
Why does the sum 7x8 catch people out? - schrofer
http://www.bbc.com/news/blogs-magazine-monitor-28143553
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TrainedMonkey
I honestly have not bothered memorizing times table. I always found it easier
to compute correct answer each time I need it. I just memorized few anchors:
any number times 10 is easy to compute, from that it is easy to compute any
number times 5, so only thing I memorized is number times itself. After that
you can turn almost any multiplication into simple subtraction or addition.

For example 7 * 8 = 7*7 + 7 = 49 + 7 = 56

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ghshephard
How on earth did you manage to get out of grade school without having
everything up to 12*12 burned into your brain? Where did you go to school?

Oh, how I envy you.

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topbanana
Nobody ever taught me the number of days in each month. I was well into my 20s
before I had it nailed

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usefulcat
30 days hath September, April, June and November

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mansr
That's pretty useless as a mnemonic. "30 days hath September, August, March
and December" fits the pattern equally well.

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webhat
Not if you remember the whole rhyme:

    
    
        Thirty days have September,
        April, June, and November.
        All the rest have 31,
        Except February alone,
        And that has 28 days clear,
        And 29 in a leap year.

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mansr
My substitution works without contradictions there too.

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Boldewyn
As a non-native speaker, is “sum 7x8” an error? Shouldn’t it be “product 7x8”?

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TomNomNom
In (British) English, equations are sometimes called 'sums'. It's a confusing
colloquialism, and you're right to be confused by it.

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lotharbot
I spent the last year tutoring math full time (approximately 28 fourth grade
students per day in small groups).

At one point we did an exercise with a blank 12x12 multiplication table. I had
students fill in what they already knew. Ones, fives, tens, elevens up to
11x10, and twos were easiest. Most of them could figure out threes and fours
pretty quickly. I taught them the finger trick for nines (9x6... hold up your
fingers, drop the 6th finger, you have 5 on the left and 4 on the right for
54.) Most of them also had 6x6, 7x7, and 8x8 memorized.

This left 6x8, 7x8, 12x6 through 12x9, 11x11, 11x12, and 12x12. Not
surprisingly, these are also the products adults tend to have the most trouble
with. I had students select some problems they didn't have memorized, and
commit to memorize them over the coming week.

Lest you think it was all about memorization, I also taught a number of
techniques for quick computation -- often taking the form of number splitting
(6x8 = 5x8 + 1x8) or quick drawings (draw 6 horizontal lines, cross them with
8 vertical lines, count the intersections for 6x8 -- this can be combined with
the previous technique by counting by 5s and then counting the remaining
intersections.)

Those students who gained proficiency in multiplication also improved quickly
in division, fractions, and various other parts of the curriculum.

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quesera
The "times table difficulty chart" is sort of fascinating.

I've always thought that 7x8 would be the hardest, but their sample set says
6x8 is.

Looks like these kids hadn't been taught the 9s-table trick, nor the "6-times
even-X always ends in X mod 10" trick. OK, I made that last one up...but
6-times even-X often rhymes, which I remember finding quite useful for
memorization.

Separately, I was always taught that multiplication produces "products", and
addition produces "sums". Perhaps the Brits disagree.

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Arnavion
The word "sum" is used here to mean an arithmetic expression or math in
general. For example, a parent might ask their child, "Have you done your
sums?" to mean "Have you done your maths homework?"

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vorg
> "It's those numbers near the middle that kids find the hardest - the sixes,
> sevens, eights and nines," says Flurrish's director

One problem with getting kids to memorize times table the English way is that
those numbers _are_ near in the middle, not at the top. The 11 and 12 times
tables can be worked out by the same process as for multiplying by 13, so why
memorize for 12 but not for 13 ? Children should finish memorizing at the easy
10 times, so they have a sense of having nailed the numbers, instead of a
sense of dangling at the difficult 12 times tables and it can only get harder.

Also, when reciting tables, why should children recite both 7 x 8 and 8 x 7
when they could be practising the commutative rule. They should only memorize
multiplying when, say, the second number is higher than the first, so memorize
7 x 8 but not 8 x 7. Children would then feel like there's less needing to be
tackled, the only really hard ones being 4 x 8, 6 x 7, 6 x 8, 7 x 8, and some
squares.

