Today I’m answering a question about Maths exams - in fact any kind of exam questions where your teen has to do calculations within time limits.
This is one you might want a pen and paper for, or want to have your teen listen in on too.
So grab one (or ideally both!) of those and get ready to take note of:
the most common ways students lose marks in Maths exams
my 5 tips to make sure that never happens for your teen again. (Get your free resource below!)
You’re listening to the Parents of Hardworking Teens Podcast, episode 17. Today I’m answering a question about Maths exams - in fact any kind of exam questions where your teen has to do calculations within time limits. This is one you might want a pen and paper for, or want to have your teen listen in on too. So grab one or both of those and let’s do this.
Good morning, good afternoon, good evening VIPs!
Wherever you are and whenever you’re listening to this I hope you’re super-well. It’s early afternoon here as I’m recording this and after a grey morning it’s turned into a gorgeous day. We’re just getting into spring here in Aus and it’s felt like a long and wet and cold winter this year. Now, granted this is relative. Very relative. Because everything here is built to stay cool, so we feel cold with anything below 20 degrees - well I do at least. I’m most definitely acclimatised. And we are definitely spoilt here particularly on the Sunshine Coast - even in winter we usually get dry, blue-sky days where it still gets into the low 20’s in winter. It’s certainly not rocket science that a sun-worshipper and cold-hater like me ended up here. But I know that all of you in the UK along with the rest of Europe have had a super-hot summer - and all the buildings there are generally built to stay warm. So, anyway, coming off the back of a wet summer - and predictions of another one ahead - and what has felt like a long winter, I’m just really loving the sunshine right now.
Now, from sunshine to Maths. I’m not going to try and come up with a neat segue here, I’m just going to dive in, because today we’re talking Maths exams and actually, this is going to cover tackling any type of calculation-based questions. It could be in Science, Economics, Geography, anything where they’re having to do calculations of some kind.
Because amongst all the great questions I’ve been getting from you all for our 3 Q&A episodes, I’ve had a couple that have actually ended up leading me to do a full episode on things you’ve asked about and this is one of them.
So, this question is from Joyce whose grandson is studying Maths Methods - which is the equivalent of A-Level Maths or Maths Analysis and Approaches in the IB.
And Joyce said:
“He just doesn’t get the marks that indicate the knowledge he has. He’s able to answer all the questions that the teacher asks during the lesson but not so confidently or quickly or correctly during exams.”
- Now just quickly - that part - I know is a factor that’s a struggle for many students in these higher levels of Maths. They can do the questions when time isn’t limited. But doing it under time pressure both adds to the stress and panic which impacts our ability to think straight, but also really does mean we simply need to work through faster. And I’ve drifted into ‘we’ here because time was definitely an issue for me in A-Level Maths. But on reflection I know that it was because I’d make small slips along the way, and then have to spend more time finding where they were and re-doing calculations when I got a solution that clearly wasn’t right.
And that was at least in part because I wasn’t thinking straight because I was panicking about the time pressure! - Urgh!
Okay, back to Joyce. She goes on to say:
“In his recent exam there were several questions which involved more than one maths concept in order to get to the answer. He seems to struggle with these. He might start off well but loses his thought process after applying one concept. Thinks he’s arrived at the answer then or gives up along the way.
Do you have a structure or any tips you could share so we can get a structured approach for answering these sorts of questions?”.
Well Joyce, you know I love structure and steps.
So let’s get into this and I want to address this with some of the most common ways I see students losing marks - which yes, include some of the issues that Joyce mentioned.
And, like I said at the start, this could be for any types of questions that require calculations, so where I say Maths, you can also substitute in there Physics, Chemistray or whatever applies to your teen.
And - although the question related to Maths Methods, these absolutely also apply to the lower year groups or the lower levels of Maths courses too. Basically,, stay tuned if your teen is ever having to do any calculations, especially in any of their exams!
Plus, to sweeten the pot a little bit for you, I’ve also taken the mistakes, tips and strategies I’m going to share with you here and put them into a really handy one-pager resource.
