Young children think division
THE MATHEMATICS problem-solving
division by sharing
AGE 4 and 5 years
CONTEXT whole class and groups
FEATURES the variety of responsesThe main part of this session was a whole-class introduction to the concept of divi-
sion through sharing. I wanted to provide the children with several models of this
while emphasising that they could choose their own model to write down their find-
ings. I demonstrated models throughout the session so that children could take
those aspects with which they currently identified and then make them their own.
As this was only a single session consisting of one visit I was unable to model a
variety of possible ways of recording over a period of time (see Chapter 10).
I introduced division through sharing by telling a story which I had invented.
Stories are a wonderful way of bringing some sense to difficult concepts in maths. In
brief the story is about twins who like everything the same. ‘If Rosy has two sweets
then Kathy also has two sweets. Rosy and Kathy like numbers that share equally.
What numbers are sharing numbers?’ The children and I discussed how we might
find this out. I asked one child to choose a number out of a bag. ‘How could we tell
if you can share that exactly?’
Most children of this age that I have taught understand the ‘one to you, one to
me’ way of sharing and when asked how to share quantities, one child did suggest
this. I had some cubes and a child demonstrated this and we agreed that five cubes
shared between two children left one cube over, so five was not a sharing number.
The importance of vocabulary and ‘one left over’ are crucial to develop understand-
ing of remainders. At this point, therefore, I had presented two ways of working out
the ‘sharing’ numbers. I then went on to discuss images in their heads. Could we
work out if it was a sharing number without actually using cubes? This helps the
mental process in mathematics: if children can do it in their heads, they should do
so. Some children were able to have visual mental recall with small quantities but
this seemed generally more difficult to them.
The children went to tables to choose numbers for themselves to work out. I had
put a tin of numbers on the tables from which they could select. I encouraged them
to put their findings on paper ‘so you can remember’. Blank pieces of paper and
pencils were available on the tables. Some children chose to work on the carpet. On
this occasion there were three adults available as some children needed more
discussion and encouragement of their own ideas. Although I suggested that they
work in pairs, most children worked on their own. This class had an open culture
where children were not apprehensive to try things out (see p. 134). The teacher
had moved away from the premise that mathematics is either right or wrong: she
was much more interested in their thinking and how to support and encourage
them. I was impressed by their independent thinking: no two children produced174 Children’s Mathematics8657part 2.qxd 04/07/2006 17:28 Page 174