# Visual aid for decimal division

Q I support a pupil in Year 6. We have been working on money percentages and he is finding it very difficult. He can't even find 10% of an amount.

A First establish that 10% is one tenth of 100%. This you can do using a blank grid of squares 10cm by 10cm. Some visually impaired pupils find it difficult to see a whole grid, in which case use materials the pupil can feel, such as 1cm multi-link blocks, which can be linked together to show parts (in this case tenths) of the whole. You could write "1%" on each of the squares.

Ask the pupil to cover different percentages of the space, including 10%, then to colour each 10% with a different colour, establishing that there are indeed 10 squares of 10% in 100%. If the colouring is in lines, the paper can be cut to make strips of 10%, which can then be counted more easily. This can then be linked to dividing 100 by 10.

Next, use an amount as 100%, eg pound;24, which you should encourage the pupil to write more fully as pound;24.00. Discuss why this has to be divided by 10 to find 10%. This step, linking the money to 100% and then a portion of it to 10%, is very important and leads to a much greater understanding of percentages, particularly those over 100%.

To find 10%, I have used digit cards and demonstrated how the digits move one place to the right, with the decimal point static, when dividing by 10.

But there is a new visual method (which some of you might already use).

When dealing with money the amounts can become complicated when a division is not exact. The fact that, in monetary terms, there are two digits after the decimal point provides a neat analogy. Steve Humble, a maths lecturer at Newcastle College, has suggested using slopes with numbers sliding off the end, to help visualise the process. The number, eg pound;24.00, is on a hill. The decimal point is a static signpost. When divided by 10, the digits all slide down the hill by one place to the right, pushing the last one over the edge so that it falls off. So 10% of pound;24.00 is pound;2.40. If anyone makes a model so that visually impaired pupils can find 10% by feel, please let me know.

Q The Year 11 group I am teaching are doing revision for GCSE maths. I am not a maths specialist but have been brought in to teach the group for a term.

In one of their revision papers there was a Carroll diagram. What are they?

A A Carroll diagram is a rectangular table, and utilises a diagrammatic technique that has its base in logic as the categorical; data displayed in the tables are either "yes" or "no".

The name is that of the author of Alice in Wonderland - Lewis Carroll (Charles Dodgson's pen name), who was a mathematician with a great interest in symbolic logic.

Here is an example of a completed Carroll diagram that could be used with pupils in the classroom, perhaps to test a statement such as "Boys like sport more than girls". In your class you could get pupils to create their own by presenting a blank diagram on the board and tallying pupils'

responses in the appropriate cell. The totals can then be used to discuss the statement.

In the table, you can see 10 boys like sport and 12 girls like sport.

Pupils might think from this information that girls like sport more than boys, but the diagram also shows that more girls than boys don't like sport. The number of boys compared with girls can easily be seen by scanning the rows: (10 + 4 =) 14 boys and (12 + 6 =) 18 girls. Pupils could be asked how the numbers might change if there were the same number of boys and girls in the class. This leads to making percentage comparisons. So 10Z14 x 100 = 71.4% of boys like sport, compared to only 12Z18 x 100 = 66.7% of girls, leading to the conclusion that boys like sport more than girls.

A diagram could be created on the floor using coloured tape or chalk and pupils could be asked, in turn, to stand in the box which best describes them. There is a thread on this topic on the TESStaffroom website - www.tes.co.uk

If you would like to know more about Charles Dodgson (Lewis Carroll) visit www-gap.dcs.st-and.ac.ukhistory MathematiciansDodgson.html

Noa-5 = 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) to spread maths to the masses.

www.nesta.org.uk

= 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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