So, let’s dive into the 4 most common ways students lose out on marks in Maths exams – and some specific tips, steps and must-do’s to make sure your teen DOESN’T.
Because here’s the thing. Maths questions are sometimes straightforward, like solve this equation.
But, they can also can be a lot more complex and tricky, with layers of info and worded requirements.
And it is often these worded parts of maths exams that trip students up or catch them out. It’s also where there are usually some simple yet often overlooked extra steps or hints on getting more marks they could - and should - be getting, with the knowledge they already have and the revision or practise they’ve already done.
What I mean by that is that they’ve done the hard work, they know the concept or methods, or as Joyce said, conceptS - more than one - that they need to use and they do know how to apply them correctly - AND they very often do it successfully in class or homework. BUT for various reasons, when it comes to exams, tests or more pressurised situations, they make little slips or simple mistakes that cost them marks (and cause frustration when they get their paper handed back).
So, here’s Common Maths exam Mistake no. 1
Stopping too early.
This is where those multiple steps or stages of working out a solution are required and so at some point along the way, your teen gets a solution. Not THE final solution but A solution, they complete a step. But - likely because it’s taken them while just to get to that point, they think they’ve got to the answer. And they stop there and are already rushing into the next question - because, yes, that time pressure.
So here’s what they can do instead. As they figure out or decide - at the very start - what they need to do, they jot down the actual steps down on their paper. On the actual answer space on the exam paper, not on the rough working sheet, cos they’ll likely forget to look back at that too.
So it would be - Find this, then that, then add them.
Sometimes, if they state this clearly, that can even gain them marks if they don’t eventually get to completing it. Students would be surprised at what you can get marks for in Maths questions worth multiple marks. For example, just stating the correct trig ratio or labelling up the diagram, without actually then working out any calculations will often earn them a mark.
And an added tip here is to - as well as stating the steps for themselves - at the bottom of the page, write out a line with the answer statement a space for the final figure and with the stated units. So they have a constant reminder of what they finally need to get to. For example, this could be: ‘final speed = gap for answer and the units: metres per second’ or whatever, so they don’t stop too early at just having found, say, the distance, for example.
So - they state the steps as soon as they’ve decided what they are - and bonus - write in at the bottom of the answer space what format the answer should be in. And I’ve got lots more to say about stating final answers.
For example here in Common Mistake no. 2.
Which is rounding too early.
If students round their answers at EACH STEP or STAGE of a multi-step calculation, there is a fair chance that their final result will be too far from the accepted range in the mark scheme for full marks. Now, if they try to write everything out in full at every step, and have to type it all back into the calculator at every step, then they’re more prone to making errors with those, so what they really need to do is to get really good at using either the memory button, the ‘Previous Answer’ button or inserting brackets on their calculator so they avoid having to do this.
Getting really well practiced at using their calculator accurately and efficiently is a skill that is definitely worth putting time into and doing that will mean that they keep the full and accurate numerical value at each step. They only round in whatever way is required at the very last step.
Now, another error that’s often made by students during their calculations is not noticing or converting different units within a question. This is Common Maths Mistake number 3.
For any calculation of any kind, all figures or data being used must be in the same units. It’s easy to miss small but important details like this in a question when under exam pressure, but if a question has measurements of both km’s and metres, or minutes and seconds, one or other part needs to be converted.
And here’s my tip on this: Check what units the final answer needs to be given in, and unless it’s clearly easier to work things out in the other unit and convert at the end, choose that final unit to convert the others into. So, if you’ve got information provided and some is in metres and some is in kilometres, and it doesn’t really matter which one you convert them all to, then look at what the final answer needs to be given as and use that as your core unit to do all your working with. That way it’s one less thing to have to convert at the end and one less step that may well be forgotten at the end.
Which brings us nicely to…
Common Maths Exam Mistake No. 4 - students not stating their final answer in the way the question demands. For example the question might state that they give their answer in cm squared but they’ve given it in mm squared. Or they’ve given an answer in minutes, when it should be converted to hours. This usually happens because they’re so focused on GETTING the answer, that they then forget that final conversion. I also see it a lot where students just leave it as the number. They have the figure 2.8 but they don’t actually state it as an answer. They need to state: Therefore the length of the ladder is 2.8metres or whatever it is. Just leaving a number with no units and no reference to the scenario in the question may well leave them short of full marks even if they have the calculation correct.
