Maths

[Ed]

My 9yo daughter is learning her times tables. It's been hard, but she is so pleased that she knows the answer to '8X7'.

And then today in the office we had a few involved sums to work out. Sarah, my co-worker, immediately reached for the calculator. Accountant Leo suggested that she used a slide rule. She just looked blank - she'd never used one. So I suggested log tables and she admitted that she'd never used them.

Progress?

[tigersaw]

I still use a slide rule. Admittedly never when it matters, but I can always reach an 'ish' answer before everyone else has found their calculator on their phone.

[Tim in Belgium]

Personally I like steam tables, especially the superheat section.

[rigor]

Slide rule, nope never used one. But good mental arithmetic is a very very useful tool. Being able to know what rough range your answer is meant to be in before you start tapping away at the calculator has saved me making quite a few mistakes

[philipMac]

there are rules for them... like, 9 x 7 = 63

to figure it out, you take 1 from whatever number you are multiplying (7-1 = 6) and then put whatever number on the back to make it 9 again (3). 63.

Do you get me?
9 x 9 = (9-1 = 8, 8 + ? = 9, so 9x9 = 81).


2, 3, 4, 5 are all easy. 6 is ok, because you just work what half 12 times is, plus six if its an odd number. 7 is a little tricky, you have to learn that. 8 is easy, evrey time you go up a 10, you go down a 2, 8, 16, 24, 32, 40 and so on. 9 easy, 10 easy, 11 easy, and 12s are fine till you get up there a bit.

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.

[the_runt69]

Duno about this but still know my times tables from 40 odd years ago when I was taught them parrot fashion, as in once 2 is 2, 2 2's are 4 etc can still do up to 12 times table without thinking about it.
Sometimes I even do the days performance figures on paper before running the macro just to keep in practice, all on paper never got on with a slide rule

[northwind]

Slide rule, nope never used one. But good mental arithmetic is a very very useful tool. Being able to know what rough range your answer is meant to be in before you start tapping away at the calculator has saved me making quite a few mistakes

Yep, exactly. There was a huge outcry when schools starting teaching approximation techniques a few years back, as if they were saying "nearly is good enough"- it was seen as dumbing down. But approximation's incredibly useful.

I see absolutely no problem with people using calculators either, fwiw, sooner or later we're going to start having wetware upgrades that can do this stuff for us anyway as we ride our hoverbikes. But there's a balance to be struck. Spending months learning times tables by rote isn't too clever either IMO.

[kitkat]

im helping a group of kids learn time tables. parrot fashion is one of the best ways to drum it into them. we practice in the playground or gym depending on weather and throw a football to each other as we chant. 9 times table is one of the easiest I find 8 and 7 tricky

[philipMac]

But there's a balance to be struck. Spending months learning times tables by rote isn't too clever either IMO.

Right. I mean, I am not a particularly stupid person, I am working in a pretty serious lab as their ("lead" apparently) scientific programmer, and contract out to banks and other people. But, I cannot remember the order of numbers. I just can't.

I could never get the tables until I found the patterns in the numbers, and I did maths (even a primary degree in it) in a way that was different to everyone else it seems.
Like northy was saying, I can understand the idea of a concept and then estimate within that range. What I cant estimate, I can brute force with some calculator work, do some estimation, and then work towards an answer. For me, it works, I got a 1.0 in maths.

I suppose it would be nice to be able to learn things by rote, and be able to look up the number 354 in an index and actually go to that page rather than going to 345, but I survive.

[northwind]

9 times table is one of the easiest I find 8 and 7 tricky

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.

[tigersaw]

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.

[melody]

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

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.

[keithd]

times tables are easy.

go on, ask me anything.....

[Tim in Belgium]

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.

[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).

[muffles]

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 :lol:

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).

[Dan]

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]

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.

[Flamin_Squirrel]

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?"

[El Saxo]

I remember when I was at school (about 11 years ago now) and had forgotten my calculator for a maths lesson - I thought I'd try to use my initiative and work it out on paper instead but needed the teacher to go over a technique for me (I think it was long division or something) - the teacher flat out refused and told me to borrow a calculator. I guess the manual working-out stuff must be disappearing off the national curriculum... :smt102

[muffles]

Except the answer's 252 ;)

Lol no it's not, it was in the original example, but I said I was ignoring the 6 x £6 vouchers as they didn't contribute to the example! I win! :p

[Alpinestarhero]

Yea, its quite bad actualy. Eveyone reaches for the calculator nowadays, but what gets me is when its for something very simple, a simple sum you can do in your head if you just put a little effort in and think clearly for one moment.

It would be great to learn how to use a slide rule, just incase my calculator dies :D

I do need the logarithmic function alot though, so a scientific calculator is quite a must for me

Matt

[tigersaw]

I do need the logarithmic function alot though, so a scientific calculator is quite a must for me

Matt

Thats how a slide rule works, its a linear / logrithmic scale

[Alpinestarhero]

Thats how a slide rule works, its a linear / logrithmic scale

Ah, I seeeeeeee

Where can I get one from? It'd be cool to be able to use one

Matt

[tigersaw]

Got mine in Boots, but that was in 1970.
Proably ebay best bet now!

[Essex of Essex]

Most pilot supplies shops will sell you a circular one, slide rule on one side and wind drift and speed calculations on the other, and even a scale to work out your Mach No.:p

[Ruffy]

Yea, its quite bad actualy. Eveyone reaches for the calculator nowadays, but what gets me is when its for something very simple, a simple sum you can do in your head if you just put a little effort in and think clearly for one moment.


Absolutely! I remember a few years ago, before full barcode zapping tills, I was buying a new rugby shirt and a couple of other bits and pieces. At the checkout I decided to add a new pair of socks. So £1.99 needed adding to the total. The assistant reached for a calculator, and promptly got the answer wrong! I politely suggested re-calculating, offering "add £2 and take off a penny", to which I got a blank look of total confusion.

Technology today is wonderful stuff, but most people seem to forget that garbage in still equals garbage out, however quickly and accurately it's been processed.

[Alpinestarhero]

Absolutely! I remember a few years ago, before full barcode zapping tills, I was buying a new rugby shirt and a couple of other bits and pieces. At the checkout I decided to add a new pair of socks. So £1.99 needed adding to the total. The assistant reached for a calculator, and promptly got the answer wrong! I politely suggested re-calculating, offering "add £2 and take off a penny", to which I got a blank look of total confusion.

Technology today is wonderful stuff, but most people seem to forget that garbage in still equals garbage out, however quickly and accurately it's been processed.


Exaclty!

Matt