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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 (scubas the same 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 sharedequally between two. He invented

'Tweedle birds', in turn giving an egg to each bird. Originally he

had written 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 or the class of 26 children.

   Placing a piece of A4 paper 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 3to 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 people." 

     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 didso, 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 +'five times, and, subtracting five, to arrive at her answer.