Basic Maths: A Lost Art

[UncouthJParticipant @uncouthj]

Spotted the Xmas subscription offer this morning. Somewhat of a maths fail though…

£20 does not 37%off of £22.50 make!

Edited By Jay Nugent 1 on 20/11/2020 12:12:10

[UncouthJParticipant @uncouthj]

Take your lump of coal and be grateful…

[JasonBModerator @jasonb]

But the real art is in being able to read and look at the other numbers, try it based on the cover price of £31.50 for six issues

[J HancockParticipant @jhancock95746]

Here's one to impress your children.

The half times table, the easy way, only 'squared numbers' though.

1 1/2 x 1 1/2 = 2 1/4

Now in all cases subtract 1/2 from first number , add 1/2 to second number, multiply together and add 1/4.

So, 7 1/2 x 7 1/2 = 56 1/4 etc, etc.

[pgk pgkParticipant @pgkpgk17461]

J Hancock

Or try to get your kids to use The Trachtenberg Speed system

pgk

[not done it yetParticipant @notdoneityet]

Posted by J Hancock on 20/11/2020 12:46:25:

Here's one to impress your children.

The half times table, the easy way, only 'squared numbers' though.

1 1/2 x 1 1/2 = 2 1/4

Now in all cases subtract 1/2 from first number , add 1/2 to second number, multiply together and add 1/4.

So, 7 1/2 x 7 1/2 = 56 1/4 etc, etc.

Simple one that. The easy way to work out any number squared by using simple algebra.😀

———

2 x 2 = ?

Easy maths add one and subtract one gives 1 x 3, which is easy maths.

Multiply the number added and taken away by itself, so 1 x 1 = 1, which is easy maths

Now add the two results together. 3 + 1 = 4, which is easy maths.

———-

Easy because you can choose the number added and subtracted to make an easy multiplication for yourself.

Derived from (a+b)(a-b) which works out as a^2 – b^2. You then add b^2 to that answer to find a^2.🙂. Easy, ennit?

———-

In your case, the half squared is one quarter. It’s what makes algebra such a useful mathematical tool.😀

[Martin KyteParticipant @martinkyte99762]

5/4 of the population don't understand fractions.

:O)

Martin

[not done it yetParticipant @notdoneityet]

Posted by Martin Kyte on 20/11/2020 13:41:41:

5/4 of the population don't understand fractions.

:O)

Martin

Like “I want my half to be bigger than your half”?🙂 Or even understanding that half the population is below average?🙂

[John HaineParticipant @johnhaine32865]

Posted by not done it yet on 20/11/2020 13:53:57:

…..🙂 Or even understanding that half the population is below average?🙂

Sorry to be pedantic but that's half below the median. Same thing for a symmetric distribution but not all distributions are symmetric.

[Paul LParticipant @paull58212]

According to the governments own figures

27% of children have substandard reading ability.

38% of them cannot write adequately,

and the other 39% cannot add up.

The youf of today eh.

[not done it yetParticipant @notdoneityet]

Posted by John Haine on 20/11/2020 14:48:59:

Posted by not done it yet on 20/11/2020 13:53:57:

…..🙂 Or even understanding that half the population is below average?🙂

Sorry to be pedantic but that's half below the median. Same thing for a symmetric distribution but not all distributions are symmetric.

Do you really think that half the population would know the difference between ’mean, median or mode’? If you have a skewed distribution the median can be different from the mean – not what most think of as ‘the average’. The mode could be a long way off with just one very clever individual (unless outliers are ignored), so lets just stick to plain old ‘average’ which most would have some idea of what it means.🙂

[Michael GilliganParticipant @michaelgilligan61133]

Posted by not done it yet on 20/11/2020 15:17:56:

Posted by not done it yet on 20/11/2020 13:53:57:

…..🙂 Or even understanding that half the population is below average?🙂

[…]

so lets just stick to plain old ‘average’ which most would have some idea of what it means.🙂

.

…. and has the added advantage of letting you keep repeating your remark.

MichaelG.

[GeorgineerParticipant @georgineer]

Posted by Martin Kyte on 20/11/2020 13:41:41:

5/4 of the population don't understand fractions.

:O)

Martin

That's an improper comment!

George B.

[GeorgineerParticipant @georgineer]

Posted by J Hancock on 20/11/2020 12:46:25:

Here's one to impress your children.

The half times table, the easy way, only 'squared numbers' though.

