What it's all about
When does order matter? If I ask my class to line up - a fire drill, for example - I need them in register order. If they're waiting to come into my classroom, it usually doesn't matter, writes Peter Hall. 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). Let's use "operation" 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. A calculator might help make the 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 can matter, 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, 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 know their two times table. I ask them to try sums the other way round and check which is easier.
Try bagpussfan's times table and arithmetic round-robin activities. bit.lytesArithmeticRoundRobins
Develop times table skills with the Piggy Buys Apples video from Teachers TV. bit.lytesPiggyBuysApples.