Mental calculation practice
 

Hello, I have searched around the forums but I haven´t found something that could answer my question.

I wonder if there is any way to practice your mental calculation skills to the standard required on military and airline aptitude tests. I have searched a bit on the web but I can´t find anything that actually teaches techniques.

Cheers!

Learn your times tables off by heart up to at least 12, play darts, work behind a bar and tot up your supermarket shop as you go round with the trolley.

And I'm not being facetious. It works - constant practice.

The main tricks are a) approximating numbers; rounding up or down to get a feeling of the magnitude of the answer; b) splitting the sum into several parts and c) did I say learn your times tables?

Anything multiplied by 5 is the same as multiplying by 10 (ie add a 0 on the end) and dividing by 2 (ie halving).

Then start multiplying 2 digit numbers by other 2 digit numbers in your head, i.e. 27 times 43 is 20 x 40 plus 7 x 40 plus 20 x 3 plus 3 x 7 = 800+280+60+21. The move onto 3 digit numbers.

When you can do those, a simple 1 in 60 rule will be a walk in the park.

Cheers

Whirls

As WG says, times tables are a massive part of it.

The best thing is to learn the times tables up to 12 (6 being the most important as a pilot), and then use this as a basis for other multiplications.

Another way to do the 27 x 43 would be to split it up into easier full multiplications:

First, the 40 x 27:

4 x 27 = (4 x 20) + (4 x 7) = 80 + 28 = 108

therefore 40 x 27 = 10 x (4 x 27) = 10 x 108 = 1080 (A)

Then the 3 x 27:

3 x 27 = (3 x 20) + (3 x 7) = 60 + 21 = 81 (B)

And using A and B above we get 27 x 43 = 1080 + 81 = 1161

This might look a bit confusing, and it might not work for you, but all that has been done is the problem has been broken down into smaller easier ones. This method does require you have a good memory!

Something as simple as swapping the numbers around can make it easier to work out and save you a couple of seconds.

Practice is the major thing, and breaking complex problems down into simpler ones makes it easier. Every time you would use a calculator, don't. Do it mentally first and then check it if you need to.

4015

whirlygig has it spot on with the Constant Practice..

you will soon find short cuts that suit you. With my lad we practice Time/Speed/Distance calculations if we are on the road for any length of time.

ie i'm at 70mph, it's 12 miles to the services, what time will we get there? sort of thing. Do it yourself in your head when you are driving an dcheck go wclose you are.

remember that most nav is done (or was in my day) on 6minute fixes...easy as this is 1/10th of an hour. Keep it simple.

Getting a feel for the order of things is very important, especially if you get the answer right but are a factor of 10 or 100 out:ok:

as for the 27 x 43 calculation..keep it simple (first off the answer should be "about" 1200 from ( 30 x 40) - so that is the order of the answer sorted.

Next find the short-cut you prefer, for me i'd go

27 x 43 = (30 x 43) -(3 x 43)

easy to work out what 30 x 43 is , and no need to work out again what 3 x 43 is (in essence you have already done that) and you get 1290 - 129 which is the 1161 answer ( a quick check on order and we are sorted)


halving numbers and the like works too. For some a 2 digit by 2 digit multiplication is a struggle (mentally you have to store many sub-answers and then recall them) and it is this storing and recollection that leads to errors and brain farts. sooooooooooo

anyone can work out 3 x 43 in a flash (129 - just in case you are struggling);)

and i'm fair safe to say that 9 x 129 wouldn't be too hard either.

all this is doing is breaking the double digit multiplication (27 x 43) into a couple of easier to manage chunks ;(3 x 43)x9

some folk find subtraction a doddle, others prefer division or multiplication - find your forte and try to stick to it.

oh...and top tip, if you find you are working something out at college/work and are just about to reach for a calculator then don't...at least have a go at working it out in your head first :ok:

now does anyone remember how to use log tables? :E

Mental calculation skills are able to be executed by people who were educated in the 1960s and 1970s, like I wuz innit.

If I ask my ATPL students to multiply the square root of 640 by ten they all try to use a calculator - and then get it wrong.....!!!!!

Sometimes they will use the Japanese plastic box to derive minus three multiplied by minus three.

God help aviation :mad::mad::mad::mad:

Log tables and maths WITHOUT a calculator - those were the days!
At least we could do numbers in our heads, don't have to reach for a calculator to work out 10% of 200.

Joking apart, as an ATPL instructor I find this is THE weakest link for most students. Regretfully it is a sad reflection on the English (lack of) education system and exams that are now little short of a joke.

As stated below go and work in shop/bar you'll soon pick up some essential key skills. One of my best students at numbers used to work in a bazaar in Algeria.

Whirlygig is absolutely spot on (especially with the darts)!

If you have a smartphone, (iphone, etc), there are some really good mental maths aps that you can practice whenever you have a spare few minutes

Fook ... that's quite hard to do in yer head with any accuracy - about 250. However, the square root of 6400 times ten is easy = 800.

As has been demonstrated, there are various way of splitting down arithmetical problems and you need to find whatever suits you.

When I was a real maths geek (as opposed to ? some might say), I liked to see if I could multiple a random three-digit number by another 3 digit number in my head before the traffic lights changed.

And who says accountants aren't exciting?

Cheers

Whirls

You and I seem to be in the same profession.

Most of my students are .....:mad:....useless.

The worst aspect is that they think they will be able to be aircraft commanders and get an ATPL by "databasing".

Well, they probably can, but a job interview is something else.

Hello young person.

Tell me now - why are vortex generators no longer used on jet transports to reduce shock-induced flow separation.

Sadly in school, its all about going through the syllabus quickly and less empthasis on Basic Maths and mental calculations.

If somebody has been using a calculator for so long and all of a sudden you take it away, it will take time to adapt, just like learning a new langauge.

A lot of people who keep knocking the younger generations, about maths, is a little bit harsh.

I find the older gen who are excellent at Mental Maths, really struggle when they have to use a computer, they practically crumble when they have to do online course and Electronic Tech Log, Electronic Perf etc.

Our company are talking about introducing Ipads, but the older generations, don't even want to make an effort to learn, in fact if they had there way, we would still be using type writters, in fact in the crew room, one guy couldn't even assign the computer to a correct printer, now that is basic, even a 6 year old could do that, however the younger gen are very good with technology, and like it or not, technology is moving forward.

Basically, what I am trying to say everyone has something to contribute, its important to remember that instead of calling people thick etc.:ok:

[With my lad we practice Time/Speed/Distance calculations if we are on the road for any length of time.

ie i'm at 70mph, it's 12 miles to the services, what time will we get there? sort of thing. Do it yourself in your head when you are driving an dcheck go wclose you are.]

I did this each day on my 1.5 hour commute home on my CPL course, after two weeks I had to stop, I started trying to apply max drift :eek:!

It is good pratice though.

Stop Using a Calculator
 

Stop using a Calculator for every day use. It is that simple.

Mental math is always used for estimations, not accuracy! I think one of the problems today is that people want to try to get an answer correct to nearest decimal, one must accept that this kind of accuracy is not required in flight! Calculations for hold corrections, wind corrections, time corrections etc. Will be sufficient if estimated.
Any pilot that can't mentally estimate an approx time knowing example your distance to go is 120 miles and you cruising at 210 kts, should not even be in a cockpit. Multi tasking is probably more the problem, to do mental calculation when you busy flying the aircraft.
From what I have seen maths within aviation is pretty basic, but try to get an easy math question first time you doing an ndb approach.