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- Calculations: solving division and multiplication problems

Tweedle birds

In this lesson, the teacher introduced

division by sharing though telling a story

about twins who liked everything the

same (such as an equal number of

sweets each). She went on to ask the

children if they could think of numbers

that could be shared equally, and the

children began to explore this in their

own ways.

     Kamrin (5 years, 7 months) invented

his own system to check if the number

'8' could be shared equally between two.

He invented 'Tweedle birds', in turn

giving an egg to each bird. To begin,

he wrote a question mark by the

'8' (the inverted'j'), adding a cross by it,

but now he scribbled over the cross and

wrote a tick to confirm his finding that

'8' could be shared equally.














Nectarines for a picnic

Miles's class were about to leave on a 

residential trip, and their teacher used a pack

of three nectarines to encourage the children

to calculate how many packs would be

needed for the class of 26 children.

   Placing a piece of A4 paper on the table

in portrait format, Miles (7 years, 5 months),

began by drawing an empty number-line.

     Due to the orientation of his paper

Miles found that he had to restrict the

number of jumps he made, changing jumps

of 3, to jumps of 6 several times, before

arriving at his answer.


Frances and the train

This class had just returned from a trip by

train to visit  a large country market. The

next day, Aaron observed, "I bet there's a

million seats on the train!", and their teacher

asked how they might find out. Several

suggestions followed (the library, the

headteacher, the computer), and then one

child suggested they "phone the train


     With help in finding the phone number,

Aaron proudly asked for the information he

wanted, and on returning to the classroom,

told the children that there had been 75

seats in each carriage, and seven carriages

on the train. Several children decided they

would like to work on this problem, and did

so, in a variety of ways.

      At first Frances (5 years, 7 months),

wrote '75' seven times, then drew a

carriage (a square) with 76 seats in it.

Self-checking, she found she had one too

many (at the bottom) and crossed it out. 




















The '99 times table'

 The children in this class had already been

 thinking of multiplication in terms of an array, 

  and knew the two, three and 10 times tables.

 They also understood how to count in 100s.

        Their teacher challenged them to work out 

the nine times table, the children all laughing

at this suggestion, and saying "no!"

    Alison (7 years, 6 months) began by writing

"5 x 99 =", then '"2 x 99" followed by a lot of 

crossing-out, and the word '"no." Beneath it 

she wrote "99 + 99 = 20098" (a logical way

of writing 298), but abandoned this. She

then used vertical strokes to represent 99,

repeating this again - but then wrote "rong"

and "no" beside them. 

   In discussion with Alison, her teacher

asked if there was anything else she could

try, and this seemed to be a 'eureka'

moment for Alison. She changed from her

iconic method of writing vertical lines - to

using standard symbols written as

repeated addition. Finally she wrote "100

+ 100" 'five times, and, subtracting five from

her total of 500, arrived at her answer.