FIFA and Really Challenging GCSE Physics Calculations

‘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:

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‘.

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

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.

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

Keep Calm and Draw Free Body Force Diagrams (Part 2)

You can read Part 1 which introduces the idea of free body force diagrams here.

Essentially the technique we will use is as follows:

  1. Draw a situation diagram with NO FORCE ARROWS.
  2. ‘Now let’s look at the forces acting on just object 1’ and draw a separate free body diagram (i.e. a diagram showing just object 1 and the forces acting on it)
  3. Repeat step 2 for some or all of the other objects at your discretion.
  4. (Optional) Link all the diagrams with dotted lines to emphasise that they are facets of a more complex, nuanced whole

The Wheel Thing

Let’s consider a car travelling at a constant velocity of 20 miles per hour.

NOT a force diagram. (Note: whilst force arrows on situation diagrams should be discouraged, there is no equivalent argument for speed arrows)

’20 m.p.h.’ is such an uncivilised unit so let’s use the FIFA system to change it into more civilised scientific S.I. units:

NOT a force diagram! (Note: it is fine to draw speed/velocity/acceleration arrows on a situation diagram, but not force arrows.)

Note that point A on the car tyre is moving at 8.9 m/s due to the rotation of the wheel, as well as moving at 8.9 m/s with the rest of the car. This means that point A is moving at 8.9 + 8.9 = 17.8 m/s relative to the ground.

More strangely, point B on the car tyre is moving backwards at speed of 8.9 m/s due to the rotation of the wheel, as well as moving forwards at 8.9 m/s with the rest of the car. Point B is therefore momentarily stationary with respect to the ground.

The tyres can therefore ‘grip’ the road surface because the contact points on each tyre are stationary with respect to the road surface for the moment that they are in position B. If this was not the case, then the car would be difficult to control as it would be in a skid.

(Apologies for emphasising this point — I personally find it incredibly counterintuitive! Who says wheels are not technologically advanced!)

Forces on a tyre

Situation diagram (note: no force arrows) and free body diagrams for road and tyre. Note also different style of arrow for speed and force.

Assuming the car in the diagram is a four wheel drive, the total force driving it forward would be 4 x 330 N = 1320 N. Since it is travelling at a constant speed, this means that there is zero resultant force (or total force). We can therefore infer that the total resistive force acting on the car is 1320 N.

It is can also be slightly disconcerting that the force driving the car forward is a frictional force because we usually speak of frictional forces having a tendency to ‘oppose motion’.

And so they are in this case also. The movement they are opposing is the relative motion between the tyre surface and the road. Reduce the frictional force between the road with oil or mud, and the tyre would not ‘lock’ on the surface and instead would ‘spin’ in place. It’s worth bearing in mind (and communicating to students) that the tread pattern on the tyre is designed to maximise the frictional force between the tyre surface and the road

And then a step to the right…

It’s just a jump to the left

And then a step to the right

The Time Warp, Rocky Horror Picture Show
Situation diagram for a person taking a step to the right; and free body diagrams for the person and the floor

We can see how important friction is for taking a step forward in the above diagrams. Again, it is worth pointing out to students how much effort goes into designing the ‘tread’ on certain types of footwear so as to maximise the frictional force. On climbing boots, the ‘tread’ extends on to the upper surface of the boot for that very reason.

Amazon.com | La Sportiva Men's TC Pro Climbing Shoe | Climbing
A climbing boot

One step beyond

Let’s apply a similar analysis to the case of a person stepping off a boat that happens not be tied to the mooring.

Situation diagram for a person stepping off an unmoored boat; and free body force diagrams for the person and the boat. Note different style of arrow for forces and acceleration.

The person pushes back on the boat (gripping the boat with friction as above). By Newton’s Third Law, this generates an equal an opposite force on the boat. There is no horizontal force to the right due to the tension in the rope, since there is no rope(!) This means that there is a resultant force on the boat to the left so the boat accelerates to the left.

The forces on the person and the boat will be equal in magnitude, but the acceleration will depend on the mass of each object from F = ma.

Since the boat (e.g. a rowing boat) is likely to have a smaller mass than the person, its acceleration to the left will be higher in magnitude than the acceleration of the person to the right — which will lead to the unfortunate consequence shown below.

The effect of stepping off an unmoored boat

The acceleration of the person and the boat happens only when the person and boat are in contact with each other, since this is the only time when there will be a resultant force in the horizontal direction.

Note that although force arrows on a situation diagram should be discouraged for the sake of clarity, there is an argument for drawing velocity and acceleration arrows on the situation diagram as a form of dual coding. Further details can be found here, and an explanation of why acceleration is shown as a double headed arrow.

The velocity to the left built up by the boat in this short instant will be greater than the velocity to the right built up by the person, because the acceleration of the boat is greater, as argued above.

The outcome, of course, is that the person falls in the water, which has been the subject of countless You’ve Been Framed clips.

Next post…

In the next post, I will try to move beyond horizontal forces and take account of the normal reaction force when an object rests on both horizontal surfaces and inclined surfaces.

Fear of Forces? Keep Calm and Draw Free Body Diagrams

Why do so many students hold pernicious and persistent misconceptions about forces?

