## What’s the best order to learn times tables in?

Sometimes, something seems so obvious to you that you can’t imagine that other people don’t already do it.

This is how I feel about times tables. I’ve always encouraged children to learn them in a particular order and have always just assumed that everyone else does too. However, the more different schools I work in, and the more I come into contact with children who are being asked to learn their times tables in numerical order, the more I have come to realise that this is not necessarily the case.

I always get my pupils to start with the 10x tables. These are easy. There’s a pattern to 1×10=10, 2×10=20, 3×10=30 that makes them easy to remember. Once the child has spotted the pattern they can easily recall them in any order. I follow x10 with x11. There’s another pattern here 1×11=11, 2×11=22, 3×11=33 that takes them all the way through to 9×11=99. They already know 10×11 from their 10x tables, and if they struggle with 11×11 and 12×11 there is a little 11x tables trick they can use to work them out.

After that we look at 2x tables. There isn’t a pattern to these, but the answers are all even numbers, they are all doubles of the question, and the highest answer is 24, so they are fairly easy to learn.

When they are confident with x2, it’s time to move on to x4. All the answers here are double the 2x tables, so while they are learning 4x they are still practising 2x. This is important as I have seen so many children forget the x table they have just learnt when they start learning a new one.

After x4 comes x8 because – you guessed it – it’s double x4. If necessary the children can look at the number in the question and do double (x2), double (x4) and double again – eg 3 x 8 –> double 3 is 6, double 6 is 12 and double 12 is 24 so 3 x 8 = 24. This means that while learning their 8x tables, children are continuing to practice x2 and x4.

By now the children are feeling confident because they know their 8x tables, and everybody knows that’s a hard one, so it’s time to drop back a notch to a couple of easier ones to get two more under their belts in quick succession. In the 5x tables, all the answers end in 5 or 0, which is a big clue to the answer, the answers are all half of the 10x tables, and most children can count really quickly in 5s so even if they struggle with recall they can work them out quickly. Then we look at the x9 finger trick so that even if they never manage to learn their 9x tables off by heart, they can work then out so quickly on their fingers that it doesn’t matter.

Then we take stock of where we are. They know their x1 x2 x4 x5 x8 x9 x10 and x11 so they can see that we are 2/3 of the way through them, and two of the so-called tricky ones (x8 and x9) are out of the way.

And so we move onto the threes. Now in my opinion, x3 really is a tricky one. There are no patterns, it’s not as easy to count in 3s as it is on 2s, 5s or 10s and there are no tricks. After x7 I think it’s the trickiest one there is. However, now it’s not so bad because they have learnt most of their tables already, so there’s only 3×3, 6×3, 7×3 and 12×3 left to learn which doesn’t seem too daunting at all.

And then of course x6 is double x3, so they can learn x6 and practise x3 at the same time.

By the time they have finished their 6x tables, the only ones left are 7×7, 7×12 (and 12×7) and 12×12, and buoyed up by the confidence of having learnt all the others it doesn’t take long to finish these last few.

If you need some idea for how to learn the times tables, rather than just this suggestion of which order to learn them in, have a look at Teaching the Times Tables.

Recently we looked at how to square two-digit numbers ending in 5 in your head.  What about the other square numbers?  Well, there’s a quick way to do that in your head as well.

Let’s look at 372.
First of all round the 37 up or down to the nearest 10.
You added 3 to get 40, so you also need to subtract 3 to get 34 (37-3=34)
Multiply these to numbers together 40×34 = 4 x 34 x 10 = 1360 (4×30=120,  4×4=16, 120 +16 = 136, 136×10=1360)
Finally, add on the square of the number you added and subtracted (here it was 3 and 3×3=9 so add 9) 1360+9=1369.
So 372 = 1369

Here’s another example: 622
Round this down to 60, and then because you subtracted 2, you also have to add 2 so you get 60×64 (6 x 64 x 10). 3 x 60 = 360, 6 x 4 = 24, 360 + 24 = 384, 384 x 10 = 3840
Remember to add the square of the number you rounded down by. 22 = 4 so add 4.
3840 + 4 = 3844
So 622 = 3844

If you’ve enjoyed these tricks then you might enjoy the Secrets of Mental Maths course from The Great Courses. It’s fascinating!

## How to square 2 digit numbers ending in 5 (in your head)

This is another trick that my family already knew, but I only learnt it recently so I’m sharing it for anybody out there who doesn’t already know.

Squaring 2 digit numbers is easy if they end in 5.

5×5 = 25, so the last 2 digits of the answer will always be 25.

To find the first digits of the answer, take the first digit of the number you are squaring and multiply it by the next ten up.

Eg 65 x 65

The first digit is 6. The next ten up is 7, so to find the first digits of the answer you multiply 6×7.

6×7 = 42

The last two digits will always be 25 so 652 = 4225

352 = 1225  (3×4 = 12 and the last 2 digits are 25)

852 – 7225 (8×9 = 72 and the last 2 digits are 25)

It’s especially useful for squaring something-and-a-half eg 7.5 x 7.5. 7 x 8 = 56. The last two digits will be 2 and 5, but here you are using ½ not a whole number, so it won’t be 25 but .25 so the answer is 56.25.  3.52 is 12.25 and so on.

If you enjoyed this trick, you might also enjoy this post on how to multiply 2 digit numbers by 11 in your head.

## Multiplying 2 digit numbers by 11

Earlier this year I discovered a trick for multiplying 2 digit numbers by 11.  I taught this to some of the children I tutor to help them work out 11×11 and 11×12 which they had been struggling with but then as it works for all 2 digit numbers they have enjoyed baffling their family and friends with their ability to perform calculations such as 54 x 11 in their head.

Apparently it’s not as big a secret as I had thought (well, everyone in my family already knew how), but I’m going to share it anyway just in case some of you don’t already know how…

First of all you split the digits of the two digit number, and these become the first and last digits of the answer. Eg with 54 x 11, the answer is going to start with 5 and end with 4. To get the number in the middle you just add the two digits together. 5 + 4 = 9, so put 9 in the middle. Your answer is 594.

35 x 11 = 3 [3+5] 5   that is 385
42 x 11 = 4 [4+2] 2   that is 462.

That’s all very well, but what if the two digits add up to more than 9?  That’s easy too. You partition that number, the units become the middle digit and the tens get added to the first digit.

86 x 11 = 8 [8+6] 68  6 → uh oh!  It can’t be 8146. That’s ok – split the 14. The 4 becomes the middle digit, and the ten (1) gets added to the first digit → 8+1=9, so the answer is 946.

Happy calculating! ## F is also for….Finger tables. We all know that times tables are really useful, so but some of them are just too hard to remember. Luckily there are tricks to help with some of the really difficult ones.

I’m sure you already know the 9 times tables trick, but if you don’t have a look at this video which explains it https://www.teachertube.com/viewVideo.php?video_id=167010. Does that make the 9s seem a bit less scary?

There is also a trick for those awkward 6s 7s and 8s.  It’s not as easy as the 9s trick, but if you are really struggling with them then it may be worth a go. Have a look at this blog post which explains step by step how to use your fingers to use the times tables you already know to work out the 6s 7s and 8s.

Good luck!

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