What level is this question in the maths curriculum?

[essex-mum18]

[quote="Guest55"]Cross multiplication should NEVER be taught as children use it when it is not appropriate:

ie x/4 = x/3 + 1


I still believe by using the cross multiplication in solving bewildered's problem i.e 1/x = 3/4 is correct and approprite.

Take your example, it will be inappropriate to use cross multiplication and should be explained to children why it is not appropriate.

x/4 = x/3 + 1

x/4 - x/3 = 1

3x/12 - 4x/12 = 1

3x - 4x = 12

x= -12

[Guest55]

You should not teach something that is not a general method - as a Maths teacher I avoid teaching 'tricks' as children forget when they are appropriate -

[essex-mum18]

I really do not think cross multiply is a trick. This method is quite widely used even in this country. I cannot say anymore if you think this method is a trick.

http://en.wikipedia.org/wiki/Cross_multiply

[Guest55]

Yes it may be widely used - and often incorrectly - it works if you UNDERSTAND what you are doing.

I have had to reteach many children who have been given 'tricks' to solve specific problems -

[SunlampVexesEel]

Sorry... still not convinced

1/(a/b) = b/a.

It's a mathematical fact; not a trick.

[Guest55]

OK but you aren't a Maths teacher -

I know it work but so does 'adding a zero to x by 10' until you get to 8.7 x 10

What you quote above is not cross multiplication -

[moved]

I don't teach children to turn fractions upside down, I just liked the simplicity of a yr 6 child's approach, sometimes children can be beautifully intuitive.

[mathsteacher]

Moving - please don't encourage that method - it only works if there are two fractions equal ...

But these fractions are equal. Sorry I don't teach this low down, so maybe there is a reason why these fractions should not be treated as equal.

[solimum]

I agree with Guest55 that there is a danger in teaching children "tricks" (effectively shortcuts which work in certain circumstances) without some understanding of what the objects they are manipulating actually mean. An obvious danger in the examples above would be if one of the quantities could be zero - you could end up dividing by zero as in the fallacious proofs that 2=1 etc. They can carry hidden misunderstandings through for many years while apparently getting good marks - then when faced with higher level algebra it all seems to fall apart

[mathsteacher]

I see the point with zero, obviously infinity is not a good solution. School teaching rather than university, I assumed that children would know this. Trying to adapt!!