Multiplication Tables

Onesies, twosies, threesies, foursies, fivesies, sixies, sevensies, ninesies, tensies...fine! But, elevensies? twelvesies?

Why did my evil second grade teacher, Mrs. Kraut make me learn my times tables up to 12? I still don't know my 11s and 12s by heart! My fragile little mind only had room for 1-10!

Now, it occures to me that it is completely pointless to teach them past 10. Are 2nd graders still taught to learn their times tables up to 12? If so, why? If not, when did primary school teachers finally come to their senses? Is it so we can more quickly figure out how many hours are in a day? How many inches in a yard?

If Mrs. Kraut hadn't spent all that time drilling 11x12=132 into my head she might have had time to teach me how to spil...spel...spell!

If it helps, I was taught the multiplication table up to 10's in 3rd grade. And this was around 1990. So they probably came to their senses in the 80's.

I was taught a 10x10 table in the late 70s. But that was in Germany, and I don't even know if we had a 12x12 table before that. Makes little sense to me, too, except maybe that you might begin to see the pattern, which could help you with the higher numbers.

Holger

I was taught in Germany in the sixties - 10x10.

America, mid-80's, 10x10.
I didn't have to memorize any state capitols, either.

America (Texas) 1970 10x10 -

Actually, I don't recall having to memorize the table per se - just do the multiplication problems.

up to 12 x 12 in elementary school in the early 70's.

Just to clarify, are you reallysaying you have trouble with the elevenses? I mean,up til 11 x 11, it's the easiest. 11, 22, 33, 44, 55...then you only have two more to memorize -- 121 and 132. On the other hand, the twelves were always tough for me.

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President of the Vernon Dent fan club.

I too was only drilled on the 10x10, but I do see a purpose for going up to 12x12. Many things still come by the dozen (donuts, inches/foot, packs of soda [pop]), so it just helps to have the answer drilled into your head instead of doing "7*12 = 7*10 + 7*2=70+14=84".

Of course, 11 is easy to memorize. And for other 2-digit products of 11 is easy too. Just add the two digits. If the sum is less than 10, stick it between the digits and there's your answer. E.g.:

53 x 11
5 + 3 = 8
583

For sums greater than or equal to 10, put the last digit of the sum in the middle and add one to the left digit. E.g.:

67 x 11
6 + 7 = 13
737

I was also taught up to the 10s however my father always used to test me up to the 12s which confused the hell out of me back then. I think it is a carry over from the old empirical measures, and I believe that before the change to metric, the entire English currency was calculated on the basis of 12, not 10 ie pounds, shilling, pence. Perhaps way back then Sterling was the reserve currency of choice so people learned to relate their own to it and thus calculate with it, much as they do against the US Dollar now.

A fine good memorizing those tables did for me. I use a calculator for everything, and have forgotten some of the tables. If you ask me 7 X 8, I will draw a blank. I remember all the squares, so 7 X 8 = (7 x 7) + 7 = 56.

It's kinda like quick dialing from a phone's memory. You do it for a while and soon you don't even remember mom's phone #.

A lot of good technology has done for us.



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¾È ³ç, ÁÖ µ¿ ÀÏ

Well, the twelve times table can be handy if you're in America and occasionally have to convert feet into inches. And worldwide, days into hours and years into months.

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Chaim Mattis Keller
ckeller@schicktech.com

"Sherlock Holmes once said that once you have eliminated the
impossible, whatever remains, however improbable, must be
the answer. I, however, do not like to eliminate the impossible.
The impossible often has a kind of integrity to it that the merely improbable lacks."
-- Douglas Adams's Dirk Gently, Holistic Detective

I thought the twelves were a cinch -- they're so musical. The hardest ones for me were sixes and eights. But maybe I'm just weird.

Slightly off topic, but anyway: I learned a great rule back in school to square or multiply number between 11 and 19. Let's start with squares (let # be any digit):

1# x 1# = 1#0 + #0 + #x#

Okay, this looks clumsy. Example:

16 x 16 = 160 + 60 + 6x6 = 220 + 36 = 256

Other multiplications (@ is another digit):

1# x 1@ = 1#0 + @0 + #x@

Example:

15 x 17 = 150 + 70 + 5x7 = 220 + 35 = 255

Speak that aloud to memorize the rule; I never forgot it.

