FIFA Calculation

FIFA and Really Challenging GCSE Physics Calculations

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‘FIFA’ in this context has nothing to do with football; rather, it is a mnemonic that helps KS3 and KS4 students from across the attainment range engage productively with calculation questions.

FIFA stands for:

  • Formula
  • Insert values
  • Fine-tune
  • Answer

From personal experience, I can say that FIFA has worked to boost physics outcomes in the schools I have worked in. What is especially gratifying, however, is that a number of fellow teaching professionals have been kind enough to share their experience of using it:

Framing FIFA as a modular approach

Straightforward calculation questions (typically 2 or 3 marks) can be ‘unlocked’ using the original FIFA approach. More challenging questions (typically 4 or 5 marks) can often be handled using the FIFA-one-two approach.

However, what about the most challenging 5 or 6 mark questions that are targeted at Grade 8/9? Can FIFA help in solving these?

I believe it can. But before we dive into that, let’s look at a more traditional, non-FIFA, algebraic approach.

A challenging freezing question: the traditional (non-FIFA) algebraic approach

Note: this is a ‘made up’ question written in the style of the GCSE exam.

A pdf of this question is here. A traditional algebraic approach to solving this problem would look like this:

This approach would be fine for confident students with high previous attainment in physics and mathematics. I will go further and say that it should be positively encouraged for students who possess — in Edward Gibbon’s words — that ‘happy disposition’:

But the power of instruction is seldom of much efficacy, except in those happy dispositions where it is almost superfluous.

Edward Gibbon, The Decline and Fall of the Roman Empire

But what about those students who are more akin to the rest of us, and for whom the ‘power of instruction’ is not a superfluity but rather a necessity on which they depend?

A challenging freezing question: the FIFA-1-2-3 approach

Since this question involves both cooling and freezing it seems reasonable to start with the specific heat capacity formula and then use the specific latent heat formula:

Cold-calling students and asking them: ‘What should we write in this box?’ is, surprisingly, an effective way of engaging the class in the process. It’s good to emphasise that we write in numbers for the the values we know from the question and symbols for the ones we don’t.
It is important to model how to deal with values that we don’t know…
This is far as we can get using the FIFA-one-two model….

FIFA-one-two isn’t enough. We must resort to FIFA-1-2-3.

What is noteworthy here is that the third FIFA formula isn’t on the formula sheet and is not on the list of formulas that need to be memorised. Instead, it is made by the student based on their understanding of physics and a close reading of the question.

Challenging? Yes, undoubtedly. But students will have unlocked some marks (up to 4 out of 6 by my estimation).

FIFA isn’t a royal road to mathematical mastery (although it certainly is a better bet than the dreaded ‘formula triangle’ that I and many other have used in the past). FIFA is the scaffolding, not the finished product.

Genuine scientific understanding is the clock tower; FIFA is simply some temporary scaffolding that helps students get there.

We complete the FIFA-1-2-3 process as follows:

Conclusion: FIFA fixes it

The FIFA-system was born of the despair engendered when you mark a set of mock exam papers and the majority of pages are blank: students had not even attempted the calculation skills.

In my experience, FIFA fixes that — students are much more willing to start a calculation question. And that means that, even when they cannot successfully navigate to a ‘full mark’ conclusion, they gain at least some marks, and and one does not have to be a particularly perceptive scholar of the human heart to understand that gaining ‘some marks‘ is more motivating than ‘no marks‘.

Update: Ed Southall makes a persuasive case against formula triangles in this 2016 article.

Physics Six Mark Calculation Question? Give it the old FIFA-One-Two!

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Batman gives a Physics-Six-Marker the ol’ FIFA-One-Two,

Many students struggle with Physics calculation questions at KS3 and KS4. Since 40% of the marks on GCSE Physics papers are for maths, this is a real worry for their teachers.

The FIFA system (if that’s not too grandiose a description) provides a minimal and flexible framework that helps students to successfully attempt calculation questions.

Since adopting the system, we encounter far fewer blanks on test and exam scripts where students simply skip over a calculation question. A typical student can gain 10-20 marks.

The FIFA system is outlined here but essentially consists of:

  • Formula: students write the formula or equation
  • Insert values: students insert the known data from the question.
  • Fine-tune: rearrange, convert units, simplify etc.
  • Answer: students state the final answer.

