Thursday, 19 December 2013

BIDMAS, BODMAS and tearing your hair out.

Bidmas or Bodmas

BIDMAS BODMAS not again!
BIDMAS or BODMAS, it doesn't matter which mnemonic you use, it always seems to cause problems for pupils. Below is an idea that is simple and works.

A student or class may be able to apply it to an exercise after your explanation. Give a few questions a week later and all is forgotten. 

Either confusion reigns in the classroom when they try to apply it to problems that are outside the exercise specifically on BIDMAS or it is completely ignored by the pupils. Below is a an activity that will help.


This is enough for any self respecting teacher to tear their hair out in frustration. I am sure we are all, as Maths teachers familiar with this problem. 

I remember reading  a post from a Maths teacher in Asia who was bemoaning his pupils inability to remember and apply BIDMAS. I felt strangely comforted by his predicament, I was not alone. 

The challenge is to build the habit of applying BIDMAS, without too much thought, it should be automatic. Below I give a suggestion as to how we can build this knowledge and response when given the cue of a arithmetic problem and still have a degree of creativty and exploration.

Calculators can do the work

I have had the occasional discussion about the usefulness of using BIDMAS with pupils, they sometimes claim that calculators can do it all for you, no need to learn the rules. This is a fairly easy argument to counter. 

If the students have calculators of their own just search out two, I always look for a scientific and non-scientific and ask them to work out 2+3x4. 

Then ask the two pupils to give their answers, often the class is amazed that the results are different, this is the opportunity to engage them in  a discussion about BIDMAS. Evidence that a calculator will not always come to your aid.

It is also vital to point out to them that they need to understand how BIDMAS works when using algebra in addition to problems they may encounter in examinations when they are not allowed to use calculators. 

A word of warning check the scientific calculator first, I happily tried this in front of a class only to discover, red faced, that the scientific calculator did not apply the rules of BIDMAS.

2014

An activity I always like to practise BIDMAS with is the year, it is an activity that can be a starter, a main activity or as a homework. 

My preference was to use it as a starter in January as the new year begins, so as I write it would be 2014. The first task would be for the pupils to record 1 to 100 in the back of their books, giving one line for each number. 

The task is to use the numbers 2, 0, 1 and 4 to create all of the numbers 1 to 100. No number can be repeated, it is up to you whether you allow the pupils to discard some of the numbers. The four basic operations can be used as well as powers and brackets.

It is worth introducing a few examples yourself. Using our previous example 2 + 3 x 4, I would show that as it stands it equals 14, we could also put in brackets, 2 + (3 x 4) which equals 14. 

But using the same digits and operations but moving the brackets (2 + 3) x 4 we now get the answer 20. This will help to highlight the power of brackets. I would also discuss powers or indices demonstrating the flexibility of allowable operations.

Organisation

If I was using this as a starter I would spend sometime giving the rules but only allow 10 minutes working time. At the end of ten minutes collect the results and share them with the class. Save the results. 

At the start of the next lesson remind them of the task and issues and repeat the ten minute task, collect results and save for next lesson. It may not be possible to make every number and will depend upon the ability of your class but it should last for three lessons. 

This slow drip and repetition will help to establish BIDMAS in your pupils long term memory. It is worth repeating every year as only by constant practise will pupils become really confident with BIDMAS.

It is worth discussing with pupils the most effective strategy to use, many will start at the number 1 and work down. Talk about why this is not a good idea and what is a better strategy.

The Simpsons and Maths

I had the great pleasure of meeting Simon Singh recently. Having read two of his books, Trick or Treatment?: Alternative Medicine on Trial and Big Bang: The Most Important Scientific Discovery of All Time and Why You Need to Know About It , both outstanding reads and highly recommended I was excited to hear of his latest book The Simpsons and Their Mathematical Secrets. What could be better, a mixture of The Simpsons and Maths? Simon writes so well, he is entertaining, informative and knowledgeable a winning combination for any author.



A related post on learning your times tables is 'How to learn your times tables'

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