# order in which to teach times tables?

Discussion in 'Mathematics' started by anon888, Jul 3, 2009.

1. ### anon888

Next year my head wants me to set up a times table challenge that runs throughout the school in which children can achieve bronze, silver and gold awards in particular tables. We want to group the tables into four levels that children can work their way through. I know that I want the first level to be 2, 5 and 10s, but I would really appreciate some advice onto how you would group the other tables by difficulty. For examples if the next level was 3s, 4s and something else, would it be better to do 6s or 8s, as both of them can be worked out using knowledge of another table? Or would 9s be better as it is easy to work out using the 10s? I have tried looking at the framework to see what the expectations are for different year groups, but it is now expected that they will do all tables up to 10 x 10 by year 4, which at the moment for our school is not very realistic.
Thank you for any help or ideas that you are able to give me

2. ### one off

Perhaps you could do 3s, 6s, and 9s

Then 4s and 8s

Since these sets have common factors

3. ### bobboots

I'm not primary so never really had to teach these for the *first* time (although sometimes you wonder!) but experience tells me:

1) 2, 5, 10
2) 3, 4, 9
3) 6, 7, 8
For some reason they find 9s easier - although this could be for all the memory techniques they are taught.

4. ### PiranhaStar commenter

I wasn't brilliant at tables, but I found 9s easier to learn as tables because of the pattern most of the way through - reduce the units by 1 and add 1 to the tens. Then I spotted that the digits added up to 9 (except for 99) and that for up to 90, the tens figure was one less than the thing you multiplied 9 by. The table I found hardest was 7s.
By the way, I agree with your order for learning them.

5. ### DMNew commenter

Can I campaign for slipping some 11s in there somewhere early on?

6. ### one off

ooooooooo I missed 7s out

I dont like them but I am surprised I forgot them

Perhaps they are hard because 7 is prime

7. ### PiranhaStar commenter

Ah, but 2, 3 and 5 are also prime. Except year 7s from one local primary tell me that 2 isn't, and it must be true because their teacher said so.
I seem to recall we also did 12s. Are these off the list nowadays?

8. ### DMNew commenter

Yes up to 10 these days. Did the teacher also tell them 1 was prime? If so, I know that teacher too.

9. ### Maths_Tutor

Philomena Ott in "How to detect and manage Dyslexia" suggests the following order:
2, 1, 0, 10, 11, 3, 4, 5, 9, 6, 7, 8, 12.

10. ### candyflossgirl

I would say:
2s and 10s first as they are vital for doubling and place value etc
Then 5s as they have a good pattern, and 11s as kids love the pattern
Next 3s and 4s as once they know these they can use them for doubling until they learn the 6s and 8s by heart
Then 9s with the finger tricks
Then onto the 6s, 7s and 8s, and by the time you get to these you only have 6 facts left to learn!
I teach the square numbers, then the others like 7x8 through rhymes and things - eg Tastes like heaven - fish and chips = 8 x 7 = 56

11. ### lancsHODNew commenter

I like to see more of your rhymes- where did you get them from, did you make them up yourself.

I use the 'median' timestable grid to reinforce tables, it basically has all the answers to timestables up to 9x9 but it doesn't have the 1's or 10's in it. There are Squares round the square numbers, it helps illustrate to children that there aren't actually that many facts to learn. Pupils chant the question as you point to the answer. for 6 they say 2x3 as the rule is you always put the smaller no. first.

12. ### frustumStar commenter

There could be several - apparently at one point there was a teacher trainer routinely teaching this to their trainees.

13. ### bombaysapphireStar commenter

My Year 9s taught me a new rhyme this week. I ate and I ate until I was sick on the floor.
For 8 x 8 = 64.
It seemed impressively memorable!

14. ### bobboots

Was a reason given for this order?
Is it specific to dyslexic kids?
Does dyslexia affect tables? Some of my best mathematicians (kids) are dyslexic.

15. ### DMNew commenter

Surely the product of I ate and I ate would be negative sick on the floor?

16. ### bobboots

Now there is an abstract concept!

17. ### DMNew commenter

Moving from abstract to surreal:
The product of I overate and I overate is the negative reciprocal of sick on the floor.

18. ### one off

So ... does that mean there was sick under the floorboards but it has been cleaned up

I like to see a practical application

20. ### qubiq

My (recently) six year old son in year 1, has just discovered a passion for learning number patterns. Following early work on 10 times tables and odd and even numbers at school, he independently and rapidly introduced counting as part of his bed-time ritual. I guess it started with the idea of counting sheep, but he then wanted to count them in tens and twos. Initially, he was keen to count them to ridiculous lengths: he was very excited to reach 1000 in tens some minutes after I had left him to go to sleep!
Anyhow, as his demands for variety and his procrastination about going to sleep got lengthier, I printed him out a multiplication square and mounted it under a shelf above his bed in an attempt to get out of the room at some point before I myself fell asleep! It's now his bedtime ritual to go through it counting up and down sequentially through all the tables to 10 x 10, some by looking some rows from memory. We then look for 'interesting' patterns and he quizzes me about what this or that one is without looking (he's so impressed!!) and recently has taken to asking me what various patterns of squares add up to.
As a result, I now know, as an instantly recallable fact, that all 100 answers add up to 55^2 = 3025: how tragic! It's developed my understanding of pattern in there. It never occured to me, although it's obvious when you think about it, that 3/4 of the answers are even. It was, however, a surprise to me to find a similar proportion of them contain a '1' in either tens or units.
In recent weeks he's called me back to tell me he's just noticed that, for instance, pairs of 9 times tables add up to 99 and he recently phoned his slightly older cousin and announced with great fanfare that 45 + 54 = 99 and expected her to be impressed... Bless! He's since generallised this to realising other pairs add up to other multiples of 11 and seems to be aquiring an intuitve idea of assosciativity.
He's noticed for himself that the six times table is just the even numbers in the three times table and is beginning to use this to recall it. He then noticed this worked between fives and tens and then, a little later, also to doubling fours to get eights. Another of his 'discoveries' is the decreasing even numbers pattern in the units of the eight times table: this makes eights easier for him than 6 or 7.
I quiz him about his ideas and prompt a few questions about his methods although his school teachers have done a great job on this already and he's clearly used to be asked 'how did you get that?'
He seems to have fluency in the decreasing order: 1, 10, 2, 5, 9, 3, 4, 8, 6, 7.
After about a month of this almost every other night he's able to recite 1, 10, 2, 5, 9 up and down fluently without looking and from memory. He finds the 0 times table hilarious. I can tell from the speed at which he counts, he's still relying on adding on for some answers within the 3, 4, and 8s, and struggles with these downward. 6 and 7 are tough for him, but he can get there if I'm not in a hurry.
I've made no particular push for him to learn them in a random access way yet, but I know from his reaction he's impressed I can recall what's in the fifth row and fourth column and he's now set himself the mission of being able to replicate this. Which is, of course, exactly what I wanted. By spending time playing with them, he's been given the opportunity to discover and discuss patterns within them. It's old-fashioned now I guess, but I was influenced by Holt in allowing play first. I haven't as yet introduced any practical apparatus to this play (the bits would be uncomfortable in the bedclothes.) Does anyone in the primary sector still use Cuisinaire or Diennes?
one_off, you mentioned "I missed 7s out... Perhaps they are hard because 7 is prime."
I wonder if it's that 7 is co-prime with all three of 10, 10+1 and 10-1. I would imagine that patterns are more or less evident in multiplication tables dependent on the base system we use. Using base six would for instance make primes stand out rather better. But then, by accident of evolution we have ten digits, so almost all humanity is stuck with denary base systems.
Q