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# multiplication tables? How to teach...

Any tricks, suggestions, games, curriculum, unschooly ideas on how to help child memorize times tables? Â Any thoughts on whether or not this is "necessary" at a certain age? Â signed, usort of unschooler in a public charter :)

I don't believe memorization is necessary at a certain age or stage. I can imagine scenarios (erosion of the child's confidence in his or her ability, beingÂ in a school system that attaches lots of value to speedy accurate and unassistedÂ computation, a child who believes that it's 'cheating' somehow not to have the facts memorized and that this represents a personal deficiency, obnoxious friends or relatives who persistently quiz the child on these facts) when memorization might be advisable. But no, not necessary.

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I honestly think you can make a case for early and complete rote memorization impeding the development of mathematical ability. If a 7-year-old memorizes all the multiplication facts through some sort of rote method (eg. daily chanting, skip-counting,Â songsÂ and drill), from then on there's no real mathematical thinking involved in getting at those numbers. When that child sees 9x7, she just remembers 63. When a child who hasn't rote-memorized that fact needs the answer, she has to think "9x7 means 9 of the 7's, which is one 7 less than 10 of the 7's, and I know that 10 of the 7's is the same as 7 of the 10's, which is 70, and 7 less than that would be ... 63." That whole, lightning-fast mental math process is very conceptual, pulling in ideas about place-value and the commutative property of multiplication, and combining various operations in a logical sequence. I find it hard to believe that building fluidity and confidence with multi-step mental math this way isn't an excellent way to build a really solid foundation in number sense and the logical inter-relationship of various operations. If kids memorize too early, they don't get as muchÂ opportunity to practice their mathematical thinking.Â

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My own experience with my kids favours this hypothesis. While they might not have excelled on a timed test of long division when they were at a 5th grade level, by the time they entered high school they were not only pretty slick with multiplication fact retrieval, but they had very strong conceptual skills that gave them an excellent foundation for higher, more abstract math.

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Miranda

Oh, and if you want tips and tricks for memorizing ....

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TimezAttack computer game; I'm sure there are also copious android and ios apps

FlashMaster electronic math-fact drill device

Pictorial mnemonic kits like the one at Multiplication.com or timestales.com

This 1970's retroÂ 'depression board' which actually served in lieu of a printed table of facts for two of my kids, but can be used in a self-quizzing fashion as well

Schoolhouse rock musical/animated learning aids

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and my favourite "tricks" guide...

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Adventures in Number Sense: why there are only about 13 'facts' you have to memorize.

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Miranda

Quote:
Originally Posted by moominmammaÂ
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I find it hard to believe that building fluidity and confidence with multi-step mental math this way isn't an excellent way to build a really solid foundation in number sense and the logical inter-relationship of various operations. If kids memorize too early, they don't get as muchÂ opportunity to practice their mathematical thinking.Â

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Miranda

I see this happening with my 7 and 9yo. Â They lag behind in being able to whiz through multiplication problems, but they are puzzling through each one and really solidifying the meaning and process. Â Some of the simpler ones they can reach the answer in Â a flash, but it is from repeatedly working the numbers until it becomes familiar. Â This method does come with some "gaps" as experience gradually fills in the blanks. Â I'm perfectly comfortable with that if it means their foundation is rock solid.

We like Times Tales and Timez Attack

I don't know where I found this information, but each number has a pattern that it follows when you multiply it by 1-9 in sequence. DS didn't memorize the table at all. Â He just memorized the patterns. Â So for 3, 7, and 9, the visual is a number keypad on a phone. Â  Â

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1 2 3

4 5 6

7 8 9

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For 7's you work bottom to top, left to right. The tens place is 0,1,2;Â 2,3,4;Â 4,5,6. So for 7 x 6, you visualize the number pad, see that the 6th number is at the top, middle. It's a 2, answer 42. Â It sounds complicated, but he caught on way faster than just trying to memorize.

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21 Â 42 Â 63

14 Â 35 Â 56Â

07 Â 28 Â 49

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For 3s, you work the opposite direction, top to bottom, right to left, and the tens place only changes every column.

For 9s you work bottom to top, right to left, and the tens place changes for each number, but you start with zero, so 9 x 9 is 8 in the tens place, 1 in the ones place, 81.

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4s, 6s and 8s use a pentagon/star configuration. Â Draw a pentagon with the even digits at each point, starting with 0 at the top and counting up in a clockwise direction. Â For 8s, you work counter-clockwise, adding one to the tens place except when going from 0 to 8. For 6's you draw a five pointed star inside the pentagon. Down to 6, up to 2, across to 8. You get the idea. My kids love drawing these patterns, and there's a fascination with how the numbers fit together, so theyÂ build a visual cue in their minds and actually enjoy the repetition.

