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<p>Except for my youngest dd, none of my four kids made any effort to memorize the multiplication facts at the typical age and stage. As they continued to progress through the Singapore Math curriculum, which uses a fairly standard scope and sequence but with little repetition or drill, they had access to a laminated card that had the multiplication table printed on it. If they couldn't quickly derive a multiplication fact from something they already knew they were free to refer to the table. The vast majority of the 'facts' either gradually became memorized just through repeated use, or could be derived so quickly that there was no point in memorizing them. By the time they got to high school level, they might have had two or three facts that they still had to work out in their heads (very quickly, I might add!), but the others were all naturally memorized and available for instant retrieval.</p>

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<p>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, songs 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 much opportunity to practice their mathematical thinking. </p>

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<p>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.</p>

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<p>Miranda</p>

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7,681 Posts

<p> </p>

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

<p>FlashMaster electronic math-fact drill device</p>

<p>Pictorial mnemonic kits like the one at Multiplication.com or timestales.com</p>

<p><a href="http://www.amazon.ca/gp/redirect.html?ie=UTF8&linkCode=ur2&camp=1789&creative=9325&tag=motheringhud-20&location=http%3A%2F%2Fwww.amazon.ca%2FSmall-World-Toys-Preschool-Multiplying%2Fdp%2FB00000IUCE%2Fref%3Dpd_vtp_b_12" rel="norewrite" target="_blank">This 1970's retro 'depression board'</a> 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</p>

<p>Schoolhouse rock musical/animated learning aids</p>

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<p>and my favourite "tricks" guide...</p>

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<p><a href="http://www.naturalmath.com/mult/mult1.html" target="_blank">Adventures in Number Sense:</a> why there are only about 13 'facts' you have to memorize.</p>

<p> </p>

<p>Miranda</p>

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6,272 Posts

<div class="quote-block">Originally Posted by <strong>moominmamma</strong> <a href="/community/t/1393107/multiplication-tables-how-to-teach#post_17508972"><img alt="View Post" src="/community/img/forum/go_quote.gif" style=""></a><br>

<p>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 much opportunity to practice their mathematical thinking. </p>

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<p>Miranda</p>

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<p>I see this happening with my 7 and 9yo. 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. Some of the simpler ones they can reach the answer in a flash, but it is from repeatedly working the numbers until it becomes familiar. This method does come with some "gaps" as experience gradually fills in the blanks. I'm perfectly comfortable with that if it means their foundation is rock solid.</p>

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<p>1 2 3</p>

<p>4 5 6</p>

<p>7 8 9</p>

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<p>For 7's you work bottom to top, left to right. The tens place is 0,1,2; 2,3,4; 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. It sounds complicated, but he caught on way faster than just trying to memorize.</p>

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<p><span style="font-size:18px;"><span style="font-size:8px;">2</span>1 <span style="font-size:8px;">4</span>2 <span style="font-size:8px;">6</span>3</span></p>

<p><span style="font-size:18px;"><span style="font-size:14px;"><span style="font-size:8px;">1</span></span>4 <span style="font-size:8px;">3</span>5 <span style="font-size:8px;">5</span>6 </span></p>

<p><span style="font-size:18px;"><span style="font-size:8px;">0</span>7 <span style="font-size:8px;">2</span>8 <span style="font-size:8px;">4</span>9</span></p>

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

<p>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.</p>

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<p>4s, 6s and 8s use a pentagon/star configuration. Draw a pentagon with the even digits at each point, starting with 0 at the top and counting up in a clockwise direction. 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 they build a visual cue in their minds and actually enjoy the repetition.</p>

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<div class="quote-block">Originally Posted by <strong>Qalliope</strong> <a href="/community/t/1393107/multiplication-tables-how-to-teach#post_17510076"><img alt="View Post" src="/community/img/forum/go_quote.gif" style=""></a><br>

<p>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. </p>

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<p>So cool! Thanks for the explanation. Off to draw pentagons now...</p>

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<p>miranda</p>

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8 Posts

<p>I might be old-school, but it seems like we don't ever have to memorize anything anymore. 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.</p>

