There’s a near certainty that everyone has seen (and possibly used) the dreaded ‘formula triangle’ approach to solving calculation problems in physics.

Formula triangle. Energy transformed is equal to power multiplied by time.

A ‘dreaded’ formula triangle

‘Wait – why “dreaded”?’, you ask. Let me explain: I think the use of formula triangles is misguided for two main reasons.

1. Formula triangles only work with problems of the format a = b × c

Now admittedly 70% of the formulas for AQA GCSE Physics (the specification used by the majority of UK schools) follow the a = bc format, but if you are aiming for a top grade, you should use a system that can handle the remaining 30% as well. Formula triangles can’t handle formulas of the type v2 − u2 = 2as, for example.

2. The formula triangle is a ‘trick’ that hides the maths

Authors such as Dr Ed Southall and Dr Jenny Koenig argue that the use of a formula triangle is a type of ‘procedural teaching’. That is to say, it is merely a ‘quick win’ that bypasses mathematical reasoning rather than models or supports it. While it can sometimes supply the correct answer, it can give no insight into why that answer is correct.

What is FIFAcalc?

‘FIFA’ is simply a mnemonic to help students structure their response to a calculation question.

Teachers and students who have tried the FIFAcalc system have reported significant improvements in marks awarded for calculation questions.

This is because it is ‘mark scheme friendly’. Marks can be awarded for substituting the correct data values and unit conversions, even if the final answer is wrong. Also, examiners will limit the number of marks awarded if the full ‘working out’ is not shown: FIFAcalc encourages a logically sequenced layout that is easy to mark.

FIFAcalc steps

Step 1: Formula

Write down the relevant formula or equation. To save time, write it using symbols.

Step 2: Insert values

Write down the numbers that are given in the question in the correct position. For example, if the speed v is given as ‘11.2 m/s’ then you write it in the same position as the v in the original formula. It’s also helpful if you write down the units, especially if there may be unit conversions.

Step 3: Fine tune

This may be a multistep process where you ‘do what you gotta do’ to reach the final answer. For example, it could involve converting units such as kilowatts into watts or even rearranging.

Step 4: Answer

You write down the final answer with the correct unit.

That’s the bare bones of the FIFAcalc system, but it’s often easier to understand using examples.

Using FIFAcalc for a 3 mark question

The animated diagram below shows a 3 mark question. It is worth 3 marks because it requires a unit conversion. Line 4 of the answer models part of the rearrangement method we can use with FIFAcalc.

Using the FIFAcalc system for a 3 mark question (animated gif).

Using FIFAcalc for a 4 mark question

The animated diagram below shows a 4 mark question. This is a 4 mark question because the examiner will be looking for evidence that the correct values have been squared as well as correct calculation of the final answer.

Using the FIFAcalc system for a 4 mark question (animated gif).

Applying FIFAcalc to an exam-style question

The following animated diagram shows how we can apply the FIFAcalc system to an example exam question and also how marks are awarded for each completed sub-section of the question.

Using the FIFAcalc system for an exam-style question (animated gif).

Many students – including those who find the mathematical aspects of Physics very challenging – have enjoyed great success using the FIFAcalc system as replacement for the ‘dreaded’ formula triangle. I hope you give the FIFAcalc system a try to see if it works for you!

Gethyn Jones

Gethyn Jones has been a Physics teacher for 30 years. He lives and teaches in London.

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