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!