On the assumption that your five-year old has a grasp of addition, these are the most important numerical facts a child can learn at this age.
Children who are good at maths have committed a lot of what they know to heart. By this, I mean that important number facts have been learnt and committed to long-term memory. Note that it is widely accepted that there are two ways to commit something to long-term memory: either learn by understanding (perhaps you’d learn the events leading to the start of WW1 in this way) or rote learning (times-tables must be learnt this way in my view.)
I digress… back to the point in hand. The more number facts a child has committed to long-term memory, the more they free up their working memory to perform more complex calculations. A child who can recall the doubles of numbers below ten can then also learn the following without much more effort:
– Near doubles: if you know that 6+6=12, you can instantly work out that 6+7=13.
– Adjusted doubles: to work out 6+8, change it to 7+7 and use your doubles. Doubles, near doubles and adjusted doubles account for the majority of addition facts to 20.
– Double 10, 20, 30 etc. and 100, 200, 300 etc. This innately teaches children place value, and excites them because they are using big numbers! You’ll get them doubling 1000, 20,000 before you know it.
– 2x table: same as your doubles!
– Halving: the reverse of your doubles. But you have to learn them off by heart: if you choose to teach doubles by adding a number to itself, whilst this is sensible in the short term, in the long term many children learning how to halve will attempt some kind of subtraction. Better to get them to learn off-by-heart early on.
– If they can halve, they can quarter. Teach it by halving, and halving again.
– And you can even lead in to percentages, because 50% is one half.
– Partitioning: if they know their doubles confidently off-by-heart, they can double any number by partitioning. Double 24? Well, double 20, double 4, then put it back together.
Of course, the other by-product of doing this is it gets children into the habit of committing numerical facts to their long term memory from an early age. Because maths is never duller than when you are still continually counting on your fingers at 9 or 10 years of age…