Maths

[tigersaw]

Originally Posted by philipMac

I have no memory at all for numbers, tables, formulae, etc but there is a logical way of getting to most of the answers fast.

Sometimes amswers just present themselves.

A couple of years ago I went into Tesco with vouchers, I wanted to put them towards a TV.
I had 6 at £36, and 6 at £6

Now to add them up it immediately presents itself in my minds eye as 180 plus 36 plus 36, then 180 plus 72, then 200 plus 52 - all that happens in a split second.
I guess thats a result of the continuous and tortuous arithmatic we were taught at school.

However, the till girl called a supervisor, who then went and fetched a calculator. I guess maths is just not taught the same anymore.

Originally Posted by philipMac

I have no memory at all for numbers, tables, formulae, etc but there is a logical way of getting to most of the answers fast.

+1

Originally Posted by northwind

thing with rote is that usually you do up to 12x12... Then, someone asks you "what's 13 times 2" and you don't know the answer.

True. Rote learning doesn't teach one to think outside of the box.

times tables are easy.

go on, ask me anything.....

Originally Posted by northwind

Are the kids teaching you?

Thing with rote is that usually you do up to 12x12... Then, someone asks you "what's 13 times 2" and you don't know the answer.

26 and without a calculator, I thank you.

Harking back to slide rules and log tables is like harking back to the days when latin was taugto ht as standard. You can argue that it makes you think a bit deeper about what you're calculating but it would be a waste of time to learn them these days. A bit of mental agility in estimating comes in handy though - like will my last tenner be enough to get two pints of bitter, a red wine and a coke? (unfortunately not in a lot of places).

Originally Posted by tigersaw

Sometimes amswers just present themselves.

A couple of years ago I went into Tesco with vouchers, I wanted to put them towards a TV.
I had 6 at £36, and 6 at £6

Now to add them up it immediately presents itself in my minds eye as 180 plus 36 plus 36, then 180 plus 72, then 200 plus 52 - all that happens in a split second.
I guess thats a result of the continuous and tortuous arithmatic we were taught at school.

However, the till girl called a supervisor, who then went and fetched a calculator. I guess maths is just not taught the same anymore.

On your first post I thought you did your mental arithmetic differently to me, but looking at the way you describe this it's similar to the way I do it. Ignoring the last 6 x £6 since that just turns into +36 straight away in my mind, I do:
6 x £36 becomes
5 x £36 + £36 becomes
(10 x £36) / 2 + £36 becomes
£360 / 2 + £36 becomes
£180 + £36 either that's the end (if I see the final sum easily which I do here) or if it's two awkward numbers i go to
£200 + £16 and then
£216.

The difference I'm doing to what you are doing I think might just be that "10 x £36" which I do - y'see it's easy for me to round to nearest 10's of multiplication and then remove/add the extra:

13 x 8 becomes
13 x 10 - 26 becomes
130 - 26 becomes
104.

I also do this sort of narrowing down if I am doing fractional/decimal multiplication in my head:

206.8 x 13.2 becomes
(206.8 x 10) + (206.8 x 3.2) becomes
2068 + (206.8 x 3.2) becomes
2068 + (206.8 x 3) + (206.8 x 0.2) becomes
2068 + (200 x 3) + (6.8 x 3) + (206.8 x 0.2) becomes
2068 + 600 + (6.8 x 3) + (206.8 x 0.2) becomes
2068 + 600 + (6 x 3) + (0.8 x 3) + (206.8 x 0.2) becomes
2068 + 600 + 18 + (0.8 x 3) + (206.8 x 0.2) becomes
2068 + 600 + 18 + 2.4 + (206.8 x 0.2) becomes (note here that 0.8 x 3 is easy to work out if you know 8 x 3)
2068 + 600 + 18 + 2.4 + (200 x 0.2) + (6.8 x 0.2) becomes
2068 + 600 + 18 + 2.4 + 40 + 6.8 x 0.2 becomes
2068 + 600 + 18 + 2.4 + 40 + 6 x 0.2 + 0.8 x 0.2 becomes
2068 + 600 + 18 + 2.4 + 40 + 10 x 0.2 - 4 x 0.2 + 0.8 x 0.2 becomes
2068 + 600 + 18 + 2.4 + 40 + 2 - 0.8 + 0.8 x 0.2 becomes
2068 + 600 + 18 + 2.4 + 40 + 2 - 0.8 + 1 x 0.2 - 0.2 x 0.2 becomes
2068 + 600 + 18 + 2.4 + 40 + 2 - 0.8 + 0.2 - 0.04 becomes (note 2 squared/0.2 squared knowledge used here - squaring a decimal is linked to squaring the original number, there is a pattern)

