Mental Maths

[Whyamistillawake]

DS is year 3 and is really struggling with his mental maths. I've had him in tears this evening because he's so 'rubbish' at maths and the worst in his class.

Background is that he's not rubbish at maths but he is rubbish at mental maths and struggles with times tables etc. They just don't seem to stick (and DD in year 2 is starting to overtake him). The school sets for maths and he's top set and at the end of last year I was told top half of top set.

I briefly spoke to his teacher about whether he should go down a set and she said no but we have parents evening this week so I'll pick up again in more detail.

In the meantime, any hints for how to get these times tables to stick? He's not completely automatic with the two times tables so is really behind and it's massively stressing him out.

In case it matters, both my sister and I struggle with mental maths (despite us both having advanced maths and my sister being a mathematican) so I think there is a genetic element at play here. It's more that 'play a cd' level - DD picks them up from that but lot DS.

Any help appreciated. I hate seeing him so upset.

Instant recall is the key. Practice. Put the poster up. Play cd in the car.
Times table place mats, etc.

www.topmarks.co.uk/maths-games/hit-the-button
learnyourtables.co.uk/en/index2.htm

There are many other great times table apps and websites if you search past times table thread.

Try completing whole multiplication grids so that the tables are always in the same order rather than random multiplication facts. He may need to see the pattern in the numbers rather than automatic recall.

Invest in timetable rockstars. Cheap but the only thing we've seen that actually has an impact.

YY to some kind of speed drilling. Squeebles apps are good. Or DS's school used Sumdog which has a Tables option. I used a Little Professor toy when I was little (and not so little - was still using it to speed up my arithmetic at A level and beyond!)

Make sure they have good ways to work it out first. So if they're doing the speed drill and can't remember, they work it out not guess. I think it's like phonics/reading in a way - if you just try to memorise cold it's a miserable job. If you can fall back on quick ways to calculate them, you start to remember the patterns and it falls into place.

Times tables
2s/5s/10s/11s are quite easy.

3s you learn, but if necessary add the number to its double or just count up quickly in 3s.

When 2 is secure, 4x is just double 2x.
8x double again.

12x is 10 x + 2x

9x is 10x - 1x

7s: not many gaps left if you can do 1-6 and 8-12! All you have left to learn is 7x7=49.

For addition/subtraction, I think it can help to find a visualisation that works for them. Whether that's hopping about a number line, or using 100s/10s/units blocks or exchanging different coins or whatever. Schools seem to teach lots of different techniques and tricks, which is better than when we were little - but think for some kids they will find it easier to pick one that works for them and stick with it.

Catkind, personally I don't buy that thinking of doubling and doubling again helps in practice terms.
What one has to do is memorize them and practice them for 10 mins EVERY-SINGLE-DAY.
To me the "hit the button" app is the best (there is one small aspect of it I don't like, but never mind).
However, whichever tool you use, it has to be done EVERY-SINGLE-DAY, Saturday and Sunday included.
On the plus side, this is a job the child has to do once in his life.

EVERY-SINGLE-DAY! ;)

I disagree Arkadia, I agree with cat. If you know the logic behind the times table, it will stick in your memory better, and can be extended to use the logic later with even bigger numbers.
So I do think practicing a lot to memorise is one way to get instant recall, but also knowing doubling and doubling etc. is worth doing imo.

By all means, do whatever works for you, but times tables can be remembered only by repetition. Nay, by repetition and nauseam.
That the 4x tables is the same as 2x2x table is obviously true, but it is a factoid. You can use it to see how decomposition of numbers works, or for 100 different things, I am sure. But that it helps you MEMORIZE it, I am not so sure. At the end of the day, you are adding an extra layer to what should be an automatic process.

Sure, I agree that instant recall by memorising is very important. But knowing the doubling method is also very useful for future mental maths. That's all I'm saying.
Say you need to do 23 x 4. You can work out by doubling 23 x 2 = 46. Then you can work out by doubling again, 46 x 2 = 92, instead of doing 23 x 4, which maybe easier for someone who struggles with mental maths.

Thanks everyone. He gets how they work and he can work them out but his mental maths is slow so even doubling numbers takes him some time and it seems to all he about speed in school.

I have a look at the apps suggested.

Nine times table.

Don't do it by 10x - 1x (well obviously you can, but that also relies on mental subtraction being good).

Use the finger trick. Hands in front of you, for 3x9 put down your third finger. then you have 2, finger down 7 answer = 27. Fast enough and adequate.

I'm not a teacher.
At this age, mental maths is all important. I suck at times tables. My memory is shot to pieces (dyslexic). It sounds like im a bit like uou and your sister. BUT I have a couple of degrees, in scientific disciplines, so maths related. In a couple of years it won't matter if you don't have instant recall. It's ok to work out 87 by knowing 58=40, and adding on the 14. You can still excel at maths without instant recall of the whole times tables.
Yes, practice, yes try to learn them. BUT it's not the be all and end all. It might be in year 3 and 4. But its not going to matter in 10 years time, so long as you can get there pretty quickly. Either by repeated adding from some that you know (5 and 10 for example). People comment on how quick my maths is (constantly switching currencies in the shops, dividing up restraunt bills) and it's not through instant recall.