Quote:
Originally Posted by QalliopeÂ
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I don't know where I found this information, but each number has a pattern that it follows when you multiply it by 1-9 in sequence.Â

So cool! Thanks for the explanation. Off to draw pentagons now...

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miranda

Growing up I loved using Wrap Ups to learnÂ multiplication &Â division. Here's a video explaining how it works:Â https://www.youtube.com/watch?v=7uv6Dj73knAÂ

I might be old-school, but it seems like we don't ever have to memorize anything anymore.Â I think it's valuable for kids to find a method that works for them to remember things. I'm sure you'll figure out what's best for your child.

Quote:
Originally Posted by QalliopeÂ
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I don't know where I found this information, but each number has a pattern that it follows when you multiply it by 1-9 in sequence. DS didn't memorize the table at all. Â He just memorized the patterns. Â So for 3, 7, and 9, the visual is a number keypad on a phone. Â  Â

Â

1 2 3

4 5 6

7 8 9

Â

For 7's you work bottom to top, left to right. The tens place is 0,1,2;Â 2,3,4;Â 4,5,6. So for 7 x 6, you visualize the number pad, see that the 6th number is at the top, middle. It's a 2, answer 42. Â It sounds complicated, but he caught on way faster than just trying to memorize.

Â

21 Â 42 Â 63

14 Â 35 Â 56Â

07 Â 28 Â 49

Â

For 3s, you work the opposite direction, top to bottom, right to left, and the tens place only changes every column.

For 9s you work bottom to top, right to left, and the tens place changes for each number, but you start with zero, so 9 x 9 is 8 in the tens place, 1 in the ones place, 81.

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4s, 6s and 8s use a pentagon/star configuration. Â Draw a pentagon with the even digits at each point, starting with 0 at the top and counting up in a clockwise direction. Â For 8s, you work counter-clockwise, adding one to the tens place except when going from 0 to 8. For 6's you draw a five pointed star inside the pentagon. Down to 6, up to 2, across to 8. You get the idea. My kids love drawing these patterns, and there's a fascination with how the numbers fit together, so theyÂ build a visual cue in their minds and actually enjoy the repetition.

I'm such a visual person. Â Trying to figure this out has made meÂ . Â But, thanks for sharing! Â One of my children might get this.Â

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Sus

For 9 there is also the finger trick, where you bend a figure forward, and then look at the digits on either side of the bentÂ one. The ones to the left are in the tens place, and the ones to the right are in the ones place.Â  So starting with your left hand pinky, 9 x 1 = 9. Â There are no fingers on the left hand side and 9 on the right. Â So 09. Â Then bend the left ring finger forward, there is one finger to the left, 8 to the right.Â ThenÂ 27, 36 and so on. Â Of course it's even easier to just see the pattern with the numbers, and see they go in order, and the digits of each answer add up to ten.

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9 x 1 =Â 09, 90 = 9Â x 9

9 x 2 =Â 18, 81 = 9Â x 9

9 x 3 =Â 27, 72 = 8 x 9

9 x 4 =Â 36, 63 = 7 x 9

9 x 5 =Â 45, 54 = 6 x 9

Cool tricks!

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Here is my take on memorizing times tables: if you have a need to do lots of multiplication, you will memorize them very easily. If you don't, it's a waste of time.

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When I was 14 I got my first job at McDonalds. We had no computers then, and we wrote down orders by pencil and paper, memorized the price of each item, and added them up by hand. I had never been very good at adding the higher single digits, like 8 + 6, or 7 + 9, etc. but after working there I got super fast at it, had all combinations memorized. I used it, and I learned it. This really drove home to me how having a practical use for something is a great drive for learning.

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DD is just starting to get deeper into multiplication. When she first expressed an interest in it, she was about 5 or 6, and she loved to draw and was a very visual learner, so I showed her how to "translate" a multiplication equation into pictures. 4 x 6 meant draw four big circles, fill each with 6 items, and add them all up for the answer. She loved doing this. She took a break from math for some time, and now is just getting back into multiplication. Not only did she remember the rule and use it to answer multiplicationÂ problems, but the more she does it the more patterns emerge to her. She is beginning to see the relationships between the numbers and understand multiplication in a way she never would if she just rote memorized the times tables. She recently started doing division and once I explained the concept she was off and running with her big circles, filling them with items. She got the connection immediately.Â

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I think mathematics, and the beauty of mathematics, is in the relationships between numbers. Which is why I don't think rote memorization is at all useful. If you get to a point where it is useful, you'll pick it up with practice, just as I did with addition at my first McJob, lol.Â

My daughter used this finger trick to help with the 6x6 to 10x10 facts: http://m.youtube.com/watch?v=twv-ynv_m9o&desktop_uri=%2Fwatch%3Fv%3Dtwv-ynv_m9o
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