Maths quiz from J

[UltraMum]

My 10 year old J wants to pose a question for you ...

 

Which number's square root is twice the original number?

 

[Viper]

I had to ask Abba and she say's 4?

[Zemanski]

Com says 0.25

 

Z

[Canopus]

sqrt(x) = 2x

 

x = 4x^2

 

4x^2 - x = 0

 

x(4x-1) = 0

 

The answer is 0 or 0.25

[UltraMum]

O.25 is right J says

 

[Canopus]

How did he work it out?

[Zemanski]

"Memory, I think." says Com.

[Viper]

Off to beat my DD.

[UltraMum]

How did he work it out?

 

I don't honestly know - he had been playing with calculator for a while and then just came and asked me the question in the kitchen ... I couldn't work it out - even when he told me the number was less than 1!

[TheNeil]

If the square root of something is less than itself then the original number HAS to be less than 1. If the square root of something is less than zero then you've entered a parallel universe where the laws of mathematics no longer apply (or you're dealing with 'impossible' numbers) - I knew that degree would come in handy sooner or later

[phasmid]

The question whats a half times a half once caused hours of heated debate in the phasmid household....oh the fun of maths!

[CarerQuie]

My 11 yo was sure it was a decimal number but hadn't got round to working it out.He was halfway there.xx

[Zemanski]

Com has understood this stuff since 5 or 6 years old, (he was asking us to cut up his sandwiches into 32 pieces (not easy) at 2 so he could calculate equivalent fractions as he ate ) but for most kids this is quite a difficult concept and they wouldn't normally meet it till well into secondary school along with the roots of negative numbers (can't be done - see TheNeil's parallel universe theory) and surds (infinitly irregular roots like the root of 2) which are GCSE level.

 

when multiplying fractions use the word 'of' rather than 'times' - it makes the process a lot easier to learn, half of a half makes more sense to most kids that half times a half.

 

Zemanski

[Canopus]

when multiplying fractions use the word 'of' rather than 'times' - it makes the process a lot easier to learn, half of a half makes more sense to most kids that half times a half.

 

Does anybody ever multiply numerical fractions in the real world any more? I learnt fractions from a socket set but this was in the days when the real world was imperial and nuts and bolt heads were sized in fractions of an inch. Kids nowadays learn metric at school and fractions with anything other than a power of 10 in the denominator are rarely encountered in metric apart from 1/2 or 1/4.

[Zemanski]

sorry, Canopus, but fractions are still part of the GCSE curriculum so if kids are following the national curriculum or want to do GCSEs they have to understand how to manipulate them.

 

Zemanski

[TheNeil]

Does anybody ever multiply numerical fractions in the real world any more? I learnt fractions from a socket set but this was in the days when the real world was imperial and nuts and bolt heads were sized in fractions of an inch. Kids nowadays learn metric at school and fractions with anything other than a power of 10 in the denominator are rarely encountered in metric apart from 1/2 or 1/4.

 

If I read you right, under the metric system there's very little need for fractions (aside from 1/2, 1/4) etc. as anything that doesn't neatly fall into a measurement usually gets dropped down to the next unit of metric measuring (e.g. instead of saying 6/10ths of a centimetre, it'd get dropped down to 6 millimetres). Using Imperial measurements you don't have anything beneath an inch (in terms of measurement unit)(well, not that I'm aware of) so it was necessary to have 5/8ths of an inch etc.

Edited July 25, 2006 by TheNeil

[Canopus]

Using Imperial measurements you don't have anything beneath an inch (in terms of measurement unit)(well, not that I'm aware of) so it was necessary to have 5/8ths of an inch etc.

 

There's the mil or the thou and there are 1000 of them to an inch. For some reason or other the real world preferred power of 2 fractions of an inch for dimensioning things. Socket sets always use the lowest common denominator where the next size up from 7/32" is 1/4" rather than 8/32" forcing car mechanics and industrial workers to learn fractions.

 

sorry, Canopus, but fractions are still part of the GCSE curriculum so if kids are following the national curriculum or want to do GCSEs they have to understand how to manipulate them.

 

I said multiplying numerical fractions, not manipulating fractions. I often multiply two algebraic fractions, or an algebraic fraction and a numerical fraction, but hardly ever two numerical fractions. How are fractions taught at school nowadays? Do schools teach kids to multiply and divide numerical fractions before they teach algebraic fractions? My mind has always worked fractions in terms of algebra since I was about 7 years old.

[Jill]

I'm rubbish at maths & after reading this I've got a right headache now

[marshmallow]

I'm rubbish at maths & after reading this I've got a right headache now

 

you and me both!

[Zemanski]

most kids (not you or Com, Canopus) work more comfortably with numbers than letters so algebraic understanding comes on the heels of numeric understanding.

By 5 or 6 Com was thinking in entirely algebraic terms but he did go through the numeric phase, just hell of a lot earlier than most - you probably did too but don't remember it.

 

this is why schools still teach numeric fractions and expect children to be able to perform the 4 basic operations with them, until most kids are familiar with the numeric version they find it very difficult to move on to the algebra (a lot of people still never really get the hang of algebra at all, it is often approached before they are ready for formal abstract mathematics - probably in the wrong way - and if the basic numeric groundwork isn't strong enough it just confuses them, for those who are good at maths algebra seems very easy and straight forward but this is simply not true for about half the population).

 

The numeracy strategy is much better than most older teaching methods at introducing algebraic thinking alongside numeric thinking and I think that children will find algebra easier with the more natural progression being established in primary schools now but for most they will always need to start with the concrete, move through the numeric and tackle algebra as the final step in their learning.