So my experience would say try your best, learn some strategies to help, and chill. It sounds like he's good at maths, and will thrive later on. Don't put him down a set because of one topic.

Yes, I totally agree with Sand. In fact, I read on G&T thread long ago that one of MNetter who is really good at maths doesn't know times table at all. Just that she can work out using other strategies very quickly.
Yes, in KS2, it's all about instant recall of times tables. It's you have try to learn it (and he will be made to learn it anyway at school), but when it comes to solving harder questions in the future, it really doesn't matter if you can instantly know 8 x 7 or you can do it by 8x5 + 14 like Sand says. Knowing logic behind it and apply other methods are far more useful for able mathematician like your ds, imo.

What can be helpful for the future is knowing the factors. So seeing 54 and knowing it is 6x9. Useful for simplifying fractions, and factorising algebra, that kind of thing.

Only yesterday I was telling my 13yo that the only time she will see 169 in maths at school is probably when she'll need to know it is 13^2.

• I think you have to try, not, It's you have try!

I would say that automatic recall is more important in weak mathematicians and people without excellent working memory, because both of those things will prevent you from either working out the answer quickly, or holding the rest of your problem in your head whilst you work it out.

Even in people who can do that though, knowing times tables helps, but there is less motivation to practice, I know I never did at school, 'cos you can answer fast enough in the school tests, which aren't actually fast enough to require automaticity.

Then just keep practicing I think OP. I'm not disagreeing with arkadia that instant recall is key, I just think having a secure way to work them out is the quickest way to get to instant recall. Then you're getting the positive reinforcement of getting it right every time (even if too slowly) rather than the negative reinforcement of trying to recall blind and guessing wrong.

If his working out is also slow I'd do some addition speed practice before the times tables probably. Even just number bonds within 20. Nothing's going to be fast if they're mentally counting up to add 8 to 56 or whatever.

Rapid mental recall is great once you have learnt the patterns but just practising the "facts" won't necessarily mean a weak mathematician will remember them.

What Arkadia said. Don't overcomplicate simple arithmetic process.
I learnt timetable before I actually knew what it was because my mum kept reading it to me everyday. Got to a point I memorised it. I actually knew the timetable up to 9 before I could add 2 digit numbers together.

That's fine, Arkadia and GHGN, if your brain works that way. Mine doesn't. So if repetition ad nausium doesn't make it stick in your head, you need other ways.

.

We played 'Plyt' - an off-line family board game. Lots of practice in there, there is a luck element to lighten things up, and anyone can join in as you can set each individual's challenge level. Meaning that everyone has to 'think' and everyone has a chance to win.
You have 5 or 6 12-sided dice, one of which is a different colour than the others. So e.g. you set your level to two dice, multiply the two numbers that are thrown within the time set by the timer, move forwards on the board by the number on your 'black' dice. You can fix one dice to a defined number e.g. 4, to practice 4 times table, and only throw the other one. Grown ups can challenge themselves by throwing 4 or 5 dice which can be easy but throws up real mental maths challenges every now and then. Our toddler DD joined in - her challenge initially was simply to recognise and name the number thrown. She has now progressed to having to find 'one more' than the number thrown. You could also have someone add two (or more) dice for addition practice.

I agree with PPs that perhaps you need to forget about memorising TT for the moment and really focus on basic addition and subtraction. Get DS to memorise doubles and number bonds to 10, then 20. There is just no getting around that.
It has been a while but we used to talk doubles/number bonds whilst on the trampoline or swings. It's really not that much: 5x number bonds to 10, 10 (or maybe 12) doubles. It's also very helpful to be able to break any number 2-9 up into two parts quickly (for bridging).

The next step to me would be work on quickly recognising 'tricks' for fast addition. Use those 17 memorised 'number facts' every time you need to do a sum. So 56 +6 = 50 + double 6; near doubles; near 'number bonds' so if he recalls 7+3=10, then 7+4 needs to be one more than 10; using 10/multiples of 10 for bridging (though that will involve knowing a few more number facts), that kind of stuff.
Effectively if he understands numbers and place value (and it sounds like he does) then he needs to memorise doubles and number bonds to 10, and pretty much everything else he can work out quickly from that.

And when that is down pat, and the child understands multiplication, times tables are within reach. I personally much prefer teaching how to work them out quickly first, memorising second (because once they are memorised, lazy children like my DS will see no reason in learning how to work them out). But in order to be able to work them out speedily, you need to be able to do addition/subtraction/doubling speedily.

