Children\'s Mathematics

Figure 9.13 Multiplying larger numbers – Ben (see p. 186)

Real problems

The children in this class were about to go on a residential trip and were planning

to stop on the way for a picnic. I used this as an opportunity to solve a problem relat-

ing to the fruit they would take.

The younger children used a variety of written methods that included drawing

squares with three dots in each, then crossing out one dot in the final pack (this was

‘one left over’): this was an iconic way of representing repeated addition.

Lewis wrote ‘nine packs are needed for 26 children so 3 × 9 = 27 and one nectarine

is going to be left over’. He had recognised the link between his repeated addition

and multiplication, and used both the ‘+’ and the ‘×’ symbols. Liza concluded by

writing ‘you have to have nine packs of three because you can’t get packs of two’.

Grace and Chang counted in threes. Grace (Figure 9.14a) first considered dividing

and then multiplying by three but appeared unsure of this. She then counted in

threes and then put numbers from one to nine alongside. She worked out that there

was one left over by counting back from her total of 27 nectarines to 26 (the number

Twenty six children are going to Salcombe. Mrs Hammond has brought some nec-

tarines. There are three nectarines in each pack. How could you work out how

many packs will be needed so that 26 children can have one nectarine each?

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