QUESTION:

Is there a particular order that is most beneficial to learning times tables? For example, I have heard that learning 1, 5, 10, 11, 2, 4, 8, 12, 3, 6, 9 is a good order. What say you?

MY REPLY:

There are many “schools of thought” on what makes the best order for teaching the times tables.

I encourage everyone out there who has a favorite order to share it with us in the comments. And feel free to explain why this is your favorite order.

Here is my preferred order — and a few notes on why:

1, 2, 4, 10, 5, 11, 3, 6, 9, 8, 12, 7

IMPORTANT NOTE: I teach the facts for the multiplicands 1 – 6 first. Only after

students have those down do I advance to the multiplicands of 7 – 12.

i.e.: When teaching the x 4 facts the first round through, teach 1 x 4 through 6 x 4. On the second round through, teach the 7s through 12s, i.e.: 7 x 4 through 12 x 4.

Using this staggered approach helps students avoid getting befuddled by the size of numbers they encounter early on. This approach builds success and confidence early on.

A few notes on my order:

1st) I teach x 2 second. That’s because you can teach multiplying by 2 as simply “doubling” the number, a concept almost all kids understand. The “doubling” approach gives teachers a good way to talk if you’re going to use manipulatives to reinforce the concept.

In suggesting that you use manipulatives, I mean that you may want to use counters such as tiddly winks, paper clips, pennies, etc. To demonstrate a fact like 2 x 7, you would first lay out a row of 7 counters, then underneath them put out another row of 7 counters, and you would have the student count them all up.

2nd) I put x 4 third because you can teach multiplying by 4 as doubling a number TWICE. e.g.,: 4 x 3: 3 doubled is 6. And 6 doubled is 12, so 4 x 3 = 12.

Again, it would be a good idea to use manipulative counters to demonstrate this concept. Here you would lay out four rows of three counters, to show the fact that 4 x 3 = 12

3rd) I teach x 5 right after x 10 because multiplying by 5 gives you a number that’s exactly half of what you get when you multiply by 10.

When teaching the 5s tables, use the trick that multiplying by 5 is the same as multiplying by 10 and cutting in half. (And, for even multiples of 5, first cutting the number in half, then tacking on a 0 at the end.)

e.g.: for 4 x 5: Half of 4 is 2. Tack on a 0, and you get 20 4 x 5 = 20 [yes, it is that easy!]

4th) You can teach multiplying by 8 in several ways, depending on what works for your children. One way is to see that multiplying by 8 is doubling a number three times. e.g., for 6 x 8: 6 doubled is 12. 12 doubled is 24. 24 doubled is 48. So 6 x 8 = 48

Another strategy for 8: Multiply by 10, then take away 2 x the number. e.g., for 6 x 8: 10 x 6 = 60, and 2 x 6 = 12. 60 – 12 = 48, so 6 x 8 = 48

5th) Multiplying by 12 offers you a great chance to introduce the distributive property for multiplication. That’s just fancy language for saying that when you multiply, say, 6 x 12, you can look at it like this: Since 12 = 10 + 2, 6 x 12 can be viewed as: (6 x 10) + (6 x 2) = 60 + 12 = 72

Most children can get used to this quickly, if they are taught it EARLY ENOUGH.

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