Right answer needs the right order

17th September 2004 at 01:00
Q) I would like to raise a concern regarding the use of BIDMAS or BODMAS (TES Teacher, June 24). Many maths teachers are unaware of the problem. Unless taught carefully BIDMAS would lead to the calculation: 20 - 5 + 3 = 12 and not the correct answer 18 since, according to BIDMAS, you must add before you subtract. There are two ways round this:

Use BIDMAS but tell students that the AS (addition, subtraction) are of equal importance and should be done from left to right in the absence of other operations. And take a similar approach to DM (divide, multiply) although this occurs less often.

* Avoid BIDMAS altogether and simply teach the order of importance of the operations. My students have no problems remembering that harder multiplication and division is more important that easy addition and subtraction. Similarly when they come across powers, which they didn't see at primary school, they are "really important secondary school stuff" and so to be done first. Brackets are "special" and always sorted out first.

After using both the above methods, I think BIDMAS makes a bit more sense than BODMAS.

This shows how we as teachers must represent ideas clearly. The question is, do we perceive the numbers themselves as integers or movements along a number line? I will explain what I mean.

We could think of the sum as +20 + - 5 ++3, then the numbers themselves could be written in the order of BIDMAS as +20 + + 3 + - 5 = 18. This would be similar to the way that we work when we are gathering like terms in algebra, (though we don't have to change the order to work them out).

In this case the addition is done first, that is the 20 is added to the 3 then the 5 taken away. This means that BIDMAS provides us with a correct order. In 20 - 5 + 3, the subtraction is the - 5 so we do that last, following the rules of BIDMAS.

I think your question is important as we need to make pupils focus on the interpretation of the calculation. I think that taught properly, BIDMAS is important as when we are transposing algebra the order in which we move the terms makes a difference. The frightening thing is that I have found a set of published tests being used in a primary school that have impossible numerical equations for their pupils to solve. In 40 of these 10-question tests 80 per cent of them had incorrect or impossible equations. For example the pupils had to fill in the correct answers in the following, 17 + 13 X ? = 90; 9 + 21 V ? = 5; ? = 23 + 5 V 4 + 14. The teacher, under pressure, had asked pupils to correct each other's work as she read the answers. If the child had incorrectly used BIDMAS they would have been told that their answer was correct (in the first example they would have written 3 as they would have added before multiplication, if you put their solution into a calculator then you would have 17 + 13 X 3 = 56).

I am a support teacher and would like to know what is meant by relative frequency. It is a long time since I was at school and I don't remember doing this.

In probability we can have a theoretical value of the likelihood of an event and we have one that represents the likelihood given the results of experiments.

The frequency of past events happening is used in calculations of your house insurance, taking into account variables such as the level of crime in your area and your health. A good way to demonstrate what is meant by relative frequency is by tossing coins. Discuss with your teacher the likely outcomes of tossing two coins together, let a tail be T and head be H, then the outcomes are TT, TH, HT, HH. Ask the teacher to calculate the probability of getting two tails (TT). This would be TT = 0.25 (there are four possible outcomes but just one that matches our selection).

Ask your teacher how many times she would expect TT if she tossed the coins together 20 times. Calculation suggests a quarter of the 20 throws would be TT, that is 5 times. Get your teacher to throw the two coins together 20 times and see what happens. She might throw 5, but she might get only 4. If she threw TT 4 times the relative frequency of getting TT would be 4 V 20 = 0.2, (this is the number of times the actual event happens divided by the number of times that the coins have been thrown). The more times your teacher throws the coins the nearer the relative frequency comes to the theoretical value. Your teacher could introduce some bias by putting some Sellotape on one side of the coin. Simulations for tossing coins and other activities can be found at :


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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