1 1/2 x 1 1/2 = 2 1/4

Now in all cases subtract 1/2 from first number , add 1/2 to second number, multiply together and add 1/4.

So, 7 1/2 x 7 1/2 = 56 1/4 etc, etc.

The way I was taught, which amounts to the same thing, was:

• Take the integer part.
• Multiply it by the next larger integer (as 1 x 2, 4 x 5, 97 x 98 etc.)
• Add 1/4

I've also found it useful to convert to decimals, as:

• 1.5 x 1.5 = 2.25

Then it can be multiplied by factors of ten, as:

• 15 x 15 = 10 x 20 + 25 = 225
• 150 x 150 = 22500

I acquired all sorts of dodges over the years, and it was very gratifying when teaching A-stream GCSE pupils to show that I could work out answers on the blackboard while they were still fumbling for their calculators.

George B.

[Neil WyattModerator @neilwyatt]

Posted by not done it yet on 20/11/2020 15:17:56:

Posted by John Haine on 20/11/2020 14:48:59:

Posted by not done it yet on 20/11/2020 13:53:57:

…..🙂 Or even understanding that half the population is below average?🙂

Sorry to be pedantic but that's half below the median. Same thing for a symmetric distribution but not all distributions are symmetric.

Do you really think that half the population would know the difference between ’mean, median or mode’? If you have a skewed distribution the median can be different from the mean – not what most think of as ‘the average’. The mode could be a long way off with just one very clever individual (unless outliers are ignored), so lets just stick to plain old ‘average’ which most would have some idea of what it means.🙂

If you are talking in terms of IQ, then half the population are below average by definition.

This is because IQ tests are calibrated to have a normal distribution centred on 100.

Neil

[UncouthJParticipant @uncouthj]

Posted by JasonB on 20/11/2020 12:33:45:

But the real art is in being able to read and look at the other numbers, try it based on the cover price of £31.50 for six issues

But we’re not buying individual issues, we’re buying 6 which retails at £22.50…

J

[Kiwi BlokeParticipant @kiwibloke62605]

Posted by Neil Wyatt on 20/11/2020 18:56:02:

Posted by not done it yet on 20/11/2020 15:17:56:

Posted by John Haine on 20/11/2020 14:48:59:

Posted by not done it yet on 20/11/2020 13:53:57:

…..🙂 Or even understanding that half the population is below average?🙂

Sorry to be pedantic but that's half below the median. Same thing for a symmetric distribution but not all distributions are symmetric.

Do you really think that half the population would know the difference between ’mean, median or mode’? If you have a skewed distribution the median can be different from the mean – not what most think of as ‘the average’. The mode could be a long way off with just one very clever individual (unless outliers are ignored), so lets just stick to plain old ‘average’ which most would have some idea of what it means.🙂

If you are talking in terms of IQ, then half the population are below average by definition.

This is because IQ tests are calibrated to have a normal distribution centred on 100.

Neil

It's a con trick. IQ test results are ordinally scaled, which means that a symmetrical distribution curve results. Mean and median scores will therefore coincide, and it appears that there are equal numbers of smart and stupid people in the population (without defining 'smart' and 'stupid' because it's difficult…). However, this scaling process is a mathematical 'fudge', and the unequal intervals between the variable's scores ('intelligence' or test results scores) are obscured. There are far more mechanisms around that impair the performance of a complex mechanism than can enhance it (brains are easily damaged or don't develop well) thus the real distribution curve of frequency versus 'intelligence', if the variable 'intelligence' is plotted with a linear scale, is very significantly skewed towards the stupid. However, pointing that out is undoubtedly even less politically correct than pointing out that some people are smarter than others.

[old martParticipant @oldmart]

One thing that annoys me is when a figure of over 100% is mentioned. Even the power of gas turbines is often a figure over 100%.

[John OlsenParticipant @johnolsen79199]

Gas turbines are a machine that can be run at a higher power than nominal for a short period of time. So if it is rated in terms of maximum continuous power, it may well be capable of more than 100% of that, for a short time. This is actually a useful feature for aircraft, where the ability to get a bit extra for takeoff is quite useful. (Of course they are usually rated in terms of static thrust.) The space shuttle main engines used to be throttled up to more than 100% for some parts of the ascent too. But then that was a pretty dodgy machine at the best of times.