<div class="quote-block">Originally Posted by <strong>Qalliope</strong> <a href="/community/t/1393107/multiplication-tables-how-to-teach#post_17510076"><img alt="View Post" src="/community/img/forum/go_quote.gif" style=""></a><br>

<p>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. He just memorized the patterns. So for 3, 7, and 9, the visual is a number keypad on a phone. </p>

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<p>1 2 3</p>

<p>4 5 6</p>

<p>7 8 9</p>

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<p>For 7's you work bottom to top, left to right. The tens place is 0,1,2; 2,3,4; 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. It sounds complicated, but he caught on way faster than just trying to memorize.</p>

<p> </p>

<p><span style="font-size:18px;"><span style="font-size:8px;">2</span>1 <span style="font-size:8px;">4</span>2 <span style="font-size:8px;">6</span>3</span></p>

<p><span style="font-size:18px;"><span style="font-size:14px;"><span style="font-size:8px;">1</span></span>4 <span style="font-size:8px;">3</span>5 <span style="font-size:8px;">5</span>6 </span></p>

<p><span style="font-size:18px;"><span style="font-size:8px;">0</span>7 <span style="font-size:8px;">2</span>8 <span style="font-size:8px;">4</span>9</span></p>

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

<p>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.</p>

<p> </p>

<p>4s, 6s and 8s use a pentagon/star configuration. Draw a pentagon with the even digits at each point, starting with 0 at the top and counting up in a clockwise direction. 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 they build a visual cue in their minds and actually enjoy the repetition.</p>

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<p>I'm such a visual person. Trying to figure this out has made me <img alt=":dizzy" src="http://files.mothering.com/images/smilies/dizzy.gif" style="">. But, thanks for sharing! One of my children might get this. <img alt=":lol" src="http://files.mothering.com/images/smilies/lol.gif" style=""></p>

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<p>Sus</p>

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<p> </p>

<p>9 x 1 = 09, 90 = 9 x 9</p>

<p>9 x 2 = 18, 81 = 9 x 9</p>

<p>9 x 3 = 27, 72 = 8 x 9</p>

<p>9 x 4 = 36, 63 = 7 x 9</p>

<p>9 x 5 = 45, 54 = 6 x 9</p>

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<p>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.</p>

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<p>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.</p>

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<p>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 multiplication 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. </p>

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<p>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. </p>

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And let me guess, you're not affiliated in theI've found very impressive way how to learn kids multiplication tables.

Namely is Aztekium App - Visitaztekium.pl/Master:grin:

I guess it can help, regards!

Miranda

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For numbers with two digits, my friend in Japan once showed me how they learn it in grade 1 there. They draw lines (and how based on the numbers and the orders you put them that helps determine whether to add or subtract...), rather an interesting and eye opening way to acquire the results without a calculator.

I am new so am unable to print links but if you look up: 'Japan multiplication with lines' on google you will find a ton of examples. Hope these two suggestions help.

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Doing factoring, division, fractions, exponents, formulas, conversions, and all algorithms require solid ready knowledge of the multiplication tables. Period!

So the sooner the better. I would say age 7-9, and no later.

For reference, at my first job I had just a cash box. I worked at a lunch counter at the local public park/pool; no calculator or cash register. I had to add things up in my head, and subtract from the money given and make change, "counting backwards".

Few to none know how to do that today.

FatherBear: lattice math? Vedic math?

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I completely disagree.As a homeschooler who worked in public and private schools, I can assure you that a child cannot move on to higher math without knowing the times tables backwards and forwards.

It depends entirely on how the higher math is taught. If it's taught in a conventional fashion, in which arithmetical algorithm execution and test-taking are considered prerequisites for learning concepts and exploring ideas, and if tools that fill in the memory-gaps are banned, then yes. But if you think a little outside the box, if you're not wedded to a rote-dependent curriculum, then no, not at all.

It worked pretty well for us. My kids did not enjoy drill, so their times-tables got memorized only very gradually -- through repeated use and while moving forward into all sorts of more interesting work. I would say that the last few facts fell into place around the 9th grade level. They all ended up scoring high A's in their high school math courses, including the two who went on to do calculus and continue math at college, and more to the point they continued to enjoy math throughout the middle-school and high school years.

Miranda

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