> Take as an example 7,203 x 6,892. If I want to know that exactly, then I reach for Mathematica
They are always trying so hard to sell Mathematica in these blog posts, but this is the lowest I've seen.
Is there any point to the 12 times table?
71–80 of 198 posts
Re: Is there any point to the 12 times table?
#72Forget 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.
You will almost certainly be working in millimetres, but because of ISO 2848, you will very likely be working in multiples of 300 millimetres:
https://en.wikipedia.org/wiki/Preferred_number#Buildings
Which is about a foot!
Re: Is there any point to the 12 times table?
#73Earlier quoted context omitted.
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.
This generalizes to multiplying any number times 11,
https://en.wikipedia.org/wiki/Trachtenberg_system#Multiplyin...
Take a number, say 142857. Prepend a 0 on the left. Underneath each digit write the sum of the digit above and the one to the right. If you work from the right, it's easier to keep track of the carries.
0142857
1571427Re: Is there any point to the 12 times table?
#74Earlier quoted context omitted.
Back in the 70's (UK) I remember doing non base 10 maths at about that age plus basic set theory much more useful than rote leaning your times table.
Did that in the US in the mid 2000s, though spent hardly a week on either IIRC. Something like base 20 Mayans, base 60 Sumerians, and base 2 computers. Do math in each and convert them to/from base 10. I think that's been dropped from most US elementary school curricula now, bit of a shame.
I believe it was introduced as part of some New Math curricula.
https://en.wikipedia.org/wiki/New_Math
Richard Feynman was pretty harshly critical of this in his stories of working as a textbook reviewer. I really appreciated that my elementary school did it, but I had a sense that most students didn't quite understand the significance (or remember it afterward if they weren't into computer programming). I think it has a lot of potential value in terms of understanding what place value is and where a place value system comes from.
When I've tried to teach programming, I've found that most people who aren't already programming enthusiasts don't remember the binary system or say they never learned it at all.
Edit: the Wikipedia article I linked to also has several examples of people making fun of non-base-10 arithmetic and kids being taught it in the New Math, including a song by Tom Lehrer!
Re: Is there any point to the 12 times table?
#75Earlier 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…
I am in the process of reading 'The Story of French' by Nadeau and Barlow. There's a chapter on how France was able to push their influence, during the renaissance, to get the world to switch to the metric system. Prior to developing the metric system, France had no standard for the pound; unlike England. This was the height of enlightenment in France, so the reformers wanted to replace the Gregorian Calendar with a…
The renaissance is usually seen as being the 15th and 16th centuries. France didn't switch to metric until the end of the 18th century, after the French revolution.
If anything, the way the French "pushed their influence" was by conquest: The first countries that adopted metric were forced to when they were conquered by Napoleon. Many of them reverted after Napoleon was beaten, but then gradually they started converting to it again,
Since you're mentioning Napoleon I assume you just got your periods mixed up. There were indeed many crazy suggestions for calendars after the French revolution...
Re: Is there any point to the 12 times table?
#76Twelve 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.
Maybe. But the thing is if it's easier to memorize the composites, why not skip primes entirely over 5? Just memorize 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 .
I'd have to run the numbers. It would be interesting to consider different subsets. I also think adding in 15 would probably worth the extra number for real-world datasets.
Re: Is there any point to the 12 times table?
#77Twelve 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.
10 fingers, and two hands, so you could count raising your hand up to count as one, then 5 fingers, then the other hand, and 5 more fingers.
I agree about the symbols, though.
Re: Is there any point to the 12 times table?
#781-10 you memorize.
13-100 you calculate it out.
100+ you use a calculator.
11-12 is half memorized/half calculated.
I think of them as introducing you to how to calculate with larger numbers you haven't memorized.
Some of them you know - 12 * 5? 60.
But what about 12 * 7? 10 * 7 + 14. or 12 * 5 + 12 * 2.
Dealing with 11 and 12 in the times tables gives you good practice for those calculation tricks that you use for numbers greater than 12. It's not worth it to memorize an additional 44 rules but it is worth it to know how to do math.
Re: Is there any point to the 12 times table?
#79This type of post is perfect Hacker News material!
1) Challenge an existing assumption about something we all do
2) Hand-wave some first-order guesses as to why we do it
3) Get nerdy with code and graphs and come to your conclusion, along with helpful suggestions for bettering the reader
With no prospect of the pre-decimal money system returning, I can only conclude that the logic behind this new priority is simply, “If learning tables up to 10 is good, then learning them up to 12 is better.” And when you want to raise standards in math, then who could argue with that? Unless you actually apply some math to the question!
Re: Is there any point to the 12 times table?
#80Earlier 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.
Or bcd or fixed point. But it all depends what you want to represent. For financial data bcd or fixed point encoded in integers is generally preferred over floating point because it's easy to make it behave the way people expect it to.