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Jan 5 2016

Understanding, then learning your multiplication tables

YES it is important to memorize multiplication tables, but NO, memorizing them should not be the way to either teach or understand multiplication!

Found the video on the net and thought it is a cool way of learning nine times table.

I always had sharp memory when it came to learning things by rote. The teacher’s “did you understand” never prompted me to introspect “have I understood”?  That is because I knew I could simply learn it by heart. This I could do far more easily and quickly than understanding the concept. And so I believed. Well this short-cut saw me through post-graduation.  Rote memorization did help me in my professionYou know we all became mathematicians for the same reason: we were lazy. - Maxwell Rosenlichtal life when explanations backed with numbers impressed. Well this is not exactly something I am proud of, in case you think it is.

Now when I am teaching Arpita, she keeps asking why? Her whys have forced me to return to my school books and try fathom basic concepts and slowly I converted from pro to anti memorization. When it came to teaching her multiplication through multiplication tables, I thought she should definitely understand the pattern behind the multiplication tables and then just learn her tables by rote. In other words, yes, YES it is important to memorize multiplication tables, but NO, memorizing them should not be the way to either teach or understand multiplication!

The love the way Arpita was introduced to multiplication in her school (Vibgyor High International School) by familiarizing her with the

Multiplication Words of

  • Groups of – 3 groups of 2 make 6.
  • Sets of – 2 sets of 4 make 8.
  • Lots of – 2 lots of 2 make 4.
  • Multiplied -3 multiplied by 4 is 12
  • Product – the product of 5 and 3 is 15.
  • Times – 3 times 2 is 6.

Despite all the efforts on her teacher’s part, I still had to answer her

Why should I learn multiplication tables? I said, because …. 

  1. Multiplication is a much faster way of adding the same number over and over again. For instance 2+2 is easy to do. But when it’s 2+2+2+2+2+2+2+2+2 then adding them is cumbersome. A quicker and more efficient way would be to mutiply 2×9.
  2. When you know basic multiplication then it is easier for you to recognize patterns quicker than when you are dependent on a computer or a calculator grappling with the very basic stuff. Remember I told you about number sequence and pattern.
  3. Multiplication tables will help you develop an intuition  for measurement and quantities and these are very rudimentary life skills. Well, you can develop a sense for estimation through physical exposure as well. But many times you are away from physical entities while dealing with problems which can be solved mathematically and that is when multiplication becomes handy.
  4. Being able to solve simple multiplication in your head through recall will aid you in solving more complex problems as now you will have extra time to concentrate and think on the entire problem.
  5. When you grow up and you will realize that many a times you have to make assumptions, deal with uncertainties and make the best out the information available. Perhaps you will be using Fermi estimates or probability or whatever whatever. Your ability to quickly compute influences the way you estimate, state a probability or come up with a plausible answer. And life will become more manageable with this ability.

I follow Audun Bie in quora (Link: Audun Bie) who had an interesting way of introducing kids to multiplication tables. You could show you kid the same online in teaching tables through paint

The following is Audun Bie’s way of doing so.

“My favourite exercise to have with kids who haven’t learnt their tables yet. Not only is it a good way to teach basic multiplication, but more than that, it show them that there are all sorts of patterns in mathematics.

Start by getting every student to draw up their own 11×11 grid, filling in the numbers from one to ten on the top row and left column:

Next, get them to fill their tables out. I’ve only done this as a substitute teacher, so I don’t really know how much multiplication the kids have had before, but they have consistently been much better at filling these out than they have seemed to believe at first. They can also help each other, and you can point out that the table is symmetrical, so once they’ve figured out 4×3, they also know 3×4, &c.

So far, all my pupils have been able to do this, but it’s fine to do the difficult ones together in class, just make sure everyone gets their table filled out completely. Next, get them to colour all the even numbers yellow. Make sure they use yellow (or some other light colour), because this will matter later.

They’ll probably start discovering even numbers at random, and take a little while before they notice the pattern. But now you have your first two discoveries: You get a neat little pattern, and there’s exactly three times as many even numbers as there are odd numbers. Spend a little time explaining this. Then, tell them to draw a red box around every number that ends in a five (show them on the board, so they get it right—you don’t want them filling in the boxes this time).

That’s quick enough. Explain this pattern to them, too. And have them draw a purple box around every number ending in zero next.

This, too is a pretty easy pattern to explain, but now you’re sure everyone knows how easy it is to multiply by ten, and how five and ten relates. For the next step, you’ll probably have to explain a little. Tell them to colour every number with a digit root of three with light green.

This is why it’s important to use the right colours. If they coloured their evens blue, it will be harder to colour these. Anyway, now you have a new pattern, but it’s probably not readily discernible to elementary school kids yet. I’d skip explanation for now, and tell them to do the same with numbers with digit roots of six.

The pattern is becoming visible now, but can probably still confuse the kids. If anyone wants to talk about it, let them. If not, go dark green on numbers with digit roots of nine.

By now, every number except 1, 7 and that hardest-product-to-learn-49 is part of some pattern that makes a lot of sense and that the kids know about. Tell them to play around with this, try to understand how the patterns work, and see if they can discover some patterns on their own (Like relations between the numbers, maybe even how (n+1)2=n2+2n+1—anything, the point is to get them to play around. And tell them to put this table up on their bathrooms (maybe make a new one if they got the colours wrong, or just want it to look better now that they understand it a bit). Maybe they can cross out every product they’ve memorized, so in the end they only have the hardest bits left (yeah, 49, I’m looking at you).

This wasn’t a question about how children should memorise multiplication tables, but if they should, but I hope I’ve made my point: Multiplication tables are excellent opportunities for showing kids who are just discovering maths that mathematics is full of patterns, and that they can be pretty exciting. And discovering those things is what mathematics should be about, from as soon as children start learning it”.



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  1. Wow very simple way to teach 9 table . Chiyu love it . Thanku Papiya dear


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