John

[Nigel Graham 2Participant @nigelgraham2]

I don't think it's fair to criticise people for not knowing the niceties of Statistics, if like me they have never been taught them, or were taught badly; and are now faced daily with a bewildering assortment of numbers and characteristics only ever described as above, below or at, an unstated " average ". Things like the lowest of a range of three being denoted the "medium ", spring to mind…

I don't know what modern school maths syllabi are like, but statistics were not in the GCE O-Level in my generation's time (mid-1960s). Or if they were, only to an extremely basic level as in as in 5 being the "average " of 3,4,5,6,7.

Nor do I recall Statistics being in a GCSE Course I took for work reasons in the 1990s, although they have a chapter in the set text-book I bought for that course, and still have.

By " taught badly " I mean taught merely a loose assortment of dull topics to be memorised for an exam, rather than also having any meaning in everyday life or work. Often too, the topics presented appear so far removed from many people's lives, that anything beyond basic arithmetic becomes rejected.

For example, that GCSE course included Matrices, taught as merely boxes of sums and abstract moves having no purpose, no link to any other mathematics and indeed even having no meaning. (I later learnt elsewhere that Matrices are an ancient Pure Mathematics concept originally called Determinants, but finding a modern use in Finite Element Analysis – hardly a GCSE topic.)

The course did not cover all topics in that text-book, which incidentally includes arithmetic of a level many of us would remember from Primary, not Secondary, school!

===

"Average " …. Having been taught (not " having learnt &quot French at school because Dorset is nearer to France than to Thirlwall Viaduct, doesn't " average " mean " fair ter middlin' ", or would that be " feeling below median " ?

[Michael GilliganParticipant @michaelgilligan61133]

Nigel,

This is a clear, and mercifully brief, description of the Mean/ Median / Mode

**LINK**

https://www.tutor2u.net/geography/reference/mean-median-and-mode

It is genuinely useful to appreciate the distinction … Hope it helps

MichaelG.

[Bill PudneyParticipant @billpudney37759]

If you put your hand to your ear, the rustle of waking pedants can be heard………….

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Bill Pudney on 21/11/2020 05:09:26:

If you put your hand to your ear, the rustle of waking pedants can be heard………….

.

Oh dear … What a very disappointing comment ^^^

MichaelG.

[John HaineParticipant @johnhaine32865]

This is about maths. Pedantry is critical.

[SillyOldDufferModerator @sillyoldduffer]

Posted by Nigel Graham 2 on 21/11/2020 00:13:17:

…

I don't know what modern school maths syllabi are like, but statistics were not in the GCE O-Level in my generation's time (mid-1960s)…

Nor do I recall Statistics being in a GCSE Course I took for work reasons in the 1990s, although they have a chapter in the set text-book I bought for that course, and still have.

By " taught badly " I mean taught merely a loose assortment of dull topics to be memorised for an exam, rather than also having any meaning in everyday life or work. Often too, the topics presented appear so far removed from many people's lives, that anything beyond basic arithmetic becomes rejected.

For example, that GCSE course included Matrices, taught as merely boxes of sums and abstract moves having no purpose, no link to any other mathematics and indeed even having no meaning.

…

I think maths could be the most difficult of all subjects to teach because so much of it has no obvious application at the time. I made the mistake of assuming there was no point in learning anything unless silly boy me saw purpose in it. It was a mistake because much of GCSE maths is foundation material, and its purpose only emerges much later if your career takes you that way.

Also poor education system, it can't tell what Nigel and Dave aged 14 are going to do in later life. Anything between Wastrel and Nobel Prize Winner! Probably we both did work needing only a moderate command of numbers, though I found it good to know powerful mathematical tools existed even if I didn't understand them. (Most of us drive cars without understanding how they work: try designing an engine from scratch.)

Statistics were certainly in my O-Level curriculum, and my children studied it too. I'd be amazed if it wasn't taught today. Just as well – I used simple statistics a lot at work.

Forty years after leaving school I discovered what matrices are for. Best way to rotate and transform digital graphics by far, and for all sorts of signal analysis and statistical work. In normal life, it's unusual to have to operate on blocks of numbers, though anyone who has used a spreadsheet will have an inkling.

Part of the power of mathematics as a language is its absolute rigour. What some see as pedantry, is actually an aid to clarity. I do maths on the forum because it allows others to understand what I mean. Either to nail down a fact, or so they can see and correct my mistakes. Engineers use maths to avoid guesswork and to have their mistakes corrected.

Maths is wonderful. Wish I understood more!

Dave

 

Edited By SillyOldDuffer on 21/11/2020 13:59:32

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