NigellaEllaElla:
Having been through times tables now with both DDs (Y4 & Y6 now) this is my advice for learning whilst awake:
- times tables are taught in an order which makes sense because of families of numbers:
x0 - anything x 0 = 0 - great first one to learn because you are an instant genius - 2,999,796 x 0 = 0 -- GENIUS. (Our school just introduced this and moved on - but it is worth celebrating fabulous 0).
x1 - anything x 1 is itself - I was taught to think of 1 as a mirror - so 8888 x 1 = 8888. (again schools tend to introduce this and move on).
Now in KS1 your DC should have been taught counting by intervals of 2, 5 and 10 - you know 2, 4, 6, 8 or 5, 10, 15, 20 or 10, 20 , 30 , 40, etc...
So basically it's that same principle but understanding that you don't count up any longer:
so 2, 5 & 10 often are the first times tables schools focus on.
x2 can be taught by walking up the even side of a street and reading (counting) up the addresses.
x5 can be taught with songs are just learning the pattern
x10 of course can be taught by showing that anything times 10 is simply that number and a magic zero added at the end: 6 x 10 = 60 or 277 x 10 = 2770
Once you have these - introduce the concept of doubling (effectively more x2 work).
(it's also important to teach that 2 x 5 is the same as 5 x 2 - it doesn't matter which way around you do this).
Then you can introduce x4 and x8
x 4 is anything x2 and then just double again
So 8 x 4 is the same as 8 x 2 = 16 and then double to get 32.
x8 is anything x 2, then double and then double again
(or if your already ace at x4 - then just double x4 result).
So 7 x 2 = 14 and doubled is 28 and doubled is 56 = 7 x 8
or 7 x 4 = 28 and doubled = 56
by the way if you think of it as 56 = 7 x 8 - you get the 5,6,7,8 to line up - so it's easy to remember.
x3 does require a bit of work - and may be easier to start with counting (with candies, raisins, etc...)
So once they get 3, 6, 9, 12 etc.... you can then formally review
3 x 3 = 9
Once you have to x 3 table then 6 & 12 are effectively doubling exercises and there is a trick with 9.
For x 6 just double what x3 would be
so 4 x 6 is the same thing and 4 x 3 = 12 and then double 12 = 24
For x 12 - if you know x3, double and double again or if you know your x6 table then just double the once.
so 12 x 5 is the same as 3 x 5 = 15, doubled = 30 and doubled = 60
or 12 x 5 is the same as 6 x 5 = 30 and double it = 60
x9 has some lovely tricks:
Turn palms upwards (so thumbs at each side) number from left thumb (1) to right thumb (10) - now you can use your hand as a calculator:
So for 4 x 9 - count to your 4th finger and fold that over (so your left ring finger) - you should have 3 fingers up to the left and 6 fingers of to the right - so left fingers are tens and right fingers are units and the answer to 4 x 9 = 36.
The other thing to observe is the pattern for x9:
9 x 1 = 09
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
9 x 5 = 45
9 x 6 = 54
9 x 7 = 63
9 x 8 = 72
9 x 9 = 81
9 x 10 = 90
first off the digit in the tens column is always one less than the number you are multiplying 9 by. Second - the digits all add up to 9
example:
9 x 3 (first digit is one less than 3 = 2) so what + 2 = 9 that's 7
so 9 x 3 = 27.
the pattern doesn't work beyond 10 (or the hand calculator trick) - but 9 x 11 is 99 (that's easy) and 9 x 12 is effectively (9 x 10) + (9 x 2) or 90 + 18 = 108
and by the way the adding up to 9 thing still works:
9 x 11 = 99 - (9 + 9 ) = 18 and 1 + 8 = 9
9 x 12 = 108 - (1 + 0 + 8) = 9
So now you know x0, x1, x2, x3, x4, x5, x6, x8, x9 and x10.
x11 can be taught any time but it's so fun it's nice to introduce it now:
so for up to x9 it's easy - just that number written 2x
1 x 11 = 11
2 x 11 = 22
3 x 11 = 33
...
9 x 11 = 99
for 10 x 11 it's the x10 rule already learned (just add magic zero)
so 10 x 11 = 110
That leaves 'the trick' for x11. Any two digit number x 11 can be worked out by splitting the tens digit from the units digit and then adding the two together and putting that in the middle (but this may involve some carrying). Some examples:
13 x 11 = 1 - (1+3) - 3 = 143
29 x 11 = 2 - (2 + 9) - 9 = 2 - (11) - 9 so you'll have to carry the ten in the (11) to the hundred's place - so that's 3 - 1 - 9 so 29 x 11 = 319
So that leaves x7 (because we already learned x12 by either doubling x6 results or by taking x3 results and doubling and doubling again).
In fact if you think about it you know x7 for 0 - 6 and for 8 - 12 - the only one you don't know is 7 x 7 = 49
there is no trick you just have to learn it is 49 or knowing 6 x 7 = 42, add 7 quickly or by knowing 8 x 7 = 56 (remember 5, 6, 7, 8) you can take away 7 quickly and get 49.
-------
In all sincerity we've found video game style multiplication practice to be the best means of really bedding down these times tables. Some useful sites include:
Table Trees: www.amblesideprimary.com/ambleweb/mentalmaths/tabletrees.html
Times Table Beat Box: www.nationwideeducation.co.uk/section/bso/index.php
multiplication dot com: www.multiplication.com/
Maths Champs: www.mathschamps.co.uk/#home - this is set up by age bands so you will have to hunt about between bands to cover all tables.
Woodlands Junior School Maths Zone: resources.woodlands-junior.kent.sch.uk/maths/ - just select multiplication and their are links to all sorts of games to help improve skills.
Finally if you want to develop speed/ fluency with tables I'd highly recommend Timez Attack - there is a free version or you can pay for more add on platforms. Basically you are a young ogre (can chose to be boy or girl) and you race through a dungeon or castle solving multiplication problems. The problems are presented both as multiple additions which you count up (by collecting up snails and then throwing them against a wall - they seem to survive the process) and then as a traditional vertical multiplication problem which you type in the answer to. Every now and then a larger ogre comes along an quizzes you and at the end of each level you are quizzed by a giant ogre. A bit stressful but both DDs got great at times tables by doing this.
Timez Attack link here: www.bigbrainz.com/
HTH