This might seem like a really strange thing to talk about – how NOT to do maths. Surely it would be better for me to tell you all about how TO do maths. Well, that’s usually my first choice when I’m teaching – but what’s also really important is recognising incorrect, clumsy or just downright bad maths because sometimes you might not realise that something that you’re doing is wrong, or when you’re reading someone else’s work you might feel that something is wrong but not be able to put your finger on it.

Well I’ve made a few videos that go through some of the mistakes that I regularly come across as a maths tutor during my lessons. Each video is only a few minutes long – I’ve given an example of the mistake(s) and then given a corrected version of the calculation or solution. The videos are not intended to be comprehensive in-depth treatments of each topic – the focus here is intended to be on the error; in future I may make some videos about how to do some of these things correctly in more detail but there’s already a million different videos out there that in a lot of cases I can’t really add anything to what is already there. Rest assured, though, that if I have something to contribute then I will do eventually.

These mistakes are 100% genuine and are ALL things that I come across all the time in my lessons with maths students of all levels. Some of the mistakes are so easy to put right as well but they just don’t get spotted in school! Fortunately (or unfortunately depending on how you look at things) I have eyes like a hawk when it comes to my students’ work and these things do get spotted when I’m sitting next to them.

One thing that I want to be clear on – it is not shameful or embarrassing to make mistakes. You need to make mistakes in order to learn. Some of the mistakes that you make from time-to-time you will feel like kicking yourself when you notice it…BUT…I have been there myself. I continue to make mistakes to this very day and I will continue to make mistakes for the rest of my life. If you see that you are making a mistake – no matter how trivial you think it is – you are not alone; countless others will be making exactly the same mistake. If you see something in these videos and you realise that you’re making that mistake, please don’t feel ashamed. It is simply an opportunity for you to do something about it and put it right – once you’ve got it sorted out then you’ll be able to recognise it much better next time.

Here’s a few examples of the videos that I’ve made

If you want to see more of these videos then visit my Videos page. New videos will be going up fairly regularly so keep an eye out for them. If you have any questions about your maths work then please get in touch with me – if I can help then I will be more than happy to do so. Just ask…

In a video that I made recently about ways to improve your QTS Numeracy I mentioned things like using a range of different resources, using things like apps to help you with your addition and multiplications. Drawing on my personal knowledge that I’ve acquired over the last few years as a professional maths tutor in Leeds and successfully tutoring loads of people for their QTS Numeracy test, here are a few free online resources that I think are really useful for those of you out there preparing for the numeracy test. Remember that there are no shortcuts when it comes to learning what you need to know for the QTS – it all comes down to how much you practice and the quality of the practice.

Online Arithmetic Drill – This is a great little tool for improving your multiplications, additions, subtractions and divisions – there really is no excuse for not knowing your multiplications when you’re going in for the QTS Numeracy test! You set what you want to do whether it’s just multiplications that you want to practice or a combination of additions, subtractions etc. set which numbers you want to be asked to multiply, set the time that you want to practice for and away you go – do as many as you can in the time that you have. I personally have this bookmarked on my computer and is one of my personal favourites! My personal best is 107 multiplications in 120 seconds up to 12×12. Try to do 15 to 20 minutes of practice a day for a couple of weeks and you’ll see a huge difference.

Worksheet Generator 1 – This site can produce a never-ending supply of worksheets (dynamically generated) for you covering additions, multiplications, simplifying fractions, addition and multiplication of fractions, rounding, percentages …. the list goes on. Not all of the stuff that’s available will be relevant to the QTS Numeracy test as the site is not designed with QTS specifically in mind but there is some good stuff there that you can really take advantage of.

Worksheet Generator 2 – Another brilliant site for worksheets. This looks like it could be aimed primarily at American schoolchildren so is, again, not specifically designed for QTS. BUT….there are just tons of topics covered. I think the ones that would be most useful for QTS Numeracy would be the sections titled

  • Elementary Math
  • Fractions
  • Decimals
  • Ratio, proportion and percent

Just have a play around with the settings until you get used to it – definitely a recommended site


I sometimes get asked by my students if I can do some worksheets for them to practice with – I have done this in the past but if I’m completely honest with you there is really no need for me to do so. I don’t want to sound like I’m just trying to find a way to get out of doing a bit of work, but using these websites you can generate hundreds, if not thousands or even tens of thousands, of questions in the time that it would take me to write out a mere twenty questions and that’s not including the tea-break that I’d probably take half way through and then the time that you would have to wait for me to email it through to you! How can I compete with a computer program that is specifically designed to mass produce questions! And what’s more is all of these worksheets are free, created at the click of a mouse and often have the option for the answers to be generated as well. Maybe it would be better for me to stick to what I’m good at which is the tutoring!



