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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?

#11

Post by zeveb »

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 smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating.

And then there are measures like a gross (144) and a great gross (1,728). Part of the reason for these traditional measures is that they are more flexible than base-10 measures: an eighth-gross or a third-gross are both integer quantities, unlike an eighth-hundred or third-hundred.

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

#12

Post by panglott »

Most of the multiples of eleven are really, really easy, and probably just has simple pedagogical value.

Multiples of 12 come up a lot because dozens are used a lot in real-world counting of length and time. Perhaps less in a metric country, but hours and days are still divisible by 12.

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

#13

Post by panglott »

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…

Base-60 math is even superior.

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

#15

Post by Retric »

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 30 also works well for this and is thus a clear step up from base 10 or 12 while being simpler than base 60.

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

#16

Post by jjp »

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.

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

#17

Post by BillTheCat »

x1798DE wrote: post #7
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.

11s are practically free, though, in base 10. The algorithm "repeat the non 11 number twice" works up till 10 x 11, where the "add a 0" algorithm for 10 kicks in. So you're just really memorizing 11 x 11 = 121 and 11 x 12 = 132.

A simple trick: For 11 x a 2-digit number you can simply take the first digit of the 2-digit number then the 2 digits of the number added together then the last digit of the 2-digit number.

Ex: 11 * 12 = 132 or 1, 1+2, 2. 11 * 45 = 495 or 4, 4+5, 5. For numbers which sum to more than 10 add the carry to the first number ex: 11 * 59 = 649 or 5, 5+9 = 14 so add 1 to the initial 5 and keep the 4, 9.

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

#19

Post by btilly »

zanny wrote: post #10
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.

That is only yet another reason in literally infinite ones why the US needs to actually push metric units. We bleed our stupidity into the UK and Canada while the rest of the world makes sense.

Makes sense..until you talk about time. Time makes no sense.

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

#20

Post by derefr »

x1798DE wrote: post #7
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.

11s are practically free, though, in base 10. The algorithm "repeat the non 11 number twice" works up till 10 x 11, where the "add a 0" algorithm for 10 kicks in. So you're just really memorizing 11 x 11 = 121 and 11 x 12 = 132.

But it's also "practically free" to just mentally do "10x + x", which I can actually add faster than my brain will return an answer from the post-10 part of the times table. (Not that I didn't memorize the 11s and 12s all the same at the time, but they got a lot less use and so a lot less reinforcement.)
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