*add it all up*
2668 + 18 + 2.4 + 40 + 2 - 0.8 + 0.2 - 0.04 becomes
2670 + 16 + 2.4 + 40 + 2 - 0.8 + 0.2 - 0.04 becomes
2686 + 2.4 + 40 + 2 - 0.8 + 0.2 - 0.04 becomes
2688.4 + 40 + 2 - 0.8 + 0.2 - 0.04 becomes
2728.4 + 2 - 0.8 + 0.2 - 0.04 becomes
2730.4 - 0.8 + 0.2 - 0.04 becomes
2729.6 + 0.2 - 0.04 becomes
2729.8 - 0.04 becomes
2729.76.

*checks it's right*
Phew, yes lol. So you can see this method kind of approximates the answer the further into detailed complications I go - and actually I tend to add it up as I go rather than doing all the multiplications up front (too many to remember, much easier to keep a running total + the currently remaining multiplication). I also managed to make a mistake halfway through while writing that! (imagine I put 0.24 instead of 2.4) Nonetheless the theory is sound that was just me mangling up a multiplication

The above is something I do pretty quickly these days in my head, probably helped by working on maths right up until I left university (did Maths at GCSE, A-level, and university).

Originally Posted by muffles

On your first post I thought you did your mental arithmetic differently to me, but looking at the way you describe this it's similar to the way I do it. Ignoring the last 6 x £6 since that just turns into +36 straight away in my mind, I do:
6 x £36 becomes
5 x £36 + £36 becomes
(10 x £36) / 2 + £36 becomes
£360 / 2 + £36 becomes
£180 + £36 either that's the end (if I see the final sum easily which I do here) or if it's two awkward numbers i go to
£200 + £16 and then
£216.

Except the answer's 252

[timwilky]

Originally Posted by Well Oiled

Harking back to slide rules and log tables is like harking back to the days when latin was taugto ht as standard. You can argue that it makes you think a bit deeper about what you're calculating but it would be a waste of time to learn them these days. A bit of mental agility in estimating comes in handy though - like will my last tenner be enough to get two pints of bitter, a red wine and a coke? (unfortunately not in a lot of places).

Slide rules AKA guessing sticks and log tables are obviously banished to the dark cupboards never to be seen again. However, at some point students need to know what a log is and how to use it. calculators speed up and improve the accuracy of calculation but you still need to know what you are doing.

Strangely enough sitting on my desk right now are two little books I bought when I attended Leyland Motors Technical College in the 70s. A red one called Mathematical formulae for use in examinations price 15p plus postage and a blue book of steam tables. I am having a clean out of my office but cannot bear to think about throwing them, they might be useful one day.

Now who can tell me the Cosine rule or the equations of a parabola and ellipse. These are things I once must have really needed to know

[Ruffy]

It's all about sense checking isn't it? If you blindly accept the answer given to you by any calculating device (be it slide rule, calculator or complex computer programme) without thinking "is that about right" then it's impossible to trap any obvious errors. Just like you'd think "that's not right" if someone offered you a 36" stilson as the right tool to remove a 6mm bolt.

Originally Posted by Well Oiled

Harking back to slide rules and log tables is like harking back to the days when latin was taugto ht as standard. You can argue that it makes you think a bit deeper about what you're calculating but it would be a waste of time to learn them these days.

Perhaps learning them verbatim is a waste of time, but going over them certainly isn't. Not going over such things isn't going to result in you thinking less deeply about them, it'll probably mean you don't think about them at all.

Yes we might have the technology to do things for us, but machines can't think for us and if you give them stupid questions they'll give stupid answers.

Reminds me of a quote from the Simpsons: "Who's calculator can tell me the answer to 5 x 9?", "Oh oh oh, low battery?"