Multiplication

Kate (8) has a drama class on Saturday. Driving home, she told me that they were talking about maths, and that some of the children in her class were very surprised to hear that she doesn't know her Times Tables.
'What are they, and why should I know them?' she asked. I replied with a brief explanation of what they were and explained that most children learned them off by heart so that they didn't have to work them out each time they needed to do a calculation.
'Oh. But I don't really understand what they are....'
I explained that it is a way of working out the total number of groups of things.
'Like, if we have 2 containers with 3 sweets in each one, how many sweets do we have?'
Sounds of counting in the backseat....
'6!' was the triumphant answer.
'Yes, 2 times 3 is 6', said I. 'Now if I have 3 containers with 3 sweets in each one, how many sweets do I have?'
We continued this little game the whole way home, using larger and larger numbers, and Kate answering correctly almost every time. And just before we got home I told her that a lot of people get caught by 0 in multiplication.
'What do you mean?', she asked
'Well, if I have no containers with 3 sweets in them, how many sweets do I have?'
'3?'
'Well, I would have 3 if I had a container with 3 sweets, but I have no container with 3 sweets!'
'Oh. I get it', she cried, 'you have no sweets. You just wish you had some!'
Now Kate understands what times tables are. Will she learn them by heart? I am not sure about that. But at least she will be able to multiply if she needs to....
Like many maths students in school, I could say my Times Tables off by heart - but it was years before I understood what they were. On the surface, people would have thought me more knowledgeable than my daughter at the same age. But I find myself wishing I could have had the same kind of understanding that she now has.