How to pass numerical reasoning tests: mental maths

At Mapped, we get asked a lot for tips on how to do well at numerical reasoning tests. Some people find these particularly stressful, and understandably they want to be as prepared as possible.

We spent a long time analysing numerical reasoning tests trying to make something better; the results being Mapped (read about how to predict high performer). Different providers vary, but no matter which one you are being assessed through there is one thing you can do which will improve your performance; improve your mental maths.

But I can use a calculator?

Well, actually, on some you can’t; regardless, nearly every numerical reasoning assessment creates a proportion of its challenge by limiting your time, and most people lose marks by silly mistakes. The people who seem to have a real edge here are those who are competent at mental maths, even when calculators are allowed.

 

Some advantages to improving mental maths:

  1. You will save precious seconds not inputting numbers into calculators and scrawling down workings. All those extra seconds add up to minutes.
  2. Even if you are not able to skip the calculator entirely, being able to quickly check that your answer is in the right ballpark will prevent silly mistakes, and give you the confidence to move on quickly.
  3. If you are good at rapid mental maths, your general processing speed will get a better, minimising the 5/10 seconds of brain freeze when you look at a new table of information or question and are trying to work out what is going on.
  4. Improving your mental computation will improve your numerical reasoning more broadly.[1]

That strong mental computation is useful may not be surprising, but what you may find reassuring is how quickly you can improve; even a couple of weeks of practice will drastically improve most people’s performance and confidence.

Why is that? For the same reason that the first month of exercise post a long sedentary period has a big effect on our fitness; because we are starting off at a very low baseline! Mental maths is a muscle, strengthened by practice.

This is partly because of mobile phones being ever-present calculators. But, in fairness, most university degrees do not use that particular part of your brain much. You have either been writing essays or have moved onto the more complex & abstract parts of mathematics leaving the humble mental calculation far behind (many a pure maths graduate has struggled on these comparatively simple tests for this very reason).

 

So, how can you quickly improve your mental math?

  1. Play Games – Play mental maths games on your phone instead of Candy Crush. There are some great ones out there. My favourite is ‘Mental Math Master’ by 5daysweekend on Android & ‘Mental Maths Exercise’ by Ramon Dormans on iPhone. If you find those a bit tough/boring you can find lots of others. You will be pleasantly surprised at how quickly you get better with just 5-10 minutes a day.
  2. Learn some tricks – There are some great tricks and shortcuts you can learn. The book ‘Secrets of Mental Maths’ by Arthur Benjamin will make you look like some kind of genius.

To give an early example of a trick in it when we were young we were almost always taught to add right to left

So with 5342 + 2152, you start with the single digits then move onto the tens, then hundreds then thousands. If a number comes to more than 9, you carry it over to the next column.

Try doing it in your head and you might get a bit lost. You are going backwards to how you have to pronounce it or write it down after all. Not to mention, if you are estimating, we are starting with the least important numbers (the smallest ones).

Instead, if you’re doing a mental calculation, try going from left to right. So for 5342 + 2152,  start with the thousands (5000+2000 = 7000), then add the hundreds (300 + 100 = 400), then the tens (40+50 = 90), and lastly the singles (2 + 2 = 4). Then you just have 7000 + 400 + 90 + 4 = 7494.  It almost doesn’t matter how long the number is. It’s slightly more tricky when a number carries over, but not much. Try the below using that method:

52 + 44 =

13 + 17 =

234 + 123 =

550 +231 =

114 + 569 =

34,124 + 16,843 =

There are loads of tricks like this which will make your life a lot easier, even for much more difficult stuff.

  1. Re-learn the basics – If you passed your GCSE maths even by the skin of your teeth, chances are you once knew how to calculate percentages, ratios, averages, use fractions and work out probabilities. If you are fresh out of a non-numerical degree then you may have forgotten, and that is absolutely fine, but just take the time to remind yourself. If you could do it when you were 16 you can certainly do it now, and even if you struggled at the time you might find it easier now as an adult.
  2. Do it in life – A very accurate summary:

 

It is correct. We won, well done us. Sadly now, as a result, we have largely got bad at mental maths. Instead of reaching for the phone challenge yourself a little every day. Divide the bill in your head. Try and work out how much your groceries will cost before you get to the counter all these little things help and will make you feel great.

 

Hopefully, that helps in some way. There is, of course, much more to doing well at these assessments, but this is always a good start.

 

 

[1] https://www.tandfonline.com/doi/full/10.1080/2331186X.2016.1212683