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Looking at the multiplication circle, it doesn't appear to have any products written. The numbers on the outside are almost definitely factors (note the lack o

Looking at the multiplication circle, it doesn't appear to have any products written. The numbers on the outside are almost definitely factors (note the lack of 10, and the relatively high frequency of 7 and 8, which are generally the hardest to memorize.) So I don't think it's a way of teaching multiplication directly, but more likely is a way of testing. My best guess is that the teacher would call a student up to the board, and then (using some sort of semi-random process, like slapping a ruler against the board) use the wheel to generate a problem for the student to solve (5x7, or 8x9). It looks like a more complex/extensible version of this worksheet: https://www.superteacherworksheets.com/multiplication/circle-multiplication_TWZFT.pdf https://www.superteacherworksheets.com/multiplication/circle...

cactusface 11y ago
Why are 7 and 8 the hardest to memorize?
- callmeed 11y ago
  I don't know why, but as a parent of 4 I definitely think it holds true.
- iherbig 11y ago
  No discernible pattern and the numbers very quickly get large, I imagine. 2 is always even. 3 only gets to 30 after 3 x 10. 4 has a quick pattern (4>8>2>6>0>..). 5 always ends in a 5 or a 0. 7's pattern is long 7>4>1>8>5>2>9>6>3>0>.. with no sense to it and the numbers get big fast. 8's pattern is short (8>6>4>2>0>..) but the numbers are unwieldy getting into the 40s really quickly. 9's pattern is easy: start with 09. Add one to tens-place and subtract one from ones-place. So it's long, but pretty: 9>8>7>6>5>4>3>2>1>0>.. I skipped 6 because it seems to me that 6 would probably be pretty difficult for the same reason 8 is difficult. Its pattern is short (6>2>8>4>0>..) but there's less sense to it than there is to 8's pattern, and the numbers get large rather quickly. At least, that's the reasoning I've always figured. I have no idea.
  - cactusface 11y ago
    Seems reasonable to me. I'd say 7 is harder than 8. I think 6 is easy because it's 2 x 3 so you're already kind of familiar with the products.
  - keithpeter 11y ago
    Just one idea: you don't come across things in multiples of 7 that often. UK: eggs come in 6s. Pizzas get cut into 4s and perhaps 8s for a really huge one, so multiples of those numbers get seen around. Half is sort of easy (all my adult students can usually find half of a figure, especially if I encourage them to think of paying it out in money with £10 notes and £1 coins). 5 fits into the decimal system nicely. Threes are easy to count up.
    - beejiu 11y ago
      > Just one idea: you don't come across things in multiples of 7 that often. Days of the week?
      - keithpeter 11y ago
        You got me there! But just thinking around weeks, apart from a fortnight do you actually count the days in multiples of 7 or just think about months or a period of weeks?
        songshu 11y ago
        I became good at sevens working in a pharmacy store room in a large hospital where we did continue to count in weeks. Boxes of 112 were common. Inside you would find blister packs arranged in rows of seven with the days of the week printed.
        keithpeter 11y ago
        Nice example!
      - deleted 11y ago
- astrobe_ 11y ago
  2 * n is easy. 3 * n is easy, just multiply by 2 and add one n. 4 is easy, just multiply by 2, two times (or multiply by 5 and subtract one n). 5 is easy. Six is easy, just multiply by 5 and add one n. 9 is easy, just multiply by 10 and subtract one n. But 7 and 8 are not 'reachable' with two operations.
  - astrobe_ 11y ago
    Actually, Using those tips and commutativity, the only thing you need to know about 7 and 8 is 7 * 8.
sorich87 11y ago
I think this is correct. I remember using a version of this as you described, in primary school (it may have been simpler, my memory is quite fuzzy). I'm 27 years old from West Africa.
dtparr 11y ago
This is actually how my 4th grade teacher did it circa 1990. We had to prove we'd memorized our times tables up to 12. So when you said you were ready, she'd draw 1-12 in a 'random' order on the circle, write the number you were ready for in the center, then work her way around the circle, pointing with a yardstick (she'd occasionally jump around to keep you from working ahead). If you got them all right, you could move on to the next number.

cactusface 11y ago

Why are 7 and 8 the hardest to memorize?

callmeed 11y ago
I don't know why, but as a parent of 4 I definitely think it holds true.
iherbig 11y ago
No discernible pattern and the numbers very quickly get large, I imagine. 2 is always even. 3 only gets to 30 after 3 x 10. 4 has a quick pattern (4>8>2>6>0>..). 5 always ends in a 5 or a 0. 7's pattern is long 7>4>1>8>5>2>9>6>3>0>.. with no sense to it and the numbers get big fast. 8's pattern is short (8>6>4>2>0>..) but the numbers are unwieldy getting into the 40s really quickly. 9's pattern is easy: start with 09. Add one to tens-place and subtract one from ones-place. So it's long, but pretty: 9>8>7>6>5>4>3>2>1>0>.. I skipped 6 because it seems to me that 6 would probably be pretty difficult for the same reason 8 is difficult. Its pattern is short (6>2>8>4>0>..) but there's less sense to it than there is to 8's pattern, and the numbers get large rather quickly. At least, that's the reasoning I've always figured. I have no idea.
- cactusface 11y ago
  Seems reasonable to me. I'd say 7 is harder than 8. I think 6 is easy because it's 2 x 3 so you're already kind of familiar with the products.
- keithpeter 11y ago
  Just one idea: you don't come across things in multiples of 7 that often. UK: eggs come in 6s. Pizzas get cut into 4s and perhaps 8s for a really huge one, so multiples of those numbers get seen around. Half is sort of easy (all my adult students can usually find half of a figure, especially if I encourage them to think of paying it out in money with £10 notes and £1 coins). 5 fits into the decimal system nicely. Threes are easy to count up.
  - beejiu 11y ago
    > Just one idea: you don't come across things in multiples of 7 that often. Days of the week?
    - keithpeter 11y ago
      You got me there! But just thinking around weeks, apart from a fortnight do you actually count the days in multiples of 7 or just think about months or a period of weeks?
      - songshu 11y ago
        I became good at sevens working in a pharmacy store room in a large hospital where we did continue to count in weeks. Boxes of 112 were common. Inside you would find blister packs arranged in rows of seven with the days of the week printed.
        keithpeter 11y ago
        Nice example!
    - deleted 11y ago
astrobe_ 11y ago
2 * n is easy. 3 * n is easy, just multiply by 2 and add one n. 4 is easy, just multiply by 2, two times (or multiply by 5 and subtract one n). 5 is easy. Six is easy, just multiply by 5 and add one n. 9 is easy, just multiply by 10 and subtract one n. But 7 and 8 are not 'reachable' with two operations.
- astrobe_ 11y ago
  Actually, Using those tips and commutativity, the only thing you need to know about 7 and 8 is 7 * 8.

sorich87 11y ago

I think this is correct. I remember using a version of this as you described, in primary school (it may have been simpler, my memory is quite fuzzy). I'm 27 years old from West Africa.

dtparr 11y ago

This is actually how my 4th grade teacher did it circa 1990. We had to prove we'd memorized our times tables up to 12. So when you said you were ready, she'd draw 1-12 in a 'random' order on the circle, write the number you were ready for in the center, then work her way around the circle, pointing with a yardstick (she'd occasionally jump around to keep you from working ahead). If you got them all right, you could move on to the next number.