This had been a tremendous insight for Frances and was also a very powerful rep-
resentation for the other children. Several of them then offered to count all of the
seats but they found this difficult: none was yet at a point where they could add or
multiply seven lots of 75 as a calculation – something I was certainly not expecting
them to do. Later that day I displayed all the children’s written methods with
Aaron’s original question and during the following weeks children were often seen
counting the different representations of seats or people and carriages displayed and
talking about Frances’s seven carriages with 75 seats in each.Evaluation: developing personal skills
In this setting children had access to an extensive range of resources including the
photocopier and telephone. Within a genuine context Aaron’s question had pro-
vided many possible ways of exploring a challenging mathematical question that
encouraged talk and the use of a range of practical and graphical responses. It also
encouraged the children to meet challenges, to take risks and to be adaptive.
I think that we all know that those features of adult planned trips we intend chil-
dren to focus on are often not those which are the most significant to them. In this
instance, interest in the train journey and the crowded carriage superseded our
planned objective of the goods for sale in the market. It can often be more worth-
while to extend children’s own lines of enquiry rather than exclusively following
pre-planned, adult mathematical activities.Multiplying larger numbers
THE MATHEMATICS multiplying larger numbers
problem-solving
working from known facts
AGE 7-year-olds
CONTEXT whole class and small group
FEATURES children need number fluency to tackle problems
For the main teaching part of this session there was a discussion on multiplication.
The children had already been thinking of this in terms of an array. The children
knew the two and ten times tables. They displayed ways of showing two times three
on the board. Jane made a set circle and put three dots on one side and three dots
on the other side. James wrote the numerals two, four and six , counting up in twos
from two.
Ayesha wrote 2 + 2 + 2 thus using a repeated addition model. I emphasised that
there are also other ways of tackling multiplication, especially with larger numbers.
‘Obviously with two times three we can do it in our head, we know it, but what if
we did not know it? Can you do the nine times table?’ Two children said ‘yes’. ‘Can
you do the 99 times table?’ Everybody laughed and said ‘no’. We had previously
reviewed the ten times table and the 100 times table. The class agreed that the 100Case studies from early childhood settings 1858657part 2.qxd 04/07/2006 17:31 Page 185