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Is there any point to the 12 times table?

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Re: Is there any point to the 12 times table?

#61

Post by jameshart »

zeveb wrote: post #11

Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really sm…

But that's not really an argument for learning your twelve times table. In fact it's an argument that basically it's trivial to learn your twelves if you already know your threes and fours - the twelves are the numbers that appear in both lists. Or you can just skipcount your four times table. Overall, seems to argue against having to learn it.

Re: Is there any point to the 12 times table?

#62

Post by michaelt »

jjp wrote: post #16
sandworm101 wrote: post #2

Forget the stats and calculus. Think carpentry, measuring and cutting wood products. If you are building things in the US/UK/Canada then you are using feet and inches. 12 inches to a foot. It's a tiny thing to learn and will serve kids well in any number of professions. Now 11, that's a total mystery. Other than it being between 10 and 12, I see no reason to memorize 11s.

> If you are building things in the US/UK/Canada then you are using feet and inches. In the UK you are more likely to be using millimetres if working from any kind of design. Working in inches and feet would depend on your age and perhaps whether you are working on an older property that was designed in inches.

In the UK your designs and plans will be in mm, but your materials will vary between metric-rounding-of-imperial, (2400x1200mm) [1] imperial-but-labeled-in-metric (1220x2440mm) [2] and imperial-in-one-dimension-metric-in-the-other (38x144x2400mm) [3]. Wallpaper? 10m x 520mm for sure [4] but doors? 1981x762mm [5]. Cement? Back to metric, with 10kg and 25kg bags [6].

You'll also probably measure long distances in miles but short distances in meters; and weigh your ingredients in grams but your body in stone.

I guess what I'm saying is if you want a rationally designed measurement system, don't copy us Brits and especially don't copy our builders.

[1] http://www.wickes.co.uk/Knauf-Plasterboard-Square-Edge-2400x... [2] http://www.wickes.co.uk/Wickes-General-Purpose-OSB3-Board-18... [3] http://www.wickes.co.uk/Wickes-Studwork-%28CLS%29-38x144x240... [4] http://www.wickes.co.uk/Wickes-9006-Wallpaper-Embossed-White... [5] http://www.wickes.co.uk/Wickes-Skipton-Internal-Softwood-Doo... [6] http://www.wickes.co.uk/Blue-Circle-Extra-Rapid-Cement-25kg/...

Re: Is there any point to the 12 times table?

#64

Post by zeveb »

martin-adams wrote: post #51
zeveb wrote: post #11

Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really sm…

>> If we were really smart, we'd switch from base 10 to base 12 But I only have 10 fingers! On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 as single digits, otherwise I could see that getting very confusing. You could't really use A and B, as then some people would be unable to find the correct seat on an airplane.

> But I only have 10 fingers!

That's why I mentioned counting on the finger-joints :-)

> On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11

Already been done, over a hundred years ago, and they're even in Unicode already[1]!

[1] https://en.wikipedia.org/wiki/Duodecimal

Re: Is there any point to the 12 times table?

#65

Post by scoates »

martin-adams wrote: post #51
zeveb wrote: post #11

Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really sm…

>> If we were really smart, we'd switch from base 10 to base 12 But I only have 10 fingers! On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 as single digits, otherwise I could see that getting very confusing. You could't really use A and B, as then some people would be unable to find the correct seat on an airplane.

You have 12 finger segments per hand.

"Finger-counting systems in use in many regions of Asia allow the counting to 12 by using a single hand."[0]

[0] https://en.wikipedia.org/wiki/Finger-counting

(Edit: silly me and trying to use Markdown)

Re: Is there any point to the 12 times table?

#66

Post by schoen »

lordnacho wrote: post #57

There's lots of questions thrown up by this. If people need to know times tables, do they also need to know powers of 2? They come up quite often if you deal with computers. What about squares? Anyone doing polynomials later on will be using them constantly. My sense is you will end up memorising the things that come up anyway, so why be so strict? You'll end up teaching kids that math is a memory game. So for fun, w…

You're right about 86400 and 1729.

I know up to 2¹⁷=131072 and also the special cases 2²⁰=1048576 and 2²⁴=16777216 (the 7s in the middle make it easier to memorize, and it seems to come up a lot). I would really like to remember 2³²=4294967296 (I always just remember "4.2 billion") and should probably get around to that.

I learned a lot of pi in middle school but even then I knew that it wouldn't be useful for anything, and it hasn't, other than knowing a lot of pi.

The start of e goes 2.718281828, so it's not a whole lot of effort to go a little beyond your 2.71 if you wanted to.

Here are some Unicode superscripts ¹²³⁴⁵⁶⁷⁸⁹⁰ in case anyone wants to use them in this thread.

Re: Is there any point to the 12 times table?

#67

Post by tempestn »

I would argue that the 11s don't really count, since knowing them is trivial. The only one that really requires memory is 11x11, and it's probably not strictly worth knowing, but then kids get the accomplishment of knowing a whole extra row essentially for free.

I agree that the 12s aren't worth memorizing though. They're pretty easy to mentally calculate, being a combination of 1 and 2, and after doing that for a few years, the memorization will often happen naturally. No real need to force it.

Re: Is there any point to the 12 times table?

#68

Post by Terr_ »

dnautics wrote: post #29
btilly wrote: post #28

Earlier quoted context omitted.

Easy divisibility is the reason why when we switched to metric, the one thing that didn't switch is time. Which means that, for example, converting from m/s to km/h is a mess. (You have to multiply by 3.6, can you easily do that in your head?) With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both…

decimals cause huge problems for computers. How do you represent 0.6 as a floating point? In the long run, the correct solution is for everything to be binary.

Why? No matter what radix you pick, there's always going to be some rational-value you cannot accurately encode. Moving to binary just gives you a different distribution of "un-encodeable values". (I'd say a larger/worse set, but I'm not yet sure how to prove it.)

In the long run, trinary gives you the best radix-economy, being closest to e: https://en.wikipedia.org/wiki/Radix_economy

Re: Is there any point to the 12 times table?

#69

Post by zeveb »

Retric wrote: post #15
zeveb wrote: post #11

Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really sm…

The first 3 prime numbers are 2, 3, 5. Base 10 and base 12 both use two of them. (12/4=3 yay, but 10/4 = 2.5 so meh) The same is true of base 6 or base 15. Every other prime number repeats so switching is pointless, unless you divide by 3 vastly more often than by 5. PS: Several ancient systems use base 60 which uses 2, 3, and 5 and may have been created by joining a base 6 system with a base 10 system. However, base…

> Every other prime number repeats so switching is pointless, unless you divide by 3 vastly more often than by 5.

It's highly probable that in duodecimal one would divide by 2, 3, 4, 6, 8 & 9 as often as one divides by 5 in decimal, and avoid 5 as much as one avoids 3 & 7 in decimal.

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