result of encountering them enough times.

(Reply to this) (Thread from start)(Parent)

	askygoneonfire 2009-11-25 09:07 pm UTC (link)
	They taught us up to 13. But I never learnt them. Ever. I still don't know my times tables despite the heroic efforts of my parents to teach me them over a period of several years. I can do my 9 times tables on my hands though...well, up to 10. But how often do you need to times 9 by more than 10? Last edited 2009-11-25 09:10 pm UTC (Reply to this)

	pthalo 2009-11-26 04:09 am UTC (link)
	taught to 1212 in america, now i'm not sure how far i have memorised...i've recited from 11 to 37*37=1369 before falling asleep before. (Reply to this)

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