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.

The FIFA method:

- Avoids the use of formula triangles
- 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.

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. […]

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

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]

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

We add the FIFA rubric:

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.

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:

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.

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):

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.

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.

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

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:

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

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

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.

### 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 how to use the FIFA-one-two! for extended calculation questions here.

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.

PS You can read FIFA Part Deux here.

Reblogged this on The Echo Chamber.

Thanks for your thoughts.

As an A Level teacher, this is a conversation I have had many many times. As recently as Thursday, I was asked about the use of triangles by two teachers relatively new to the profession. Furthermore, developing maths skills early is one of my key things when planning our school’s physics curriculum and also my individual lessons. I have a couple of thoughts in response to your article.

Firstly:

I wonder if you’ve slightly misrepresented the use of the formula triangle as a problem solving tool. I would argue that it’s an algebra avoidance tool only. It does not do anything other than allow a pupil to rearrange by shortcut with a total lack of algebraic understanding.

I wholehearted agree that pupils likely to go on to study a science at higher level should be highly proficient with an algebraic approach, however I disagree that they’re a fatally flawed approach full stop. For a student who is not proficient with an algebraic approach (despite the maths dept’s best efforts) and unlikely to be a member of the a level science demographic, I would argue that any method which allows them to access a level of scientific proficiency should be welcomed.

Controversial – possibly. Enabling them to have a working chance of getting past F-I and onto F-A – almost certainly.

Secondly:

As an A level teacher I would argue that teaching this to Y12 is not detailed enough. Arguably, nor is it detailed enough for GCSE now that sig figs are an element of the course. For me, FIFA is ideal for KS3 (Y7-9 for those at schools persevering with a 2 year KS3) development of maths skills.

Once into Y10/11, I would advocate teaching FRICCUS which I think was part of the old spec OCR Adv Phys A Level support documentation – fairly sure this is where I got it from anyway.

F – ormula

R – earrange

I – nsert data (in correct format!)

C – alculate

C – check calculated correctly

U – units

S – ignificant figures

Admittedly somewhat less catchy and memorable than FIFA but it does cover all of the elements that pupils need to be aware of in a GCSE question now. It also has the added benefit of making checking their work part of the process rather than simply a thing teachers bang on about to no avail…

Thanks for the comments.

I love FRICCUS — and have used it and will use it with A-level students.

I have been dragged kicking and screaming out of the “rearrange first” camp for two reasons: 1) AQA GCSE mark schemes reward correct substitution and encourage substitute first; 2) students (bizarrely, in my opinion) almost always find it easier to rearrange after substitution.

FIFA isn’t intended as the last word: it’s a temporary scaffold to help a subset of students that struggle with this task — that’s it. It will (hopefully) fade away as students progress.

With A level, I avoid introducing FRICCUS too early as I don’t want to overload students (esp as the MAT I work for has an Induction Test at the end of Oct which students have to pass). I would estimate that half my Y12 group have no issues with calcs so don’t need FIFA. I only use it to walk through solutions with students who need support.

With respect, I think you’re wrong on formula triangles. I did lean on them heavily in the past but I honestly believe they’re bad news and best avoided. Some students from our set 3 got the grades and opted to do A-Physics, so I’m glad I didn’t teach them triangles! Also, some students may opt for Applied Science or similar courses, so I think they need as much prep as possible.

Thanks for reading — and leaving such thought provoking comments!

One more thing, basic rearrangement in the sense of “Express missing number problems algebraically” is on the KS2 Maths curriculum.

Thanks for your replies.

When talking about using triangles, I’m typically referring to the lowest set kids (2 X set 6 per year group). I would only use the triangles for those who basically cannot do algebra – though would still model it properly.

We have a very strong science dept with uptake being very strong for 6th form. As an entry criteria, we ask for a 6/5 combination as a minimum so it’s unlikely a foundation tier student continues into science. Admittedly one or two may was the case to go on to do applied, but for the overwhelming majority their journey ends at GCSE.

I note your point about rearranging first and have also noticed this wierd issue. However, by hammering this skill throughout the 5 years of KS3 and 4, we’re noticing an upswing in confidence and ability with regards to rearranging. We also asked maths to do as much of their teaching of rearranging equations as possible using the GCSE formulae – they are no longer just wierd combinations of letters in science which has made a positive impact too

Sorry, and please excuse my sheer ignorance about advanced/applied mathematics and physics. However, I DO know a bit about

The World’s Most Beautiful Game.⚽Please tell your arm-chair footballing student that for brainiacs FIFA ’20 and previous EA games can never match the full-spectrum brilliance, strategy, challenge, and excitement of building a Club (or national) dynasty with your own hands and brain as SEGA’s and Sports Interactive’s

Football Managerseries of games. Not even close. 😉 😛I remember Football Manager on the Spectrum 48k — now that was a great game (and I don’t even like football)!

