Although a lot of people feel uncertain when faced with ‘problem solving’,
YOU HAVE ACTUALLY BEEN DOING IT ALL YOUR LIFE. Planning a trip to the cinema
with your friends, getting ready for a party and organising your time so you can
fit in everything you would like to do are all examples of everyday problem
solving and I am sure you can think of more.
Problem solving in ordinary life is
- knowing what you are aiming to achieve
- knowing what you have at the moment
- knowing what else you need to help you
- taking the necessary steps to reach your goal
Problem solving in Maths is
- knowing what you have been asked to find
- picking out the facts that you have been given
- working out if you need any extra information
- solving the problem.
As you can see, they are very similar and you are probably very good at the
You can also be good at the second type as there are six simple questions
that you can ask yourself that will help in nearly all cases.
Q 1) WHAT AM I BEING ASKED TO FIND?
Make sure you know EXACTLY what you are being asked to find and WRITE THAT
DOWN, or UNDERLINE it, so you don’t forget.
Q 2) WHAT FACTS AM I GIVEN?
Work out EXACTLY what facts you have been given and either WRITE THEM DOWN or
UNDERLINE them, so that you don’t forget anything important. Sometimes
information is given that you don’t need but it is also common to miss vital
details so this is a very important step.
Q 3) WHAT TOPIC AREA DO I NEED TO THINK ABOUT?
Look at the two sets if information that you have in front of you.
At some point during your course you HAVE met situations where these are
What are the key points for this topic?
- Think about the key things that you know about this area of the
- Is there a formula that links what you have been asked for and some, or all,
of what you have been given?
Easy formulae you should remember such as distance = speed x time but if you
can’t think of one, CHECK THE FORMULAE LIST AT THE FRONT OF THE PAPER.
Q 4) DO I UNDERSTAND WHAT NEEDS TO BE DONE?
If there is no obvious formula you may have to try other methods to work out
what to do. These could include:
- Drawing a diagram This helps you to picture the problem
- Making a list This helps put information in order
- Guessing and checking This helps to narrow down the possibilities till
you reach the correct answer
- Trying an example using simpler numbers This helps to make sure that you
are using the correct process eg. dividing and not multiplying .
Q 5) DO I HAVE ALL THE INFORMATION I NEED?
Sometimes you don’t have all the information that you need to work out your
answer in just one process.
Check to see if there might be some other information that you need to work
out first, such as an angle or a length. Sometimes you have to work out a couple
of pieces of information before you can put it all together to find your
Q 6) HAVE I BEEN CAREFUL?
- Careless errors?
Many marks are thrown away in exams by careless errors. Take particular care
with the things that seem easy such as decimal points and basic arithmetic.
- Shown all working?
What exactly does this mean? Pretend that you are explaining how to do the
piece of Maths to someone who has not met it yet but would understand if shown
carefully how to do it. You would write down what you started with.
You would write down each step and show how you moved from one line of
working to the next.
You would finish with a clear indication that you have reached the
You would NOT just put random bits of working on the page (I hope).
- Correct units?
Check that you have used the correct units of measure in your answer. Eg. Kg
or g? £ or p? units for area or units for volume?
- Logical answer?
Check that your answer makes logical sense! This is another VERY important
step that is frequently missed. Recently I have seen answers where the short
side of a triangle was larger than the longest side, a car has travelled over
1000miles per hour and a queue has had half a person in it!
DON’T THROW MARKS AWAY like the pupils above!