Why can't mathematicians use just one word for an operation? There are loads of words that are really asking you to add. I think this is why pupils who are trying to solve word problems find it difficult to work out what to do.
Mathematics is tied to language. Although the operation is to add, there are subtle differences implied by the language. For instance, "I increase your salary by pound;10000 a year" is more glamorous, with a potential that it could happen again, than "I will add pound;10 000 to your salary."
Is increase a more grown-up word? How does this work in other languages? Any ideas, readers? For fun, here is a short poem covering the words for "add": Increase
and, sum, more than, add
a fuss, to plus, the total
I am teaching my middle group year 10 about scale and would like to tie this to some kind of course work. Have you any suggestions that might make this more meaningful for them?
Firstly I will give you a story and then a suggestion of how this could be used as the basis for a piece of coursework - cross-curricular with art and ICT would be great. I was given the following story by a graphic designer who had to create "visuals" for a window display:
"The display involved a number of A0, A1 and A4 posters. When creating a design it is important for the client to see how the visuals work together in a scaled mock-up and accuracy is important to show what the differently sized elements would look like in each window.
"The display was to be in four windows of different sizes. I had to work from an A4 sheet with a scaled drawing of the building showing only one exact size, a shutter width of 800mm. I measured the shutter on the A4 drawing as 18mm, giving a scale of 18:800. I used this to work out the actual sizes of the windows by measuring the dimensions on the A4 sheet and applying the scale that I had calculated. The dimensions were only approximate, as the drawing I was working from was a small photocopy of a larger plan. So an error of a millimetre could affect the final measurements by a great deal. I had to devise my own scale in order to show how the A0, A1 and A4 posters would fit in the windows.
"When we got the final measurements, I found I had been out by 14 per cent, so all of my drawings were 86 per cent smaller than the actual windows."
It would be useful to explain through demonstration as part of the introduction how the designer came up with the scale, by measuring the window in the drawing and writing the measurement down next to the value that has been given for the actual size.
Pupils might need to be reminded that, for a ratio, the units used in the measurement of the item and in the measurement on the picture must be the same.
Using the designer's story and an A4 diagram as an example, give the story to pupils to read and discuss in pairs. It would be useful to have to hand A0, A1 and A4 sheets as a demonstration of the size that the "visuals" have to be. They will have been created on computer using a design package, making the alteration of the drawings to the more accurate measurements a much less cumbersome process. See www.mathagonyaunt.co.ukarticlesindexJan242003.html for copy of text and diagram.
The discussion could include the notation for representation of ratio and equivalent ratios. The calculation of percentage error and how this might be useful in rescaling the 'visuals'.
The pupil's coursework stimulated by this introduction could be that of a similar project but based on their own locality. Provide them with a photograph (this could be of local shops) and the measurement of a single item in the window. They are given the same brief as the designer of having to create 'visuals' for a shop window. Initially they need to work out the scale of the plans and then scales of the 'visuals'.
When their designs are complete then they are given the actual window measurements so that they can calculate their percentage errors and re-form their designs to the 'real' values. Extensions might include looking at other ways in which people in the world of work might be using ratio and scale.
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. Email your questions to Mathagony Aunt at email@example.comOr write to TESTeacher, Admiral House, 66-68 East Smithfield, London E1W 1BX