times and the ten times table were easier than the two times table. I said that ten and
100 are ‘friendly’ numbers because they are easy to work with. I then said I thought
99 was a friendly number: there was puzzlement about this. Then Sophie asked ‘is it
because it is near a friendly number?’ but she did not explain further. I wrote 99
times three on the board. ‘How would we work out this? Could we use our knowl-
edge of the 100 times table?’ Thomas said that three times 100 is 300, then you take
one away – which is 299. We considered that answer and I wrote it on the board.
Tom had carefully thought this through but he needed to reflect further. The chil-
dren did not respond but there appeared to be a lot of thinking. I asked them to con-
sider the repeated addition model.
Dervla wrote ‘99 + 99 + 99’ on the board and stopped. I wrote ‘100 + 100 + 100’
and asked the children what the difference was between 99 and 100. We established
that instead of taking just one away from 300 we needed to take three away. I then
asked them what knowledge they would use to work out the nine times table.
The children worked alone or in pairs on multiplication calculations with larger
numbers. Blank pieces of paper and pens were on the table so that if they needed to
they could work out their ideas on paper.
Alison first chose two times 99 and then wrote, after much crossing out, ‘99 + 99
= 20098’ (Figure 9.12). This is a logical way to write 298: children often write the
hundreds like this. It shows that they are really being resourceful because they have
never written numbers beyond 100. Alison then went on to choose 99 × 5. At first
she used an iconic method of writing a stroke 99 times in a set ring and then she
proceeded to carry on with this method for the other four lots of 99s. Alison found
this method difficult with such large numbers because she often lost count.
In discussion with Alison I asked her if there was anything else she could put
down to show 99. She seemed to be perplexed, so I said, ‘think about repeated addi-
tion’. This seemed to be a ‘eureka’ moment for Alison because she had made the con-
nection between counting out 99 five times and substituting that method for the
symbol. Alison had moved through the iconic to the symbolic response which was
much more efficient and less error prone. She used repeated addition for 99 and for
100 and was able to subtract the amount needed to come to her final answer.
Ben, 7:4, first chose to use repeated addition to work out nine times seven (see
Figure 9.13). He later abandoned that idea and used his mental skills because he did
not need to see the numbers repeated. He easily moved on to the 99 times table.Evaluation of the session
Although I felt the session had not gone too well perhaps because it appeared to chal-
lenge some of the children beyond their limits, they were very enthusiastic and
shouted out how great they thought it was. I felt that a lot of the children did not
apply their knowledge of multiplication, for example of repeated addition. Generally
the children found working with multiples of 99, a difficult concept to grasp. Some of
the children seemed to struggle to get a sense of larger numbers because they were only
used to working with numbers up to a hundred. Counting back from larger numbers186 Children’s Mathematics8657part 2.qxd 04/07/2006 17:31 Page 186