Tables are just number facts in a logical order. Children need to know them but should not be expected to memorize them without understanding them. When they do understand them, they find them easier to memorize AND apply in ‘real life’ mathematical situations.
Is your child ready?
The idea of ‘tables’ will only begin to make sense when your child has reached a certain level of understanding…
- He trusts the ‘count’
- He knows that when he counts 5 objects, and then adds 2 more objects and wants to count how many altogether, he doesn’t need to count the 5 all over again because it hasn’t changed. It’s still 5. He counts on from there.
- He knows number facts stay the same
This is more advanced than just trusting the ‘count’. He knows that, eg 5+2=7 is true in any context. That is, he knows that 5+2 will give the same result whether it’s 5+2 cars, dogs, peas…or anything, and he doesn’t need to work it out all over again just because the objects change.
If he ‘gets’ these two ideas it’s fine to start thinking about developing his understanding of number facts and then ordering them logically.
Choose a low number, eg 5, to ‘make’ addition facts about.
These are the facts: 0+5=5, 1+4=5, 2+3=5, 3+2=5, 4+1=5, 5+0=5.
If your child has just been presented with a list of addition facts like this about 5 (or any number) and expected to learn them by rote, beware. A list of number facts is way too abstract for kids at this level.
Your child needs to find out for himself the different combinations that add up to 5. He needs to experiment with ‘hands on’ materials and record his findings as he goes, either on individual cards or pieces of paper that can go up on a wall somewhere.
‘Here are 5 cars and 2 garages. Put some cars in one garage and the rest in the other.’ (He does eg 3 and 2)
‘Let’s describe the number fact for this situation…three and two makes five’ (You’re modelling this)
‘I’m going to check this quickly with my fingers too. Three fingers and two more…yes, that’s five.’
‘Three is one part, two is the other part, and five is the whole amount of cars.’
‘Now I’m going to write it down like this…3 + 2 = 5′ (You write 3 + 2 = 5 on a card and put it up somewhere.)
‘Now have a go yourself.’
‘Here are 5 horses and 2 paddocks. Put some in one paddock and the rest in the other.’ (If he does 3 and 2 again that’s fine…any combination is fine)
Prompt him to describe the number fact.
Prompt him to check if it’s true on his fingers.
Prompt him to tell you about the two parts and the whole amount of horses.
Prompt him to write it down on a card and put it up. It’s important that HE does the writing.
Next question to ask is ‘Is there another way you could share them between the 2 paddocks?’ (BTW ‘sharing’ is not the same as ‘sharing equally’.)
If he can’t think of another way, show him one. Go through the process as before and leave it at that for now.
If he can show you another way, get him to record it on another card and put it up on display. Then ask him to show you one more way if he can. If he wants to explore more possibilities…that’s great.
Continue making number facts about 5 in different ‘real life’ situations for a few minutes over a few days. Be as creative as you like in coming up with different situations.
Over time his cards will show all the number facts he’s discovered in a random order. Some will be repeated…that’s good.
This is where he notices there’s a pattern… without you saying a thing.
Ask him to describe the pattern to you.
Helping the ‘Aha!’ to arrive
If he’s ‘made’ lots of number facts over and over about 5 but hasn’t noticed the pattern yet, you can ask him to put the cards under each other in a list. This might be enough to help him notice it. It’s better if he ‘discovers’ it by himself.
If not, ask him to remove any double-ups and say ‘Let’s just keep one example of each fact in this list.’
Order the first four in front of him without saying anything. Then ask him if he’s noticed anything about how you’ve rearranged them.
If not, explain, and see if he can do the last two.
Repeat the process over time to ‘make’ and order number facts about 6, 7, 8, 9, 10 (one at a time!)
Memorizing number facts
Making the facts with materials and understanding them doesn’t mean your child will remember them. Whether you use songs, stories, software or charts to help with memorizing, it’s best to focus on a few facts at a time and take turns to say them afterwards (you say one fact, he says the next, etc). Stay on these until he knows them and continue to practise them even when you’ve moved on to focus on the next ones.