And after that, memorising. Here, repetition of course is key (DS used squeebles). And all kinds of things to help trigger your memory. DS loved things like 'I ate and ate until I was sick on the floor' (8x8=64) and noticing patterns like 5678 (56=7x8). For the 9x table rather than 10x-1x, or the finger calculator as mentioned above, DS learned by knowing that the tens figure will be one smaller than the number you're multiplying by, and the unit/ones figure will be the number bond to ten of the number you're multiplying by. But for your DS, OP, I think this is quite far off yet. Though those aide-memoires like the 'sick on the floor' one might help give him some confidence, but won't take you anywhere systematically. He needs to memorise doubling, and number bonds.
Maybe sell it to him by pointing out how few number facts he actually needs to learn, and that knowing them and applying them for fast mental addition will allow him to not have to memorise so many multiplication facts? E.g. that he can save himself memorising the entire 4x table if he can just double fast enough.

First and foremost, automatic recall of times tables is not indicative of mathematical prowess – far from it.

Marcus du Sautoy is an excellent counter example. He is a mathematics professor at the University of Oxford, festooned with awards and honours for his publications, popular books and lectures. But his parents were told not to bother trying to get him into a selective secondary school. Why? Well, one of the main reasons was he wasn’t good at remembering his times tables.

He became enthused about maths when he encountered more inspiring topics as a young teen in his comprehensive school. (He claims to be slow at arithmetic to this day.)

And he’s not a complete aberration. Please tell DS there are many talented mathematicians who are wobbly on mental arithmetic!

Having said all that, it is certainly useful to commit the times tables to memory if you possibly can. And Y3 is still early days so DS – and you – shouldn’t despair.

I’d be interested to know what DS’s strengths are. When I was at primary school we learnt the times tables by chanting them aloud but this might not suit a child who is more visually than verbally oriented. If DS is a visuo-spatial thinker, good at jigsaws and lego, he might prefer to learn from filling a times table grid and taking advantage of the inherent patterns amongst the table entries – as has been mentioned by others. It doesn’t matter if he has to figure out the elements of the table initially rather than remembering them, in fact it’s probably a good thing.

In Y5 – Y6, my DS’s teacher had the class filling out these grids regularly and she always timed the children so they could try to beat their previous times. (It was a small class.) Your DS might want to try this at home - without the rest of the class around. It could boost his morale to have proof that he is actually speeding up even if progress is slow on a day-to-day basis!

Previous posters have mentioned quite a few helpful patterns and techniques. I’ll only add that remembering even x even = even, odd x odd = odd and even x odd = even might be another modest addition to the box of tricks.

Good luck to DS!

Having said all that, another thought. DS (also Y3, fairly able mathematician) would for the longest time use 'counting on' as his main strategy for addition, using fingers where possible, up until very recently. He knew his doubles and number bonds in his sleep since reception, but he didn't use them, apply them. And I think a key reason for this was that they were encouraged, at school, to 'count on'. The main thing in Y1 and Y2 was to get all children to really 'understand' addition, and addition on a very basic level is 'counting on'. Everything else is 'technique'. Yes, using multiples of 10 for bridging is faster, but it's just a technique for doing that elementary thing, counting on, more quickly. So whereas they were taught techniques like that, and encouraged to memorise things like doubles, the focus was very much on 'understanding' addition rather than on techniques for doing it fast (and on understanding place value).
Now in Y3 the focus has definitely changed! Addition/subtraction/place value are now assumed, and need to be applied (fast!) for e.g. times tables, new techniques such as column addition etc. It's only since this school year that DS has started to move on from using his fingers for counting on/back. And that's despite knowing his number facts and understanding the techniques for a good while. But counting on is just not fast enough anymore. Luckily for getting that speed, for him it's just a matter of applying what he knows already, but was too lazy to do until now. For other children this move to Y3 is really showing up gaps, be it in not understanding addition/place value, in not having memorised number facts, or not having understood those techniques. Up until Y2 you can get away with not really 'getting' how +9 is the same as +10-1 for quick addition, you can just count on by 9 instead. It's slow but will get you the correct answer. Now that it is supposed to help you do multiplication, you need the technique / number facts for speed.

Point being, memorise those doubles and number bonds. Your DS in KS1 got away with slowly working them out, and stayed in the top set. Now in KS2 he needs to memorise those basic number facts, apply the basic techniques for fast addition, in order to get away with being able to work times tables out rather than having to memorise them all.

Thanks everyone. These tips (and thoughts) are all ones to apply.

I thought it would be worth updating that we had parents evening and the teacher is not in any way concerned. She says he needs to work on his tables but she says she had said that to pretty much everyone. With DS she says he understands the concepts which is far more important to her than speed..

Whay does concern her is he has a big confidence issue with maths. He thinks he's rubbish and he's really not - he's very strong. We've seen this as well - basically since the start of school he's thought he's bad at maths and he's consistently had reports saying he's good at maths!

It's weird - it's only maths he has this confidence issue with.

We will keep on with the mental maths as being faster will improve his confidence I think but it appears it's not the issue I thought it was!

GHGN, I am a bit sad to read your post tbh, I thought you teach able children. I thought you understood. There are children who get it without repetition, and there are children who get concept, but not good at memorising.
Repetition may work for most average kids. But may not work for others.