The “Fine-tune” stage is not — repeat, not — synonymous with re-arranging and is designed to be “creatively ambiguous” and allow space to “do what needs to be done” and can include unit conversion (e.g. kilowatts to watts), algebraic rearrangement and simplification.

The FIFA-One-Two

Uniquely for Physics, instead of the dreaded “Six Marker” extended writing question, we have the even-more-dreaded “Six Marker” long calculation question. (Actually, they can be awarded anywhere between 4 to 6 marks, but we’ll keep calling them “Six Markers” for convenience.)

The “FIFA-one-two” strategy can help students gain marks in these questions.

Let’s look how it could be applied to a typical “Six mark” long calculation question. We prepare the ground like this:

FIFA-one-two: the set up. (Note that since the expected unit of the final answer is given, this is actually a five marker not a six marker; however, the system works equally well in both cases.)

Since the question mentions the power output of the kettle first, let’s begin by writing down the energy transferred equation.

Next we insert the values. It’s quite helpful to write in any “non standard” units such as kilowatts, minutes etc as a reminder that these need to be converted in the Fine-tune phase.

And so we arrive at the final answer for this first section:

Next we write down the specific heat capacity equation:

And going through the second FIFA operation:

Conclusion

I think every “Six Marker” extended calculation question can be approached in a productive way using the FIFA-One-Two approach.

This means that, even if students can’t reach the final answer, they will pick up some method marks along the way.

I hope you give the FIFA-One-Two method a go with your students.

You can read more about using the FIFA system here: ‘Using the FIFA system for really challenging GCSE physics calculations‘.

Talk from Chat Physics 2021 https://chatphysics.org/chat-physics-live-2021

Update: Ed Southall makes a very persuasive case against formula triangle in this 2016 article.

FIFA for the GCSE Physics calculation win

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Student: Did you know FIFA is also the name of a video game, Sir?

Me: Really?

Student: Yeah. It’s part of a series. I just got FIFA 20. It’s one of my favourite games ever.

Me: Goodness me. I had no idea. I just chose the letters ‘FIFA’ completely and utterly at random!

The FIFA method is an AQA mark scheme-friendly* way of approaching GCSE Physics calculation questions. (It is also useful for some Y12 Physics students.)

I mentioned it in a previous blog and @PedagogueSci was kind enough to give it a boost here, so I thought I’d explain the method in a separate blog post. (Update: you can also watch my talk at ChatPhysics Live 2021 here.)

The FIFA method:

  1. Avoids the use of formula triangles
  2. Minimises the cognitive load on students when approaching calculations.

Why we shouldn’t use formula triangles

Formula triangles are bad news. They are a cognitive dead end.

Screenshot 2019-10-27 at 15.34.54

During a university admissions interview for veterinary medicine, I asked a prospective student to explain how they would make up a solution for infusion into a dog. Part of the answer required them to work out the volume required for a given amount and concentration. The candidate started off by drawing a triangle, then hesitated, eventually giving up in despair. […]

They are a trick that hides the maths: students don’t apply the skills they have previously learned. This means students don’t realise how important maths is for science.

I’m also concerned that if students can’t rearrange simple equations like the one above, they really can’t manage when equations become more complex.

— Jenny Koenig, Why Are Formula Triangles Bad? [Emphases added]

[Update: this 2016 article from Ed Southall also makes a very persuasive case against formula triangle.]

I believe the use of formula triangle also increases (rather than decreases) the cognitive load on students when carrying out calculations. For example, if the concentration c is 0.5 mol dm-3 and the number of moles n required is 0.01 mol, then in order to calculate the volume V they need to:

  • recall the relevant equation and what each symbol means and hold it in working memory
  • recall the layout of symbols within the formula triangle and either (a) write it down or (b) hold it in working memory
  • recall that n and c are known values and that V is the unknown value and hold this information in working memory when applying the formula triangle to the problem

The FIFA method in use (part 1)

The FIFA acronym stands for:

  • FORMULA
  • INSERT VALUES
  • FINE TUNE (this often, but not always, equates to rearranging the formula)
  • ANSWER

Lets look at applying it for a typical higher level GCSE Physics calculation question

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We add the FIFA rubric:

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Students have to recall the relevant equation as it is not given on the Data and Formula Sheet. They write it down. This is an important step as once it is written down they no longer have to hold it in their working memory.

