Some fundamental ideas sit happily at the bottom of most of the maths we do but most of the time they are ignored. My mission - and you're welcome to adopt it - is to mention them a bit more often. The first idea I think my pupils need to practise is commutivity - or, when does order matter?
If I ask my class to line up - if we're doing a fire drill, for example - then I need them in register order. If they're waiting to come into my classroom, then it usually doesn't matter. But what about simple arithmetic? Does it matter whether I work out 5+3 or 3+5?
This is a great opportunity to investigate. We need to be able to generate two numbers and an "operation" (+, -, [s5] or x). At my school we have some "operation" dice but these can be made with the help of some stickers, or get your pupils to make their own.
Let's use the dice to generate a sum: three dice showing 4, [s5] and 8 would give us two options (4[s5]8 and 8[s5]4) and we can work these out. We might use a calculator, or not. I'm not solely interested in the numeracy skills here and a calculator might help us to make that point more easily.
We can write down lots of sums and hopefully discover for ourselves that + and x yield the same result regardless of the order, whereas - and [s5] don't. These two "failures" are useful because they remind us that order does matter sometimes, and that for subtraction and division we must be careful.
But for addition and multiplication this commutivity is helpful: we can use it to make long addition sums easier. If we take 4+7+6+3+9 and reorder it into 4+6+7+3+9, then we can see the 10+10+9 answer more clearly.
It is really odd when pupils tell me they can't do 2x7 because they don't know their seven times table, but they can do 7x2 because they do know their two times table. I ask them to try sums the other way round and check which is easier. This helps them to see that when they are learning a new times table, they already know quite a lot of it.
Peter Hall is an advanced skills teacher of maths at Beacon Community College in Crowborough, East Sussex
Arithmetic made easy: try bagpussfan's times table and arithmetic round-robin activities.
Develop pupils' times table skills with the engaging Piggy Buys Apples video from Teachers TV.