 

Zemanski

[phasmid]

There was an advert on the tv many moons ago that featured algebraic equations...within minutes I was sitting down writting him a page full of them to work out...and he did as well with virtually no help other than a swift explanation of what it meant.

[Canopus]

The numeracy strategy is much better than most older teaching methods at introducing algebraic thinking alongside numeric thinking and I think that children will find algebra easier with the more natural progression being established in primary schools now but for most they will always need to start with the concrete, move through the numeric and tackle algebra as the final step in their learning.

 

I never touched algebra at primary school. The maths course was heavily biased towards calculations involving integers and money and the school operated a strict no calculators policy. I found numerical calculations like how to multiply two 4 figure numbers tedious so took more interest in real maths. Was the school to blame or was it me?

[Zemanski]

probably the teaching methods at the time - things have improved considerably in maths over the last few years.

 

Personally, I've been teaching basic algebra and algebraic thinking at primary level for over 20 years but then I'm a maths specialist and didn't generally follow the textbooks the way a lot of teachers did.

 

Z

[Canopus]

probably the teaching methods at the time - things have improved considerably in maths over the last few years.

 

I think you are right. Before the National Curriculum, primary schools could set their own curriculum and teachers tended to teach what they knew or were interested in. I wouldn't say there were any mathematicians amongst the teachers at my school but thankfully they didn't make the blunder of teaching kids to execute calculations from left to right. I can't ever recall being taught square roots at primary school although my class had a lesson on square numbers and I got into a discussion about square roots. The teacher denied that the square root operator could be used on a number that isn't a square number. My O Level maths book described how to use square root tables in great detail.

[mossgrove]

My O Level maths book described how to use square root tables in great detail.

 

 

I'm old enough to have been issued with a book of Logarithms when I was 12!

 

Simon

[bid]

Did anyone else have a slide rule at school??

 

Boho

[mossgrove]

I never had one, but I remember my mother used to use one. I never, ever got the hang of how to use it though.

 

Simon

[bid]

Your mother??

 

I'm not that old, Simon!!

 

Boho

[TheNeil]

My dad had a slide rule (used it at work before electricity was invented) and I found it while clearing out some of his stuff at Christmas. I couldn't figure out how the hell anyone could calculate anything with it. I'll stick to using fingers and toes

Edited July 26, 2006 by TheNeil

[littlenemo]

I'm not that old, Simon!!

Boho

 

I must be, cos i remember when the geek's object of desire was a circular slide rule. So much easier to use than the standard 6inch ruler style And yes, I got a 'log book' at 12. The best thing about it was working out how it all worked, because the teachers never explained it, they just said "It works. Use it."

[UltraMum]

I'm old enough to have been issued with a book of Logarithms when I was 12!

 

Simon

 

Same here ... got told off by a physics teacher for using it to divide by 9! In my defence - I had used logs to do the rest of the sum - it seemed just as easy to carry on and then convert the final answer rather than to convert then divide!

 

 

Did anyone else have a slide rule at school??

 

Boho

 

At school and in my first job - used to calculate radiation doses using a slide rule!

[mossgrove]

At school and in my first job - used to calculate radiation doses using a slide rule!

 

That's one of the things my mother used hers for (She was a Radiologist).

 

Simon

[Kathryn]

I was never taught to use a slide rule but I do have fond memories of logbooks; they were all the help we were allowed at O level. No namby pamby calculators like the youth of today.

 

K x

[Canopus]

I never got to see a set of mathematical tables until I was in Y9. My primary school didn't have them and I used a calculator despite knowing how to use tables. The square root tables can only be used directly for a number between 1 and 100. To calculate a square root of a number outside this range you have to make use of the trick that sqrt(100x) = 10sqrt(x). For example, sqrt(176,400) = 100sqrt(17.64). Now you can use the tables to look up the sqrt(17.64) which is 4.2, so sqrt(176,400) = 420.

[UltraMum]

That's one of the things my mother used hers for (She was a Radiologist).

 

Simon

 

I was a radiotherapy radiographer

[Zemanski]

my dad was a builder and we were taught to use a slide rule because we might not always have a calculator to rely on - always bothered me that I might just as easily not have a slide rule but Dad didn't seem to get that point

 

Z

[Guest flutter]

well i did look at this thread and my head hurt so i pop in and out

i ws told at o level time by the math teacher that i was not allowed in his class cos i was soo rubbish at it

he was sssssssssssssssoooooooooooo right

but the funny thing is i have vivid memories of trying to learn times tables, and not really winning, so have taken the great step of saying sod it life is too short for me and mine to wory bout them, but i am the idiot in the corner going through the tables to get the answer as in one at a time by rote

[Zemanski]

Com may be a whizz at algebra, flutter, but take heart - he can't seem to learn his tables either

 

Z

[Canopus]

A lot of mathematicians have difficulty with basic numeracy. I have no problem with linear algebra or vector calculus but I have difficulty adding integers. Darts players are good at numerical calculations on the spot but few could ever handle advanced maths. I haven't encountered many builders who know trigonometry.

[katkin]

My son is doing HND in civil engineering which involves three dimensional trigonometry and other lovely things that stop conversation at the dinner table. After he'd explained what you would use it for (I think he said roof trusses and bridges) 6yr old piped up "so it's a bit like a square based pyramid shape then" Well I was impressed - I left maths at o level ( though a respectable B grade - not bad for the girl who got 8% in first year exams) And yes I had a log book too, and I was better at algebras than all those silly fractions. Though the most maths I do at work these days is possibly naming shapes! Love Kat