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.

April Fools’ Day

Be very careful if someone asks you for an unusual favour tomorrow.  Or even if they tell you a strange story or you read about bizarre events online.  You might be the victim of an April Fools’ Day prank.  You certainly wouldn’t be the first person to be caught out though.  A day where people play jokes and tricks on one another has been around for many centuries and is found in cultures across the world.  The Romans had the festival of Hilaria, while the Holi festival in India has a long tradition too.  April Fools’ Day is our version.

Nobody knows exactly when April Fools’ Day began and the reasons why 1st April is the day for pranks are uncertain too.  The original “Feast of Fools” in the Middle Ages, which shared many of the same traditions and ideas, was in December but the day for playing jokes on your friends, neighbours and anyone you can catch out had shifted to April by around the 15th Century in most of Europe.  In Medieval times, April 1st marked the end of the New Year celebrations and there is evidence that a day of jokes and tricks was incorporated into the New Year festivities.  It has also been suggested that the original “April fools” were people who continued to celebrate new year in spring even after it had been officially moved to 1st January.

Different countries have their own slightly different traditions but the basic idea is always the same – to try and trick someone into doing something or believing a far-fetched story, and then revealing the prank by proclaiming them an “April Fool” for being gullible enough to fall for it.  The tricks are normally harmless, so that the victim is just left feeling silly rather than suffering any injury or loss.  Traditionally, if you want to play an April Fools’ joke on someone, you have to do it before midday, otherwise you are the fool yourself.  The date marks my sister’s birthday and I always used to say she was an April Fool, but she was keen to remind me that she was born in the evening so the rest of the family are the fools!

Over the years, tricks have become bigger and more elaborate, particularly in recent decades when modern media like TV and the Internet can be used to make even the most outlandish tales seem credible and huge numbers of people can be fooled at the same time.  Some of the most famous April Fools pranks include the BBC’s news report (complete with video footage) in 1957 of Swiss farmers picking spaghetti off trees, when hundreds of people contacted the BBC asking where they could buy a spaghetti plant, and the announcement in 1995 by the manufacturers of Polo mints that they would no longer be able to make mints with holes in because of European legislation.

The fact that so many newspapers, broadcasters and media companies are eager participants in April Fools traditions means that releasing real news on 1st April can be difficult because people assume it is a hoax.  In 2004, Google chose 1st April to launch its new Gmail service offering a bigger and better mailbox than any other email service at the time.  As the company had perpetrated several elaborate hoaxes in the past, many people assumed the announcement was another one and Google had to publish supplementary details to convince everyone that it was a genuine story.  And they were not the first to be caught out this way.  In the 16th Century, a French nobleman and his wife were said to have escaped from captivity on April 1st by dressing as peasants.  When their ruse was discovered and reported to the guards, the tale was dismissed as a prank and by the time the truth was discovered the captives were miles away.  Those guards were truly April Fools!

While the exact origins of the tradition are lost in the mists of time, most people agree that having a day devoted to light-hearted tricks and jokes is generally a good thing provided the pranks are harmless and the hoax is revealed quickly.  Nobody likes to be caught out as an April Fool but we can usually admire the creativity of a well thought out and convincingly delivered trick and join in with the laughter, and perhaps even laugh at ourselves for falling for the joke.

This post was written by my fabulous husband – Blue Badge Guide Ian Braisby.

Related post: Poisson d’avril

Finding a square of a 2-digit number in your head

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!

Related post: How to multiply any 2-digit number 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 [14] 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!

Related posts: finger tables, how do you know if a number is divisble by…?How to square a 2 digit number ending in 5 in your head

F is also for….Finger tables.

F is for...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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