how is your child being taught to add fractions?(22 Posts)
My daughter is struggling with adding fractions so thought I would help. Big mistake. She is fine adding things like 3/4 and 3/4, geting 6/4 then simplifying to 1 and 1/2. Issue is when adding, for example, 1/4 and 5/6.
I was taught that you look at the denominator and find the lowest commmon denominator betwen 4 and 6 which would be 12, change 1/4 to 3/12 and 5/6 to 10/12, add them to get 13/12 then simplify to 1 and 1/12.
Daughter is being taught that you multiply the denominators together, so 4 x 6 = 24, then change 1/4 to 6/24, change 5/6 to 20/24, add to get 26/24 then simplify it at the end.
I totally appreciate that the two methods give the same end result. Is this a conscious shift though in the way of teaching, am I misremembering my own days at school, or something else? By trying to help her I actually made things worse as she glazed over totally at the mention of "lowest common denominator".
Depends on age and ability. If bright and fairly young, I would still expect the lowest comment multiple approach to be used. Older, and under a C grade, then I would probably expect the ‘trick’ method, possibly complete with silly window grid to accompany it.
It’s actually more work to do it her way, and will often require a lot of simplification. However, it means they don’t need to understand LCM in order to tackle it.
I was taught the same method as you if it's any help. My daughter hasn't reached this stage yet so I don't know how it will be taught. The only consolation is at least the school's method is one you can understand and adapt to yourself! It's not the first time I've been a bit lost by the various methods of teaching employed now :D
Multiplying the den is how I was taught too and I’m almost 40. The reason (I was told) is if you look for the lowest common den then you will probably have to use a calculator at some point, which makes you slow. Multiplying the den makes you work faster.
My dh is the same age and taught in Asia and learned the same way as me, by multiplying dens.
She's 12 - in her first year of secondary in Scotland. She was taught addition of fractions in primary school but it was never an issue....the first term of secondary has been about covering a lot of different topics so the teacher can get a handle on what the kids have been taught and identifying gaps in their knowledge. Fractions appears to be a particular sticking point for lots of them - not just DD.
The LCM method strikes me as much more mathematically literate. I think in practice one does a mixture , after all often the LCM will actually be the product. If that LCM doesn’t leap out at one it is a bit of a waste of time to thrash around looking for it.
I don’t not think there’s a great difference in the methods. You are finding the lowest common denominator, she is finding the most obvious common denominator. You both need to simplify after.
In your example I’d hope she could understand you can work in 12ths or 24ths. I probably use a combination. If a LCD jumps out then great but if not the multiplication method is guaranteed to give a common denom.
Maths teacher here. Pupils in the UK are usually taught to multiply the denominators together. This is easier for weaker ability pupils rather than finding the LCM. It does mean they can end up working with large numbers that need simplifying and this does cause other problems. Personally it annoys me but I have got used to it. I find pupils arriving at our secondary school from other countries tend to have been taught the LCM method.
I work in Y6 class and we teach both methods, they choose whichever they feel most confident with. Those who are good at maths and know their times tables really well tend to go with LCM method.
It just shows how much maths teaching has moved on since I was at school. Methods for doing long division and long multiplication have changed too, and I don't ever recall being asked to "estimate" anything.
I teach LCM method to the higher ability kids because they understand it, and it avoids all the simplifying at the end. Lower ability get confused and waste a lot of time trying to find the LCM, so I teach them to multiply the denominators. Middle ability groups get the LCM method lower down the school, but if they don't grasp it or its taking ages then those pupils then use the multiplying denominator.
Most pupils in England are now taught traditional methods for long multiplication and division too, but I don't know if that's true of other UK countries.
I think the important thing is that the child understands that before you add the fractions they have to be put over a common denominator. That has to be a common multiple of the original denominators. Whether it is the least such number or the product or something in between will not matter other than to affect the amount of simplification at the end. The LCM requires a lot more fluidity with tables so you can spot the smallest number in both tables but will suddenly get hard for numbers above the usual times tables when kids need to be then able to find prime factors in order to systematically work out LCMs. The product method in contrast just involves a lot of brute force arithmetic and spotting common factors at the end to cancel. I have no idea how much the last part really matters but recall some teachers’ obsessions with all fractions ending up in their simplest form.
An easy trick to find the LCM is to take the highest denominator and x it by 2 which often supplies it. If it doesn't just x again by 3 and then 4 etc until you do find it.
Fresta - if we are going the LCM route then this is a neat idea for the very simplest problems, but if you are going to test repeatedly isn't it better and more efficient to look systematically for (possibly repeated) common factors of 2, 3, 5 etc. and pulling them out before taking the product. Then you are getting across the key underlying idea of finding the common prime factors, without necessarily using those scary words. And there is a lot of effort potentially buried in your "etc", especially if you suggest working through all whole numbers. You might look at 1/21 + 1/39 as an example. Kids ought to be on a path to grasping how to address that efficiently by identifying the common 3 rather than doing several multiplications of 39. Once you get to examples like that it also reminds you that finding LCM is sometimes a better plan than going first for the product, which in this case is a horrible idea.
So you are saying that the best way would be to x the denominators by each other and divide the answer by the highest common factor to get a common denominator?
To be fair, and I see the point about the lowest common multiple often being the product, the chances of a 12 year old being asked to add 1/39 and 2/71 are pretty remote. It's mostly up to twelfths.
I would have thought most 12 year olds are working with fractions other than simple ones. My dd's maths is really complex and she's year 8 and the Y6 curriculum in my school demands that children can simplify, add, subtract, order and multiply and divide fractions much greater than 12fths.
We're in Scotland. Curriculum is totally different.
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