I suggested the second number being _higher_ than the first for memorizing
multiplication instead of vice versa because children also need to memorize
addition tables up to 9 + 8, and because they'd do that before times tables,
it's better to for the second number to be _lower_ than the first for that.
Another benefit is kids wouldn't even need to say "plus" or "times" when
reciting, just the two single-digit numbers because whether it's addition or
multiplication is implied by which number is greater, e.g. "3, 2 is 5", "7, 4
is 11", "2, 7 is 14", "7, 8 is 56", "6, 6 is 36".

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tempestn
I was with you up to the last sentence. Dropping the operator just seems to
obfuscate things unnecessarily.

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vorg
You're right, perhaps...

    
    
      3 and 2 is 5
    
      7 and 4 is 11
    
      2 seven's are 14
    
      7 eight's are 56
    
      6 by 6 is 36
    

to get rid of mathy words "plus" and "times".

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abuddy
The trick is to remember the product of every number multiplied by itself and
go from there.

It's easier for me to know that 7x7 is 49 or that 8x8 is 64. Then I either go
up or go down. If asked what the sum of 7x8 is I remember that 7x7 is 49 and
add 7 to it or remember that 8x8 is 64 and substract 8 from 64.

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patio11
I thought I was the only one. Since grade school, I've pre-cached that as "The
one I always get wrong is 56."

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wglb
Me as well! Amazing.

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lotsofmangos
Alternative reading: Why the hell is an Eton educated Chancellor of the
Exchequer so unable to field questions on primary school arithmetic, that the
news is now seriously trying to float the possibility that 7x8 is in some way
particularly tricky?

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jqm
This is hilarious and brings back memories.

Being lazy, I didn't actually memorize times tables combos knowing I could
just figure it out. For example, the 9x series is just 10 times minus the
number (9x4? just 10x4 = 40-4= 36). Or I would just sum up the numbers in my
head. To this day I still haven't memorized the full times tables and I'm not
sorry. Although, it retrospect it might have actually been faster to memorize,
it probably contributed to mental development thinking about the problem each
time rather than spitting out a burned in answer.

But there was one combo that didn't have a quick cheat and I couldn't do
easily by simply adding. 7*8. So I flat out memorized that one because I
didn't have an option. I think it's one of only a few table combos I actually
have "memorized".

The teachers were never the wiser or if they were they didn't let on.

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pge
I find 7x8 one of the easiest to remember, because I was taught to remember
56=7x8 (5-6-7-8)

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maho
As a homework problem (University), we once had to find all such equations, in
all possible bases. Turns out there is only two, and they are both in the
decimal system: 56=7x8, and 12=3x4.

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PaulHoule
I think there are patterns that help for most of the facts; the 2s, 5s, 9s,
and 10s are dead easy. Then there are facts involving powers of twos, squares,
the 3s are easy too, really 7 is the first prime that isn't hard at all, and 8
is the hardest fact.

After coaching my kid through Common Core, It recently hit me to think of the
progression

14 x 2 -> 28 x 2 -> 56

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echaozh
When I was in middle school, I had a book (in Chinese), teaching children how
to carry out some simple calculations fast. It had a back story, with village
boys trying to help out the adults when they're stuck with such simple
calculations.

It mentioned some interesting facts and I can still remember them today. Like
when you divide anything by 7, you get a permutation of the string 142857 as
the fractional part. Also notice how 14, 28 and 57 (yes, I mean it) are
multiples of 7.

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bruceboughton
57 isn't a multiple of 7?

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balbaugh
One of my grade school teachers taught me a trick for 7x8. She would tell us
to think of the grades one would have to pass before reaching the 7th and 8th
grades of school... 5th and 6th. Thus, I will always remember that 7x8=56.

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michaelhoney
I am glad I learned my times tables and would encourage everyone to do it.
It's not that hard and it pays dividends for life. Having complete familiarity
with human-scale numbers is part of being a numerate human.

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Grue3
As I read the headline the answer popped into my head instantly. Mind you, I'm
only good at multiplicating one digit numbers. If it's more than 12*12, I'm
toast.

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danbruc
I hopefully read the article to finally learn why some products are harder to
remember than others...but no why in there.

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theforgottenone
Why does the word "product" catch people out?