Holger

PS: Of course, this rule is trivial if you know the distributive law (correct term?). But it's sooo handy!

you guys are doin this math thing way to complicated.
i suggest a calculator

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Either let me fly or give me death
Let my soul rest-take my breath
if i dont fly ima die anyway
Ima live on but ill be gone anyday

DARK MAN X

Youngest Son just finished third grade, and they did do multiplication tables to the 12s.

Middle Son just finished fifth grade, and they had to memorize all of the state capitols.

-Melin

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Phenomenal woman
Bitch Corporate Lawyer
That's me

I went through grade school in the mid-70s.

Multiplication: 10x10

We learned nothing about state capitols, but we did have to memorize all 50 state capitals.

And yes, we covered spelling! :-)

I teach third grade, and for the last two years I've taught 0-12s. However, I think this year I'm going to focus on 0-10s (which is all my district requires). Students grew confused--it's a lot of numbers to work with and memorize--and I want to be sure they really get the 0-10s.

I'll probably offer the 11s and 12s as enrichment for the kids who whiz through the first 10 (well, technically, 11), but this way the lower kids have a greater chance at success. I teach the concept of multiplication so that they can find the answer of, say, 11 x 12, but they just won't have it memorized.


BTW, I learned 0-10s in 3rd grade, and learned the 11s and 12s later on my own.

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"Me fail English? That's unpossible!"

"English? Who needs that? I'm never going to England."

I only learned through 10, back in the 50's, but I was aware that going up to 12 had been possible in earlier days.

Lsd (not the drug, the pre-1971 British coinage) might have been a factor.

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John W. Kennedy
"Compact is becoming contract; man only earns and pays."
-- Charles Williams

Personally, I'm not to thrilled with the concept of teaching multiplication by tables. I know I didn't understand multiplication until my mother had me throw away the tables and start looking at the problems as an addition based concept.

I focused on the concept a bit too much in my teaching last year, I think. We did so many multiplication riddles, illustrations, etc. that my kids didn't study/memorize facts. So, when I'd give them a timed test (3 minutes for 40 problems), many of them didn't finish because they were sitting and adding 7 nine times to find 7x9, and the like. They got the right answer, and they all understood multiplication concepts, but when it came to the tests...well, they need to finish them to pass them.



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"Me fail English? That's unpossible!"

"English? Who needs that? I'm never going to England."

My dad taught me this when I was a kid. I still think it's just about the coolest thing I ever learned. Here's how you can do your 9's tables on your fingers: Hold your hands in front of you, palms facing your face, fingers spread. For this demo, bend your middle finger of your left hand down. now, counting from left to right, this is your third finger, thus, we are solving for 3 x 9. Each digit to the left of the bent middle finger represents 10. Each finger to the right of the bent finger represents 1. Add them up, and you'll get 9 x 3 = 27. This works for any finger you choose. I'm not sure I explained it very well, so let me know if you have any questions.

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"I think it would be a great idea" Mohandas Ghandi's answer when asked what he thought of Western civilization

Sometimes I still have to find ones I remember and then add to reach the ones I don't. 12's? You gotta be joking.

If you lived in an area where you had to buy a Pee-Chee brand folder, it came with a 12 X 12 multiplaction table.

When I got bored in college, I would draw up multiplication tables. In one particularly dull class, I got up to a 25 X 25 table.

From now on I know that 323 is not a prime number.

I think Porpentine was on the right track. So many things come in dozens (inches, eggs, intelligent people) that it makes a certain amount of sense to memorize the multiplication tables for them. Granted, you can figure it out with 10s and 2s, but it's quicker if you have it memorized.

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Carpe hoc!

That 3 song really rocked

Quadell: OH YEAH!
That 3. It's a magic number...

______________________________________________
I'm just a Bill, Yes I'm only a Bill.
Your Pal,
Frankd6

In case no one knows their multiplication tables...