Here is my latest video which is giving my top tips and advice for A Level Maths and Further Maths students who are looking to do one or more of the Sixth Term Extension Papers (or STEP).

These exams are ones that really get people worried – don’t get me wrong, they are tough exams – but they’re not impossible. You just have to prepare well and not get overly nervous about them. Easier said than done I suppose. Well, as a private maths tutor over the last several years I’ve tutored many people for these exams (mostly STEP I and STEP II but occasionally for STEP III) so I’ve come across a lot of things that work and a lot of things that don’t work when preparing to take the exams.

This video will hopefully give you a nudge in the right direction when it comes to getting ready for the STEP exams. It’s a bit longer than I had originally planned but I think it was important for me to be quite thorough so have a bit of patience because there might be something that you can take away that really helps you – after all I want to see you succeed as much as anyone!

STEP tuition is a favourite of mine – I love tutoring for these exams because even now the exams are a good challenge for me and there’s always something new to learn. Some of the questions are just so imaginative and really test your knowledge and ability to think carefully through unfamiliar problems.

If you are preparing for the STEP exams then I wish you the best of luck. Please feel free to send me an email or to get in touch with me if you have any questions about the exam – I’ll be glad to help if I can.

Here’s the next video in my Ten Ways series – this video is for those of you out there looking for ways to improve your QTS Numeracy. I know that there are lots of people out there who are looking to do their QTS Numeracy test who feel that they’re going to have a rough ride. Well the good news is that as a professional maths tutor in Leeds over the last several years I have done loooooads of tuition for QTS Numeracy so I’ve got a few tips here in this video that might help. It is quite a long video – I didn’t actually expect it to be as long as it was but at least you’ll be getting your money’s worth!

The video, as with my GCSE Maths and A Level Maths videos, is not just giving a list of topics to revise for the test although it does mention a couple of topics that might be particularly useful. I didn’t want to make a video just giving all of the topics to revise because I think there’s already a ton of websites and other videos out there already doing just that. What I did want to do was to bring something unique and new; to share my personal experiences, observations and advice that I’ve learned over the last half a decade or so – no-one else can give you that.

I hope that this helps you out a bit – I’d love to hear any of your comments; your own advice that you can pass on to others preparing for the test and your own personal experiences of the test itself.

So here is my first monthly review video – I decided to make this video just to share with you what’s been going on over the last few weeks in my life as a professional maths tutor. Sometimes I get some really interesting questions from my students during lessons and I thought that it would be a good idea to share some of those questions and their answers with you.

In this video, for example, I discuss weak and strong forms of proof by induction – usually A Level Further Maths students will only really get familiar with weak induction but strong induction is a lifesaver in some cases where weak induction just wouldn’t cut it. I also talk about functions as I was asked some really good questions about functions in one of my lessons when I was doing transformations of graphs with a GCSE student of mine.

I made a couple of videos over the last month – one was about how to improve your GCSE Maths and the other was how to improve your A Level Maths. There will be another couple of videos over the next month so keep an eye out for them.

Other things that I touch on are a couple of books that I read over the last month. The first was Alan Sugar’s Autobiography – I know, I know, it’s not exactly a maths book but I read it anyway. I also read Surely You’re Joking Mr. Feynman by Richard Feynman, which is another autobiography, and I started reading, or should I say working through, The Works of Archimedes (that’s the famous Greek scientist Archimedes).

And lastly I introduce my new friend the Soroban (Japanese abacus) which I’ve started to learn to use. I’ve only been learning for a weeks or so but things are going in the right direction. I’ve found a link that is really useful for learning – it doesn’t tell you how to use a soroban but it throws up random addition problems so that you have to try to figure them out on the soroban; it’s something called Flash Anzan and has been really useful so far in getting me used to the various combinations that you need to know to use the soroban.