Three halves make a whole?

Our Prime Minister, David Cameron, came in for some criticism this year for his use of the word 'half', when, in answer to a question about what were the Houses of Parliament like, he replied, 'half museum, half chapel, half school'. 'You can't have three halves!' was the outcry.

Obviously, what he said is not intended to be an exact statement of proportions, but even so this looks as sloppy as the often-heard 'I'll have the bigger half'.

However, on reflection, Cameron is OK in what he says here. You can have three halves of a set, for example, if the halves overlap. For example, a teacher could say, half of the children in my class are Asian, half of them are male, and half of them walk to school.

So, if, we were to assume that there are 100 quintessential qualities or features that characterise the Houses of Parliament, it is quite possible that 50 of these are shared with those of a museum, 50 of them are shared with those of a chapel, and 50 of them are shared with those of a school. This is because the quintessential qualities of museums, chapels and schools are not unique to each of these kinds of places.

So, it seems alright to say that Parliament feels like half museum, half chapel and half school!

There! It's not often you get me supporting our Prime Minister; but fair's fair.

How old are you?

In our church we have a spot in our Sunday morning services where we invite children who have had a birthday that week to come to the front to receive a small gift. 'When was your birthday' said the pastor to young William. 'On Friday' he replied. 'And how old are you?'  'Four and a half', replied William!

Very interesting that reply, isn't it? On Friday he was four. But now he is more than four. Hence the 'four and a half'!

When we teach children simple fractions, like halves and quarters, we tend to major on the idea of a fraction as one or more equal portions of a whole unit. So we use images like a pizza or a rectangle cut up into a number of equal parts. But William's response reminds us that children's early experience of fractions also includes the idea of a fraction describing a point on a number line, a point 'lying between' one integer and the next. So 'four and a half' means a point on a time line 'somewhere between four and five'.

I suggest that we would do well to make much more of representing fractions as points on number lines, especially if we are teaching children about mixed numbers.

Thanks, William. And happy four and halfth birthday!