Hi X Benedict:
Not sure exactly how far your DS is along with times tables but lets presume he has x1, x2, x3, x5 and x10 fairly securely. (If not - these are the first tables children learn - usually x1, x2, x5, x10 and then x3). Also ensure that at this stage he's clear that multiplication is just a fancy way of explaining multiple additions of the same number (i.e. 5 x 5 = 5 + 5 + 5 + 5 + 5) - but mathematians like short cuts so 5 x 5 is a lot easier to write, because it gets even worse when it's bigger numbers like 12 x 12)
The next step is to ensure that he understand the concept of doubling.
This is crucial so that he can benefit with x4 (if you want to know what 8 x 4 is then double 8 (effectively 2 x 8) then just double again for 8 x 4 - or in other words if he knows his x2 table he just doubles again for x4) and x8 (double, double again and double again or if he knows x2 table just double and double again for x8/ or if x4 is solid then just double for x8) and x6 (so if he knows his x3 table he just works it out for x3 and then doubles again). x 12 is effectively doubling the x6 table (or if you only know x3, then double (for x6) and double again (for x12).
So basically with understanding doubling you should then know:
x1, x2, x3, x4, x5, x6, x8, x10 and x12.
The next thing to explore is x9:
9 has great patterns:
First off the integers in the answers always add up to 9.
Second - up to x10 - the answer always starts 1 lower than the number you are multiplying 9 by
1 x 9 = 09
2 x 9 = 18
3 x 9 = 27
4 x 9 = 36
5 x 9 = 45
6 x 9 = 54
7 x 9 = 63
8 x 9 = 72
9 x 9 = 81
10 x 9 = 90
So if your DS can learn those tricks then he can think through 5 x 9 - the answer will start with 4 and what +4 = 9 --- that's 5 - so the answer in 45.
The next two aren't so tricky:
11 x 9 = 99 (9+9 = 18 and 1+8 = 9)
well that's pretty straightforward
12 x 9 = 108 (1+0+8 = 9)
12s sometimes can be easier to think about as (10 x 9) + (2 x 9) = (90) + (18) = 108
[You may want to introduce concept of tripling now with x9 table - so if 3 x 9 = 27 what would tripling it be (27 + 27 + 27 which effectively is 3 x (3 x 9) or = 9 x 9 = 81)
So that leaves the 7s times table and 11s times table.
Start with 11 first - again lots of patterning to explore.
1 x 11 = 11
2 x 11 = 22
3 x 11 = 33
etc...
9 x 11 = 99
10 x 11 = 110
now over 10 there's a trick
11 x 11 (with two digit numbers take the number you are multiplying 11 by - separate the two numbers so you have 1 - x - 1 then replace the x by adding the two separated numbers together - so you get 11 x 11 = 1 - 2 - 1 = 121
with numbers that a larger you may have to carry:
28 x 11 = 2 - (2+8) - 8 = 2 - (10) - 8 = (2 + 1 carried over) - 0 - 8= 308
28 x 11 = 308
Works and then is great fun to use and show off.
So at this point you know everything but your 7s - but in fact the only 7 you don't know is 7 x 7 which is 49 - so if you memorize it (or can add 7 to 6 x 7 = 42 quickly - you know it too!
That's the full 12 x 12 tables.
Practice helps tremendously and these days with all the video games out there and fantastic maths websites you have tons to help:
As others have suggested above:
Woodlands Junior school's Mathszone (mutliplication & division) are brilliant practice: resources.woodlands-junior.kent.sch.uk/maths/
Multiplication dot com has all sorts of fun games: www.multiplication.com/games/all-games
Mumsnet also has a times table fill in the grid game which is very useful practice: www.mumsnet.com/learning/maths/interactive-times-tables-activity - and Pearson's Maths Champ also has games which help practice these skills: www.mathschamps.co.uk/games7-9 - more challenging practice is available on 9 - 11 options as well.
Timez Attack (and the division game for inverse multiplication facts) are brilliant practice in a dungeon format where you're a little boy or girl ogre and go through solving multiplication / inverse multiplication problems. There's a free version or you can pay for more elaborate platforms. We found the free version was find. A word of warning when the big ogre comes out and quizzes you it can be very stressful - so be prepared - it is hard at first but the point is to know it under pressure and to build up speed. Great once the basics are known but speed needs to be built up. Link here: www.bigbrainz.com/
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Well that should be quite a lot to get on with. I think the real help for my girls was to understand and crack those patterns and similarities between different factors (times tables - so x2, x4, x8 family/ x3, x6, x9, x12 family and x5/ x10 family). Really work on concepts of doubling and tripling - which then will strengthen mental maths within the tables. And then encourage practice as and when.
There are a lot of APPS now available for smartphones/ tablets/ i-pads (i-phone or android formats) - nice article about that here: www.education.com/magazine/article/multiplication-apps/. These are ideal whilst waiting to collect a sibling (or for them during a less - ballet/ swimming/ etc...).
As with everything little and often really does make a difference.
He will get there - keep encouraging him and really celebrate when he cracks it!
HTH
