Primary maths question on fractions

[IslaValargeone]

Can I ask how subtraction of mixed fractions is taught.
Do you covert into an improper fraction and then find an lcm if necessary or do you subtract the whole numbers first and then 'borrow' from one of the whole numbers if necessary?
Hope I've explained that

[snowball3]

I teach converting to an improper fraction, then into fractions over the same denominator before subtracting and converting back to a mixed fraction

[IslaValargeone]

Thanks snowball, do you think it would be a problem to have learnt to do them the other way? My dc is going back to school after a year of HE and some of our methods may be different. I am getting jittery about her being confused if she is forced to do things the way the teacher does them.

[SquirtedPerfumeUpNoseInBoots]

Do you mean like 2 1/2 minus 1 1/2? Then you work out in improper fractions 5/2 (2x2+1) minus 3/2 (2x1+1) ans 2/2 = 1.

Or 1/2 minus 1/3? Lowest common denominator 6. So 3/6 minus 2/6 ans 1/6.

[GrimmaTheNome]

I'm pretty sure that when my DD had something like 2 1/2 - 1 1/3 she would subtract the whole number first to get 1 1/2 - 1/3 then 3/2- 1/3 then 9/6-2/6 = 7/6 = 1 1/6

[youngermother1]

Grimma, why subtract the whole number, then convert to improper fractions? just adds a step, straight to the improper for me

[karatekimmi]

I wouldn't worry too much, I'd change to improper fractions, but as a secondary school teacher it is a topic that is repeaters over and over as they never seem to get their heads round it!

[GrimmaTheNome]

It may be something she decided to do for herself, I don't know if she was taught to do it - a simplification step to keep the numbers in the rest of the calc smaller seems reasonable to me.

[HumphreyCobbler]

mostly teachers do not rigorously insist on 'correct' method nowadays. My most frequently asked question in maths is "How did you work that out?" and we discuss the different ways it can be done.

Although I do teach rather more basic maths (year 1).

[gabid]

Exactly, I personally would find it easier to substract the whole number first and then look at the fractions. But I think children are taught several methods (at least in secondary most are aware of several methods to do things, not only fractions).

If the result is correct, then what does it matter?

[DeWe]

I'd subtract the whole number and then the fractions. I'm a mathematician and I'm sure that was how I was taught, and dd1.
Converting into improper fractions is an extra step that they're more likely to make a mistake on. And then they've got to convert back afterwards, where more mistakes can be made.

[Elsjas]

My dd has been taught to subtract the whole numbers first and then deal with the fractions.

[MorningPurples]

I generally encourage my weaker pupils to get into the habit of always converting to improper fractions at the start, and then back at the end. If a child has a good grip on maths, then they get to the point of being able to spot when they need to, and when they can just deal with the whole numbers first and then the fractions (which is certainly easier for those questions where you can just do that simply). But too many of them don't recognise that for questions like 4 1/3 - 2 1/2, you can't do it quite as simply as that.

In those cases, I find many pupils struggle with the idea of 'borrowing' from the whole number and/or get confused about which way around subtraction goes and so don't recognise that they need to. (i.e., the common mistake they make is to do 4 - 2 = 2, and then 1/3 - 1/2, convert that to 2/6 - 3/6, and then decide that is 1/6, rather than realising that as it's the wrong way round, they need to borrow from the whole number).

I think because subtraction is so often taught using a number line, going from the smallest number to the biggest number, some children don't always see it as 'taking something away from the biggest number', and therefor are more prone to thinking things like 2 - 5 is 3, because in their minds, it means 'going from 2 to 5 is three jumps'. This can sometimes cause problems when doing subtraction in a more conventional written format (e.g., column subtraction) or examples like here, with fractions.

So it is sometimes easier for older children who are being taught these more formal, written methods, are simply need to get the right answer, to just learn the rule that they should always convert to improper fractions.

For my younger pupils, it's sometimes helpful to go back and teach fraction subtraction on a number line as well: so 4 1/3 - 2 1/2 becomes 1/2 (up to 3) + 1 (up to 4) + 1/3 (up to 4 1/3). Then they still have to add fractions at the end, but many are more comfortable with that.
And of course I keep reviewing the idea of subtraction on a number line (counting up) meaning the same overall as subtraction by taking away, so that hopefully when they are older, they won't have the confusion of 2-5 or 5-2.