Good stuff. I would tend to rearrange to get my desired unit the subject before putting the numbers in. That would be FRIC: formula, rearrange, insert, calculator.

I agree that rearrange first is the way to go, but FIFA works well for a subset of students who struggle with that.

Thank you. I have also been getting students to underline words in the question and add the symbols, thus helping in the recall of the correct formula.

This discussion has been very timely. I have just been teaching non-physics science teachers my preferred approach to teaching the solving of calculation problems at GCSE.

Step 1: Get students to trawl the question and underline any variables mentioned. This includes both variables whose value is given and the one being asked for in the question.

Step 2: They must then list these variables vertically putting in values and units where given and putting a ‘?’ for the unknown variable.

Step 3: Convert any non-SI units to the correct one.

Step 4: They can then look at their equation sheet to identify the equation that contains this list of variables and write it down (all students should have the equation sheet in their exercise books to refer to. They can be learning the equations but I believe that regular selection and application of these equations is the best way of establishing intelligent memorisation). There are only 28 equations in total for AQA so this matching process is relatively manageable.

Step 5: As per AQA guidance (and against my instinct) I get them to write the values-substituted version of the equation

Step 6: Re-arrange, solve and select correct units if necessary.

What I also told the heads of science in the groups I was training is how vital it is to agree a common approach across the department so that whatever the chosen approach is, it is experienced consistently from Year 7 to Year 11 irrespective of teacher and becomes second-nature.

The steps listed are great: straightforward, detailed modelling of the process (which novices always find harder than we appreciate). And Step 4 is absolutely the way to make them familiar with the equations.

Two comments though:

Step 3 will work for *most* exam questions, but what if units are not SI e.g. kWh or km/hr or similar (I’m not sure if the AQA spec rules out use of non SI units or not). That’s why, personally, I prefer the “creative ambiguity” of the “Fine tuning” stage, where part of the job is to look carefully at the units.

Should the process be “faded” over time? If students are able to identify all variables with just highlighting would you still insist that they write out the grid? I can see arguments on both sides for this one…

Thank you for your thoughts.

With regards to step 3 I think you have a valid point but would imagine questions phrased in a way where non-SI units can be used will be targetting grade 7+ at which level the appropriate students should already be confident with the basics and can be given SLOP on applying calculations with non-SI units.

On your second point, it is like a clown on a tightrope. The students need to be secure on process first and can then explore their own methods later. However, I do think listing variables formally is a good habit and important preparation for A-level when they are likely to be juggling a larger number of variables in calculations.

Fair point about the non SI units, but given that they are exactly the sorts of unit they are more likely to encounter outside the classroom, we should be equipping them to deal with them also. I know, limited time and resources force our hand, but just sayin’ …🙂

Love the clown on the tightrope analogy and I agree that enforce a rigid system first before fading is essential. BTW did you read https://emc2andallthat.wordpress.com/2019/01/04/dual-coding-suvat-problems/ It’s an alternative approach that I think works well.

I have been writing my dissertation on this very topic!

I do agree with the vast majority of what you have said.

I think the reason students find it easier to substitute in first is how it is a lot more similar to the type of questions they experience in maths i.e. 4x=12 where they are used to rearranging number. The inverse operation of multiplying by 4 is dividing by 4. Whereas with F=ma the inverse operation of multiplying by a letter the seem to struggle with more / is less logical.

I only hesitate with substituting first and converting later. Although I guess that comes from the potential to gain the substitution mark as if they incorrectly convert then substitute, they would lose the mark?

As for triangles, I’ve seen too many examples of them going wrong and or failing to address formulae with more than three variables.

At the most basic level, if students can solve 4x=12 then they should be able to solve any three-part formula. One method to rule them all as it were.

That is one interesting topic! The concrete mathematical analogy works — when the students are sitting in front of you(!) but seems to evaporate as soon as you’re gone 😦

Would love to read a copy when you are done.

Good luck!

Thanks!

I will send a copy your way.

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Thank you for this blog too! I seem to have just stumbled across a couple of your things and they are great. Having just switched to AQA and come across an exam question with a “random” equation, where some of my students tried (and failed) to force it into a triangle, I felt I had to do more to ditch their inbuilt desire to use triangles, and push “proper” rearrangement more. And this does seem to fit the AQA markschemes really well (although I tend to encourage them to convert units before inserting into the equation). I’ve been using it with year 9 students this week and it seems to have gone well.

Delighted to hear this! Thank you for commenting 🙂