Division decision

19th March 2004 at 00:00
Q Having worked with various age groups supporting pupils in their maths lessons, I have found that pupils often have a problem with changing fractions to decimals. They're OK on short division, what they keep forgetting is which number they should be dividing by, the top or bottom. Have you any methods that you have found successful to help them remember?

A The example I am about to explain was suggested to me by a Year 11 student who has severe dyslexia. I have since tried it successfully with other older and younger age groups both.

We were converting 2Z5 to decimal format and after some discussion he wrote a little "L" in front of the top number (numerator). He said it reminded him to put the division box around the 2, so making sure that he did the question the right way round.

He then moved the denominator to a position outside the division box as I have done in the example below.

This leads to demonstrating that 2Z5 = 0.4.

There is perhaps a better way to demonstrate 2Z5 as a decimal - by multiplying the top and bottom to change into tenths: 2 x 2 = 4 = 0.45 x 2 10

Q I help pupils in an after-school club at our secondary school. One girl had difficulty with finding fractions of amounts. She was in the bottom maths set and was trying to revise for GCSE maths. Maths was always my weakest subject at school. When I showed the pupils how to set up short division to find the answer they didn't have a problem but when I began another example they didn't know how to tackle it.

A I had a similar experience with a boy who was also in bottom set for maths, though in top set for science. I was helping him with his maths as he needed to understand the algebra they were doing in science.

He had successfully managed to solve simultaneous equations in word format but had difficulty with finding fractions of amounts.

What was interesting was that some of the basic skills he was doing at the lower level didn't seem to be difficult for him when met within the algebra.

The question I shall use as an example of bridging his understanding from question to short division is that of finding 3Z4 of pound;3.

His first response was pound;1, because he divided by 3. This indicated that he had not related fractions of amounts to division.

I drew a square on a page with a cross through the middle. I asked him what fraction of the whole square each section was.

We talked about dividing the whole amount into four equal pieces and that this was 1 V 4, which is written as 1Z4 ; thus reminding him of the meaning of the notation used for fractions. It might be that you need to start by ripping up whole sheets of paper and asking pupils what fraction is created.

Having established that each section of the cross was a quarter of the sheet, I then gave him three pound;1 coins and told him that I wanted the pound;3 to go in the rectangle with the same amount of money in each quarter.

He could see straight away that if he put pound;1 in each space there would be a space left over. He asked for 50p pieces, and placed them on the grid as shown.

He then asked to change the two 50p pieces into four 20p and two 10p pieces. Once he placed the 20p pieces he was able to answer the question: 3Z4 of pound;3 is pound;2.25.

We then related this to using short division to find the answer, finding 1Z4 of pound;3 and then multiplying by 3 to find 3Z4 of pound;3.

When amounts are simple it is good practice to look at mental methods to arrive at the same solution - in this case to find a quarter by halving and halving again. Thus, half of pound;3 is pound;1.50 and half of pound;1.50 is pound;0.75. Adding pound;1.50 to pound;0.75 gives pound;2.25.

Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) www.nesta.org.uk to spread maths to the masses. Email your questions to Mathagony Aunt at teacher@tes.co.uk Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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