Partly, I think, because of the apparent clash between our intuitive, gut-level knowledge of real world physics. For example, a typical student might find the statement ‘If I push this box, it will stop moving shortly after I stop pushing because force is needed to move things‘ entirely unobjectionable; whilst in the theoretical, rarefied world of the physicist the statement ‘The box will keep moving at a constant velocity after I stop pushing it, unless it is acted on by a resultant force such as friction‘ would get a tick whereas the former would get a big angry X and and a darkly muttered comment about ‘bloody Aristotleans.’

After all, ‘pernicious’ is in the eye of the beholder. Physics teachers have to remember that they suffer mightily under the ‘curse of knowledge’ and have forgotten what it’s like to look at the world through anything than the lens of Newtonian mechanics.

We learn about the world through the power of example. Human beings are ‘inference engines’: we strive to make sense of the world by constructing general rules based on the examples presented to us.

Many of the examples of forces in action presented to students are in the form of force diagrams; and in my experience, all too many force diagrams add to students’ confusion.

A bad force diagram

Force Diagram 1: version 1 (really bad)

Over the years, I have seen many versions of this diagram. To my own chagrin, I must admit that I, personally, have drawn versions of this diagram in the past. But I now recognise it has one major, irredeemable flaw: the arrows are drawn hanging in mid-air.

OK, let’s address this. Is this better?

Force Diagram 1: version 2 (still bad)

No, it isn’t because it is still unclear which forces are acting on which object. Is the blue 75 N arrow the person pushing the cart forward or the cart pulling the person forward? Is the red 75 N arrow the cart pushing back on the person or the person pulling back on the cart?

From both versions of this diagram shown above: we simply cannot tell.

As a consequence, I think the explanatory value of this diagram is limited.

Free Body Diagrams to the Rescue!

A free body diagram is simply one where we consider the forces on each object in the situation in turn.

Force Diagram 1: version 3 (much better!)

We begin with a situation diagram. This shows the relationship between the objects we are considering. Next, we draw a free body diagram for each object; that is, we draw each object involved and consider the forces acting on it.

From version 3 of Force Diagram 1, we can see that it was an attempt to illustrate Newton’s Third Law i.e. that if body A exerts a force on body B then body B exerts an equal and opposite force on body A.

Another bad force diagram

Force Diagram 2: version 1 (very bad)

This is a bad force diagram because it is unclear which forces are acting on the cart and which are acting on the person. Apart from a very general ‘Well, 50 N minus 50 N means zero resultant force so zero acceleration’, there is not a lot of information that can be extracted from this diagram.

Also, the most likely mechanism to produce the red retarding force of 50 N is friction between the wheels of the cart and the ground (and note that since the cart is being pushed by an external body and the wheels are not powered like those of a car, the frictional force opposes the motion). Showing this force acting on the handle of the cart is not helpful, in my opinion.

Free body diagrams to the rescue (again)!

The Newton 3 pairs are colour coded. For example, the orange 50 N forward force on the person (object A) is produced as a direct result of Newton’s 3rd Law because the person’s foot is using friction to grip the floor surface (object B) and push backwards on it (the orange arrow in the bottom diagram).

This diagram shows a complete free body diagram body analysis for all three objects (cart, person, floor) involved in this simple interaction.

I’m not suggesting that all three free body diagrams always need to be discussed. For example, at KS3 the discussion might be limited at the teacher’s discretion to the top ‘Forces on Cart’ diagram as an example of Newton’s First Law in action. Or equally, the teacher may wish to extend the analysis to include the second and third diagrams, depending on their own judgement of their students’ understanding. The Key Stage ticks and crosses on the diagram are indicative suggestions only.

At KS3 and KS4, there is not a pressing need to explicitly label this technique as ‘free body force diagrams’. Instead, what I suggest (perhaps after drawing the situation diagram without any force arrows on it) is the simple statement that ‘OK, let’s look at the forces acting on just the cart’ before drawing the top diagram. Further diagrams can be introduced with a similar statements such as ‘Next, let’s look at the forces acting on just the person’ and so on. Linking the diagrams with dotted lines as shown is, I think, useful in not losing sight of the fact that we are dealing piecemeal with a complex and nuanced whole.

Conclusion

The free body force diagram technique (whether or not the teacher decides to explicitly call it that) offers a useful tool that will allow us all to (fingers crossed!) draw better force diagrams.

  1. Draw a situation diagram with NO FORCE ARROWS.
  2. ‘Now let’s look at the forces acting on just object 1’ and draw a separate free body diagram (i.e. a diagram showing just object 1 and the forces acting on it)
  3. Repeat step 2 for some or all of the other objects at your discretion.
  4. (Optional) Link all the diagrams with dotted lines to emphasise that they are facets of a more complex, nuanced whole

In the next post, I hope to show how the technique can be used to explain common problems such as how a car tyre interacts with the ground to drive a car forward.

You can read Part 2 here.

FIFA for the GCSE Physics calculation win

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:

  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]

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

Screenshot 2019-10-27 at 16.04.29.png

We add the FIFA rubric:

Screenshot 2019-10-27 at 16.13.00.png

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.

Screenshot 2019-10-27 at 17.55.45.png

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

Screenshot 2019-10-27 at 18.01.07.png

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.

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.

Screenshot 2019-10-27 at 16.58.23.png