teaching of Maths

[teachersaspirations]

hi
my dc has come home with exercises in how to work out the HCF (highest common factor) & LCM (lowest common multiple)
when I asked them what they were used for, they didn't know
and the teacher has not explained why they are useful
(this has happened with more than 1 dc in different years)
why is maths being taught like this?

[Vivacia]

Like what exactly?

[teachersaspirations]

I should explain
I was hoping that they would explain why & how they are used rather an arbitrary exercise
like cancelling of fractions & the addition of fractions

[Vivacia]

Ah, I see, why aren't teachers explaining why it's useful knowledge?

[teachersaspirations]

yes
and not only that, the way that it is taught is a full-proof method, but not the most expedient (well from the method I have seen in mymaths)

[noblegiraffe]

I've never actually found the LCM or HCF in a mathematical way for adding or cancelling fractions, it would be a bit of a sledgehammer to crack a nut really.

What do you mean by the most expedient method?

[Vivacia]

That's interesting giraffe. For example, how do you add fractions without using the LCM?

[noblegiraffe]

You can use any multiple of both denominators, it doesn't have to be the LCM. If they use the LCM it will save on simplifying the answer.

If you tell kids to use the LCM it just adds another layer of complication.

[Vivacia]

But using the LCM is more efficient and removes the step of cancelling (if a simplified fraction is needed)?

[noblegiraffe]

Yes, it's better to use it, but you don't have to. If you can immediately see what the LCM is, then fine. However, if you quickly spot another common multiple, or in a pinch just multiply the denominators together, that's ok. If you had to faff about figuring out the LCM, would it necessarily save time over cancelling?

[Vivacia]

Thank you for taking the time to explain what you meant.

[teachersaspirations]

I think it would be better to use smaller numbers if possible, therefore the LCM is preferable, and if you look for an LCM then it teaches you to look for patterns and smplifications not just go with the multiplication as the numbers get pretty big pretty quickly

unless we are using computers and calculators for everything

[noblegiraffe]

teacher what was your most expedient method? Was it using prime factors?

I really can't see that where the LCM isn't immediately obvious that calculating it using prime factors is really that preferable to finding any old common multiple when adding fractions.

Unless, perhaps, you are given huge numbers, in which case just use a calculator.

[ParsingFancy]

Oh I shall be using LCM tomorrow doing some work on the house. I have two types of tiles, of different sizes. I'll find their Lowest Common Multiple, and that will give me the pattern repeat.

Eg if one tile is 15 cm and the other 10 cm, the LCM will be 30 cm.

HCF now... When did I last use that? Hmm. Will try to think of an example.

[noblegiraffe]

The standard LCM questions are "two bells chime at 9am. One chimes every 6 minutes, the other every 9 minutes, what time do they next chime together?"

Or something about lighthouses and seeing their beams at the same time.

It's not the most gripping topic!

[teachersaspirations]

18 & 24
mymaths splits
18 into 2,9(3,3)=>2x3x3
24 into 2,12(2,6(2,3)=>2x2x2x3
full-proof but then I lose the will to live
I suggest looking at 18 & 24
and splitting as (3x6) & (6x4)
then just using one of the 6's
to give 3x6x4 as the LCM

[paperclipsarebetterthanstaples]

Were you in class? How do you know that the teacher hasn't explained? Dc may have missed the explanation or can't be fussed telling you?

[noblegiraffe]

But that only works because 3 and 4 neatly don't have any common factors.
Say you decide to split 18 into (2,9) and 24 into (2,12)
Then you use one of the twos and do 2x9x12 and get the wrong answer. You could even spend ages faffing around trying to get a couple of neat pairs where they don't even exist.

Try teaching that as a method!

[ParsingFancy]

Mm, can't off the top of my head think of a practical uses of HCF. However once you get into algebra, the ability to extract HCF will make life an awful lot easier. So the technique's worth learning.

[teachersaspirations]

paper
2 different teachers with 2 different kids not having any explanation is why I don't think it is being explained
giraffe
I think it is about mental agility, you can always use the mymaths method
but I suggest it is about actually looking for simplifications
and I think using 2x9x12 would give the right answer, you just have to simplify once more at the end

[noblegiraffe]

2x9x12 wouldn't give you the right answer if the question was 'what is the LCM of 18 and 24' isn't that what your DC is being asked to do?

I think that a teacher who has just shown a class the prime factor method and suggests that this would make adding fractions easier would be met with a sea of baffled faces

[teachersaspirations]

if the question is what is the LCM of 2 numbers, then you are right

I am not a teacher, I just have to explain what an LCM can be used for when they come home from school and also that sometimes there may be simpler & easier ways of solving the problem if you look...........

[paperclipsarebetterthanstaples]

There's only so much you can cover in a lesson... And ime lots of children will say 'she didn't teach me...' my colleague was asked my a senior manager why he hadn't taught Little Johnny how to convert a fraction to a decimal after a parent complained (really!!) luckily me colleague was able to show the manager little Johnny's maths exercise book where he'd completed and had written feedback on a whole page of conversions... Just saying.

[ClayDavis]

Are you suggesting that 2x9x12 would be OK for adding fractions then?

[teachersaspirations]

paper
this is not an isolated example, but you may be right some of the time

clay
for adding 1/18 & 1/24

[noblegiraffe]

Teacher, I really hope that you didn't show your DC your 'expedient' method. Did it just happen to work for the numbers that you picked or did you realise that the other numbers in the pair needed to be coprime? Chances are any child attempting what you did will get the wrong answer, it is not a good method.

I don't think that not mentioning fractions when teaching LCM and HCF using prime factors is the crime of the century, because if they said 'when will I ever use this' I'd be lying if I said they'd use it for that. They are not going to be asked to add 1/18 and 1/24 by hand, and I would encourage use of the fraction button on their calculator for unwieldy calculations.
However, when doing fractions I would expect to see HCF and LCM mentioned (unless with a really bottom set!). But certainly not using prime factors to find them!