And last but not least - the fifth most Common mistake in Maths exams… Similar to mistake number three, in that it is also often forgotten in the final stage of the answer, it’s not giving the answer to the correct degree of precision.
Unless otherwise stated, most exam boards say that students should give an answer to 2 decimal places, however it’s quite common for the level of precision to be stated in the question. For example to the nearest tenth, or to the nearest thousand. Or even, one that sounds more simple but catches a lot of students out, how many items. Like it might ask ‘how many tins of paint are needed to paint the wall?’ and if the answer is 5.2, even we’d normally round down to 5 in numbers, because of the scenario, the painter will actually need 6 tins. Because 5 won’t be enough. They’d have to buy the 6th tin to actually be able to complete the job because 5.2 tins are required.
But even when the questions aren’t sneaky like that, even when they are just numerical solutions, when students have gotten caught up in the process of working out, especially in a multi-step problem, it’s easy to either gloss over or forget about an instruction beyond the calculation itself.
So, similar to Mistake number one where we can put the final step or completed statement at the bottom of the page to help prevent these mistakes, a tip I give to students is to write out that statement with the precision stated as well. For example it might just be X equals ‘blank’ to 3 significant figures, or to the nearest second - actually write that from the question at the bottom before you start as a place to put your final answer and as a way to remind yourself.
Now each of these things might sound like small things on their own. But each of these mistakes are often responsible for students dropping down a full mark or grade in an exam. Because it only takes one mark to drop or climb up a full grade overall if your teen is hovering around a grade boundary, but also, a few of these small slips added together can actually make quite a significant difference.
Either they miss a chunk of a question, like Joyce mentioned by stopping too early, or a mark or half mark here or there but done a few times on one paper all add up.
You might also be thinking that these sorts of little details sound harsh to mark students down on. But this is the reality of mark schemes. And they aren’t changing any time soon, so we need to know exactly how they do work in order to play - and win - at this game.
So have your teen check and double check in their next Maths exam or any type of test that involves calculations:
That they’re keeping all figures in full throughout all steps of a calculation and only rounding at the end; that they’re being careful of units WITHIN a question and whether any conversions need to take place before the calculation is started; and then again at the very end, and then also being careful to round to the degree of precision required and state their final answer in relation to the scenario or context of the question.
Like I said, I’ve pulled out these particular mistakes and my tips to overcome them from my 18 Tips for Tackling Calculation-Based Questions resource. If your teen is in Next Level Coaching or previously came to or has access to the Exam Mastery Workshop then they’ll have the whole resource.
But I’ve made this one-pager podcast resource so that everyone can grab these 5 for free. Just go to www.rocksolidstudy.com/17 and then print and have your teen stick them up for constant reference during exam prep or revision, or even better - go through and pick out the top one or two they really need to be aware of or focus hard on, cut them out and stick them to their book or their forehead - just joking - but do whatever needs to be done until these small but mighty tips, systems and strategies become routine and habit.
We don’t actually want your teen having to think about these on top of everything they’re having to think through and do in the actual exam. We want them to become automatic steps. That’s why I have Next Level Coaching, so that your teen can take all the skills and strategies from the 10WGT and turn them into habits, doing them accurately and automatically and having them pay off every time - but without having to always consciously think about them.
So Joyce, thank you so much for your questions, I hope that this has been helpful and I really hope that it’s helpful to all of you podcast listeners and your teens. Remember to go grab that one-pager of tips - www.rocksolidstudy.com/17 - AND if you have a question you’d like me to answer on a future episode of the podcast, send it in an email with the subject line: Podcast question.
Have a brilliant week everyone, I really appreciate you hanging out with me today, I hope that the sun is shining for you wherever you are - I’m off for a dog walk now, poor Bon didn’t get her walk this morning as today did not start off so sunny! But I can’t wait to be back here with you again for another episode next week and I’ll see you then!