**GIGANTIC SILLY GRAPHIC deleted**

[Note: This message has been edited by Nickrz]

I was taught 1-12 in school, but I didn't ever memorize them. To get 7x8, I still think "7 doubled is 14, doubled is 28, doubled is 56".

I learned how to multiply from the "Multiplication Rock" album, from the Schoolhouse Rock series. But the 7 song wasn't catchy, and the 8 song was boring, so I never got those. That 3 song really rocked, and Little-Twelve-Toes... oh yeah. I still occasionally hum them when I have to count by 3s or some such.

Your Quadell

Personally, I'm not to thrilled with the concept of teaching multiplication by tables. I know I didn't understand multiplication until my mother had me throw away the tables and start looking at the problems as an addition based concept. That is when I started understanding multiplication as a concept, rather than as just something done by rote, like spelling. The tables might be usefull, but I see to much reliance on them, rather than the concepts of math they were made from.

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>>while contemplating the navel of the universe, I wondered, is it an innie or outie?<<

---The dragon observes

I read a book once on mental arithmetic; it suggesting memorizing the times tables up to 20. After that, there are many tricks to break things down and do even complicated problems without pen and paper. I never did sit down and do it, though.

7 * 8 was the only one I could never remember. Then someone showed me:

56 = 7 * 8

Get it?

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Mastery is not perfection but a journey, and the true master must be willing to try and fail and try again

But an "A" for effort Louie.

quote:
That 3 song really rocked

Quadell: OH YEAH!
That 3. It's a magic number...

Do you guys know there's an album out called "Schoolhouse Rock Rocks!"
with various rock and rap artists doing covers of the old
Schoolhouse Rock tunes? Blind Melon does a great, trippy version
of "Three is a magic number" - probably the best song on the
record. The Lemonheads, "My Hero, Zero" is pretty good, too.
Better than Ezra's version of "Conjunction Junction" is OK,
but really can't hold a candle to the original - I don't
know why they even bothered trying.

**GIGANTIC SILLY GRAPHIC deleted**

[Note: This message has been edited by Nickrz]


Thank you Nick, oh thank you, thank you!

Learned the concept of multiplication in 1973 (2nd grade. Was not forced to memorize anything (New Math in elementary school--lots of associative properties and set theory and base twelve or six or whatever) until 7th grade and algebra,,,,oops, junior high, conservative teacher, like the old days, memorize those times tables up to twelve. This was probably 1979 and maybe just about the last gasp of teachers who made students memorize things. By the way, no teacher ever made me memorize the state capitals, though for some reason I know them.

I have "Schoolhouse Rock Rocks"! It's very good - in some parts. The rap version of Mr. Morton is great.

I'm gonna have to agree with Gail about memorizing. I don't like to memorize stuff, because it's boring. (In Calc, rather than memorizing the quadratic formula, I just derived it on the test.) But still, it helps. This is even true with literature. After I memorize a couple poems, boring as it is, I find I appreciate them better. Something will come up in my life, and it'll trigger a line, and I "connect" with it.

I just wish memorization wasn't so dern boring!

Your Quadell

I had as much trouble w/ memorizing multi tables as anyone, but I'm glad I had to. How're you going to do squares later if you haven't memorized what 2x2 5x5 etc are -- without counting?

I had some mega-trouble with my 4s though.
Mid 80's NYC public schools. We were supposed to go up to 12s. In order "pass up" to the next level, you had to stand in front of teacher (could be private if you were shy) and answer each verbally. No more than 5 secs for each question, and not in order.

Boy she was tough (but nice too). She let me read as much as I wanted as long as my other work was done. (my definition of good teacher!)

30 minutes of work down the drain. *sigh* Sorry about ruining the thread like that. And thanks, Nickrz, for deleting it.

