Kids love all those tricks!! I used to pretend I didn't know the short cuts and they enjoyed showing me.
I would say another thing to make clear is the progression of numbers in times tables, i.e. explain that the number is growing by it's own value each time. I know that's not much help with the quick fire answers, but it does give the children an idea how the number has grown and where the answer might lie.
As for songs, Ginny, our daughter knew every word of all the Boyzone hits, but couldn't sing her tables!!??
Ruler Of The World (lighthearted)



