Children\'s Mathematics

for the information he wanted. Returning to the classroom, Aaron proudly

announced that there were 75 seats in one carriage and seven carriages on the train

on which we had travelled home. A group of ten children subsequently explored this

question in a variety of ways that were appropriate to them.

Differentiated responses

• Several of the youngest children drew random shapes, some drew squiggles and
  one child drew a person: all were able to talk about Aaron’s question and con-
  tribute ideas.


• Some children used iconic responses based on one-to-one correspondence. They
  drew circles or squares, sometimes checking their count by making a mark inside
  the shapes they had first drawn. One child used tallies and another used dots –
  also icons – to represent the seats.


• Several children drew either seats in a carriage or people on the seats – picto-
  graphic responses – including Aaron (Figure 9.9). He drew some seats with a thick
  pen and then counted them: finding he had only drawn 22 seats, he added more
  with a thinner pen in the remaining spaces, only stopping when there was no
  more space on his paper. He then counted the total number of seats and beneath
  his drawing he wrote ‘32 seats in the carriage’ and then said ‘it’s full’.

Figure 9.9 Aaron’s train

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