Feeling ashamed :o,
Louie

Being a teacher, who loves to teach math, I definitely have opinions on this subject. The new way of thinking on memorization of times tables is "don't stress memorization, just make sure they understand the process".
Memorization is not scene as authentic learning and one can memorize their times tables and still not know how to "think".
But I disagree. That view may work on states and capitals--which are not necessary knowledge. But students who don't memorize their times tables probably won't get very far in math. I'm an elementary teacher and I've had occasion to talk to high school math teachers and every one of them has said that memorization of times tables is an absolute necessity.
<sigh> I know someone is going to say but I don't want to get far in mathematics. But I can't think of one career where math is not used even a little.
I also have a view that learning is a really cool thing and learning something challenging like your 11's and 12's has it's own reward---that feeling of accomplishment
but I guess that comes from being a teacher.
One more thing--if you've learned your times tables to 11-12--for example 2x0 all the way to 2x12--you don't really have much to learn when you get to 11's and 12's you already know most of them.

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Gail
"Any major dude with half a heart surely will tell you, my friend--
Any minor world that breaks apart falls together again...."
-Steely Dan

Louie - there's a thread over in the "About this message board" forum for testing silly graphics before you post them here. ;)

When I learned multiplication (early 90's) I only learned up to 10's. Of course, my schools have always been lacking in strong math. I didn't even learn how to multiply 3 digit numbers by 3 digit numbers on paper until my junior year! (Well I figured it out eventually but it was only a guess...I didn't actually see it done until a looong night at Subway) They never taught us theory. I can figure things out if I go through the theory thing now, but memorizing the problems was pointless. They've long been forgotten now that calculators are available. I'm fortunate because I pick up on math concepts easily, so I can work it out without the memorization. But just spring a hard one up like 5*8 and I'm toast. (Someone said they had troubles with 6s and 8s....me too) If they are going to make calculators so readily available at such young ages, they should make sure to teach theory. People forget and become lazy, and then when they're caught without a calculator they're really in a jam! So either do away with calculators or start with theory because memorization plus calculators is as good as not learning at all. I'm not sure this post made any sense at all...it's late. Sorry...

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~*brandie*~
"Where it is a duty to worship the sun it is pretty sure to be a crime to examine the laws of heat."
~John Morley

Since we're on multiplication, here's a fun little piece for all you math fanatics.

What is the smallest number that can be expressed as the sum of two different sets of cubes? (All the cubed numbers must be positive integers.)

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Cave Diem! Carpe Canem!

Olen, I'm just gonna guess that it's the sum of 1 cubed and 1cubed, which would be 2, figuring, that the two sets of 1 are different sets.

Well, zero of course:
X^3+(-X)^3 = Y^3+(-Y)^3 = 0
But I suspect this isn't the answer you had in mind. Nor, probably is:
1^3+1^3+1^3+1^3+1^3+1^3+1^3+1^3 = 2^3 = 8.

Am I right in assuming that you mean all the numbers being cubed are positive whole integers and that each integer appears only once?

Hmmm. I'll have to get a pencil...

Oops! You SAID they were all positive integers. Sorry. Never mind.

PB

Texas, 1960, 2nd grade - yes, we took it to the twelves and did it, as I'm sure many did tho' I've missed any mention of 'em, w/good old Flash Cards!

Frankly, I'm glad I went through that, although I'm sure I wasn't at the time.

ooooo... a math puzzle

olentzero, are you thinking of "Ramanujan's number", the number 1729? It's the smallest number that can be written as the sum of two cubes in two different ways:
1729 = 1^3 + 12^3
1729 = 9^3 + 10^3

or were you thinking of something else entirely?

I had to memorize up to 12 x 12 in CA, US back in about 1938, but I have to say that
12 x 12 is really gross. . .so to speak.

Ray

You see people, this is why blocks and legos and puzzles are important for little kids. They ingrain the concept of whole positive integers, spacial and geometric relationships, etc. If you think of the 12x12 table (which is the one I had to learn, by the way) in your PeeChee folder as a wall of blocks, it becomes easy to visualize the products. Arithemetic is all about spatial relationships, and kids who are comfortable with these tools won't have problems with the numbers.

Incidentally, studies show that early music lessons help, also...

And the prize goes to lynne! Nice work, fellow Doper. I'll spare you all the 1729 rant I've worked up, but suffice it to say it's popped up in some odd places.

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Cave Diem! Carpe Canem!