Screenshot 2019-10-27 at 16.18.15.png

Note that this is less cognitively demanding on the student’s working memory as they only have to recall the formula on its own; they do not have to recall the formula triangle associated with it.

Students find it encouraging that on many mark schemes, the selection of the correct equation may gain a mark, even if no further steps are taken.

Next, we insert the values. I find it useful to provide a framework for this such as:

Screenshot 2019-10-27 at 16.27.41.png

We can ask general questions such as: “What data are in the question?” or more focused questions such as “Yes or no: are we told what the kinetic energy store is?” and follow up questions such as “What is the kinetic energy? What units do we use for that?” and so on.

Screenshot 2019-10-27 at 16.35.54.png

Note that since we are considering each item of data individually and in a sequence determined by the written formula, this is much less cognitively demanding in terms of what needs to be held in the student’s working memory than the formula triangle method.

Note also that on many mark schemes, a mark is available for the correct substitution of values. Even if they were not able to proceed any further, they would still gain 2/5 marks. For many students, the notion of incremental gain in calculation questions needs to be pushed really hard otherwise they will not attempt these “scary” calculation questions.

Next we are going to “fine tune” what we have written down in order to calculate the final answer. In this instance, the “fine tuning” process equates to a simple algebraic rearrangement. However, it is useful to leave room for some “creative ambiguity” here as we can also use the “fine tuning” process to resolve difficulties with units. Tempting though it may seem, DON’T change FIFA to FIRA.

We fine tune in three distinct steps (see addendum):

Screenshot 2019-10-29 at 12.17.55.png

Finally, we input the values on a calculator to give a final answer. Note that since AQA have declined to provide a unit on the final answer line, a mark is available for writing “kg” in the relevant space — a fact which students find surprising but strangely encouraging.

Screenshot 2019-10-29 at 12.16.46.png

The key idea here is to be as positive and encouraging as possible. Even if all they can do is recall the formula and remember that mass is measured in kg, there is an incremental gain. A mark or two here is always better than zero marks.

The FIFA method in use (part 2)

In this example, we are using the creative ambiguity inherent in the term “fine tune” rather than “rearrange” to resolve a possible difficulty with unit conversion.

Screenshot 2019-10-27 at 17.20.42.png

In this example, we resolve another potential difficulty with unit conversion during the our creatively ambiguous “fine tune” stage:

Screenshot 2019-10-27 at 17.33.05.png

The emphasis, as always, is to resolve issues sequentially and individually in order to minimise cognitive overload.

The FIFA method and low demand Foundation tier calculation questions

I teach the FIFA method to all students, but it’s essential to show how the method can be adapted for low demand Foundation tier questions. (Note: improving student performance on these questions is probably a more significant and quicker and easier win than working on their “extended answer” skills).

For the treatment below, the assumption is that students have already been taught the FIFA method in a number of contexts and that we are teaching them how to apply it to the calculation questions on the foundation tier paper, perhaps as part of an examination skills session.

For the majority of low demand questions, the required formula will be supplied so students will not need to recall it. What they will need, however, is support in inserting the values correctly. Providing a framework as shown below can be very helpful:

Screenshot 2019-10-27 at 17.47.24.png

Also, clearly indicating where the data came from is useful.

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The fine tune stage is not needed, so we can move straight to the answer.

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Note also that the FIFA method can be applied to all calculation questions, not just the ones that could be answered using formula triangle methods, as in part (c) of the question above.

Screenshot 2019-10-27 at 18.06.16.png

And finally…

I believe that using FIFA helps to make our thinking and methods in Physics calculations more explicit and clearer for students.

My hope is that science teachers reading this will give it a go.

You can read about using the FIFA system for more challenging questions by clicking on these links: ‘Physics six mark calculation? Give it the old FIFA-one-two!‘ and ‘Using the FIFA system for really challenging GCSE calculations‘.

PS If you have enjoyed this, you might also enjoy Dual Coding SUVAT Problems and also Magnification using the Singapore Bar Model.

*Disclaimer: AQA has not endorsed the FIFA method. I describe it as “AQA mark scheme-friendly” using my professional own judgment and interpretation of published AQA mark schemes.

Addendum

I am embarrassed to admit that this was the original version published. Somehow I missed the more straightforward way of “fine tuning” by squaring the 30 and multiplying by 0.5 and somehow moved straight to the cross multiplication — D’oh!

My thanks to @BenyohaiPhysics and @AdamWteach for pointing it out to me.

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