# Following the order of operations

A. Understanding the order of operations is important for algebra-solving equations and it's a major topic in arithmetic. In computing it has always been recognised as being important among scientists and engineers. However, it's frightening how many of those among us are unaware of its significance. In fact, there is published material that's still used in schools with short 10-question tests that have incorrect answers.

This is confusing for non-mathematicians and for children. In my adult workshops I see if the group understands the order by asking them the answer to something simple, such as 3 + 7 x 2. I get them to check this with a calculator and then we discuss conventions. The answer is 17 as the multiplication has to be carried out first.

To answer your question, I also used to use BODMAS for order of operations until I was working with a scholarship pupil from St Paul's in London and he told me they used BIDMAS. This is preferable as it's easy to understand. As you correctly say, the "I" stands for "indices", so the next most important operation to be performed after brackets is "to the power of" or index number. In this example (3 + 2)2 - 5 the 3 + 2 is worked out first to give 5. This is then squared to give 25. Finally, five is subtracted to give an answer of 10.

A document on the internet (www.ex.ac.uktroltroltrolze.pdf), written by Frank Tapson, talks about possible meanings of the "O". He says it can mean "of", "over", "operations" or "order". His search of the internet uncovered 684 sites using BODMAS and only 71 using BIDMAS. What is important is that your pupils are happy with the mnemonic you give them and they understand the correct order of operations. This poem may help.

Bidmas

Begin with the bracket This opens the packet.

Interest next in power Exponential its flower.

Destined for division A quotient for vision.

Magnificent to multiply Sum replication imply.

Ascending to addition Totalise the rendition.

So lastly now subtract BIDMAS rules you enact.

I am a non-specialist teacher and have been teaching top-set Year 11 maths.

One of the ideas students found difficult to conceptualise was creating diagrams for vector problems, such as those for boats in water travelling with a current, aeroplanes in the sky when there is a wind blowing. I felt they didn't have a feel for the problem. What do you suggest?

Q. I am a great believer in learning from experience, particularly where applied maths is concerned. My vision of vectors when I was doing applied maths A'-level were from a dusty old textbook and diagrams drawn on the board.

These seemed to magically take this diagonal resultant and create a parallelogram of forces to enable the calculation of the answer.

Bored already? I certainly was. It wasn't until I did my degree that I really understood where all this came from. The "illuminating light" came when we drew vectors on squared paper and they were described as journeys.

I have given a diagrammatic example of an aeroplane flying in still air as a vector and a representation of the wind also as a vector.

A. In the second diagram the two are combined to give the resultant flight path of the aeroplane as a vector (note vectors have both magnitude and direction).

The resulting flight path can be worked out by drawing a scale diagram or by calculating the resultant given the speed and direction of both.

It is important for students to have this "feel" for what actually happens.

They could use ping-pong balls on tables and sketch the paths with and without external forces; push a person and record the path; throw a beach ball in the air and see what happens when a fan is turned on. They can film these events using a digital camera to get the slow-motion effect.

I have also found a website that has a computer simulation programme on it.

Visit http:illuminations.nctm. orgmathletsvector2.

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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