The A Level Chemistry 21 Day Boot Camp started today, and the first topic I felt I needed to cover was calculations – it seems to be the area that most students really worry about. Rather than producing documents or videos to explain how to do each different type of calculation, of which there are many great examples online already, I thought what was needed more was a change to the way many students approach calculations.

As the mathematical demand of A Level chemistry syllabuses has increased over the last few years (and will definitely increase as you move from Year 1 to Year 2 content) I tried to think of the top five ways students could change the way they work so that they build their confidence and avoid common mistakes.

#### 1. Ditch the formula triangles

I feel a bit guilty about this, because I am part of the problem. Only this morning I posted a couple of videos on YouTube aimed at my year nine and ten students, and they were choc full of formula triangles. The irony is, I had never heard of them before I started teaching – algebra was just algebra to me, and luckily I never found it particularly challenging.

Younger students do sometimes find algebraic rearrangements hard, and so I resort to the use of a formula triangle *if they need it to reduce their cognitive load. *If a student is in the first two months of an A Level chemistry course and relying on triangles to rearrange formulae, I am worried. Most of the rest of the course is going to involve algebra with more than three components. So what techniques can students use to help remember the relationships between different chemical quantities?

#### 2. Understand units

By understanding the units used to measure enthalpy changes, concentration of solution and other commonly used quantities, students shouldn’t have to rote learn formulae. The unit mol dm^{-3 }already tells a student how to calculate concentration, so long as they understand the way it is presented (in many ways, the GCSE convention of writing mol/dm^{3} is much more visual, but I always encourage pupils to say the units out loud as much as possible so that the meaning of the word ‘per’ is more ingrained).

It is a shame that most exam boards haven’t adopted the convention of using g mol^{-1} as the unit for molar mass; glossing over it as some sort of unitless quantity does not do any favours to their understanding. Instead, I try to encourage students to think about the meaning of the term molar mass – the problem with abbreviations like M_{r} is that they can quickly divorce students from any sense of reality when performing calculations and they lose sight of what it is they are supposed to be working out. Which brings me easily to the next tip…

#### 3. Estimate your answer

Chemistry can be a pretty abstract subject, and it’s all too easy for students to compartmentalise and never really see the links between real world measurements and the six mark calculation in front of them. But there are a few ways students can sense-check their maths to see whether they have made any common errors or omissions. If they explicitly consider the M_{r} of a substance to be the ‘mass in grams of one mole’ they can more quickly estimate whether a given mass is likely to be more or less than one mole as well as estimating the size of the answer.

Titration calculations are a very important place for students to estimate, since there are often many steps involved and so many potential sources of error. For example, consider the reaction between sodium hydroxide and sulfuric acid. If 2 moles of the base is needed to react with one mole of the acid, and the solutions are equimolar, the volume of base will be double that of the acid. This is a quick way to estimate whether the solution of unknown concentration is more or less than that of the substance it is titrated with.

Percentage mass calculations are also easy to check to see whether they fit in a wider context. If a substance is described as an ‘impure sample’, for example, of calcium carbonate, it would seem foolish to then calculate a percentage of calcium carbonate that is, say, less than 50%. I know I would be sending back a sample of ‘impure gold’ if it turned out to be more than half composed of substances other than gold!

#### 4. Pay attention to significant figures

As students make the transition from GCSE to A Level they often struggle with the distinction between significant figures and decimal places. The easiest way to differentiate is to think of decimal places as something usually set aside for the recording of measurements. If a balance records a mass to two decimal places, then it makes sense to write a mass of ‘1.00 g’. Should we then use this in a calculation to find the number of moles, the answer is likely to be much less than one and then using decimal places does not make sense; instead, we should give our answer to the same number of significant figures as the data we used to calculate it.

If we use more than one piece of data measured to differing numbers of significant figures, we should use the *minimum* number of significant figures in our final answer. The idea of significant figures vs decimal places also leads us to different ways of reducing the percentage error in a measurement – in the example above, the percentage error can be reduced by a factor of ten by using a 3 decimal place balance; but it could also be reduced by simply weighing a larger quantity.

#### 5. Write it all down!

Calculators have come quite a long way since I was at school. It’s great that improved display functions mean that students can clearly see quite detailed calculations on their screens. However, it has maybe led to an increased tendency for students to stop recording anything as they work through a large calculation problem. The other reason students stop writing things down is simply confidence – I often have to work with whiteboards with students for several weeks if they feel they have lost their way, as the fear factor stops them from making any kind of on-paper commitments.

There are so many obvious reasons for writing down calculations as you perform them, that I am surprised my hair hasn’t turned more grey from the number of stubborn students I encounter who still won’t take on board this simple piece of advice. Two students can write completely the wrong answer for a six mark question – and it can be really, really wrong if they miss something out (like a million times smaller than the real answer) – and yet, one student can still obtain five marks and the other obtains zero. The difference, of course, is that the student who wrote down their working only lost one mark because they only made one mistake in the calculation. It was a big impact on the final result, don’t get me wrong – I don’t want them working for NASA – but that’s how the system works.

The truth is, of course, that the student who wrote all their working down was more likely not to make that one mistake anyway. If we take away the jumping through hoops we all feel a little obliged to do for the sake of the final assessment, the fact of the matter is that putting the process down on paper takes it out of your head, leaving you more room in your working memory to figure out the next step *and* to check if your answer makes sense. It’s a win-win situation. I will even let you borrow my pen.

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