Is there more than one way to add fractions?

[17leftfeet]

Dd does it like this

2/3 + 1/6

Both denominators need to be the same and whatever you do to the denominator you do to the numerator so it becomes...

4/6 + 1/6 =5/6

Apparently they were told a different way of doing it today which has confused her so she asked me

I have no idea as that's exactly how I would have done it

Any clues?

I would have done it that way too

Me too

And me.

Another one who would do that (and so would DS).

There is another way she might have been taught.

For the children who aren't good at spotting the lowest common multiple, they might be taught to make the common denominator the multiple of the others

 2/3 + 1/6

= 26/36 + 13/63

= 12/18 + 3/18

= 15/18

= 5/6

It is what my (y10) daughter often does as she doesn't spot common factors very well. But the way everyone above ^^ did it is of course much better!

DD (Yr 2) covered some work on fractions last term and she was taught to do them the way you have described. I genuinely cannot think of another obvious way, unless they were doing something like converting the fractions to decimals and adding them together

There is a horrible grid method which will be hard to type...

Whoops! It's sideways. Can you read it?

It's not a very good method because it doesn't teach understanding, just a process. So when you forget the process you're screwed. It wouldn't surprise me at all if this is what your dd was shown.

OMG Hiding that's terrible! That's basically the method I did with cross multiplying the denominators but laid out in a complicated way that doesn't aid understanding of the underlying maths at all.

And I would love to see how they expand it to work with adding 3 fractions!

maybe she is referring to the next step of simplifying the fraction if necessary or converting an improper fraction
E.g 10/7 = 1 3/7

Or 5/10 = 1/2

?

I have never seen that grid method of adding fractions despite having done a few years in the UJs. You are correct-it does not aid understanding as to what the children are actually doing when they add fractions so wouldn't help with their 'fluency' or ability to apply the strategy at all.

However you do it, you MUST make the denominators the same. So either find the first common multiple, or multiply them by each other to find a common multiple that can be used. If they are a mixed number to start with, it is best to convert the mixed numbers to improper fractions, then add those. You can sometimes add the whole numbers first, then convert the rest, but this can easily trip you up if you try to do the same when subtracting.

I checked with her, it is that horrible grid method

She has a mental block when it comes to grid methods and the teacher is very specific about which method they have to use and marks it wrong if they use the wrong method

Sigh!

Oh dear 17!

That sounds like a teacher teaching a subject they are not not very confident with. It really is not a good idea to force a method on students, especially ones like this grid. The beauty of maths is that there is always more than one method to arrive at an answer, and none of them will make the answer any more correct.

I hate to think of your poor dd having to learn something she doesn't understand by rote! Does she get taught a variety of methods, or just one that she must use? If the latter I would personally be having a quiet word with the teacher.

that grid method looks awful!

I agree with your common.donominator, or the longer one where you multiply the denominators that TeenandTween said

I'm not sure if I made that last sentence clear... (Go easy on me- first day back after holiday has fried my brain!)

If the teacher is saying, "today we will all learn to use this particular method; tomorrow we will learn a different one." I would presume that the teacher is saying students can select the one they like best once they know them.

But if the teacher is saying "this method is the only method and youmust use it correctly" then I would have a serious problem and would want to discuss this. It is quite tricky though, because it may be due to poor subject knowledge.

(Sorry these are getting a bit long- I can get quite passionate about this!)

I think it is reasonable to try to teach more than one method, but then as soon as the method has been taught to let the child pick the one that they can understand and follow best.
But I don't like the grid method above as it hides understanding rather than enhancing it (imo).
(Unlike grid method for multiplication which I quite like).

Exactly teen! I totally agree.

I like the grid for quadratic equations

I don't know any other grid methods.
it's important for children to learn the method that suits them best.

They get taught a method then have to use that method until they learn a new method then they have to use the new method

I've spoken to the teacher about marking it wrong when dd gets the answer right as although she is able she had confidence issues in maths

Previous teachers have marked it right and added a note to try and use the correct method

They won't care which method she uses next year when she does her sats, they will just care if she gets it right!

Hmmm... So perhaps not poor subject knowledge then!

It does seem quite harsh to force students to use a method that they don't get on with. I try to introduce them to a few, ask them to choose their favourite then do a practice with that method only. What's the point trying to learn a method that you know you don't like? Or that you don't understand?

I think you're right in saying it can lead to confidence issues. And it must be very frustrating having to learn a method when you already know that you would prefer to use a different one.

Any way, I'll shut up now, as I do get quite wound up about this!

As you were...

This 'new method' (the grid) is not simply an alternative though, it's a worse method than the one she already uses. It's not efficient, in that she will have to simplify her answers if cross multiplying doesn't give the lowest common denominator.

I'm a secondary maths teacher and horrified that this method is being taught in primary, especially to kids who can cope with common denominstors. I've shown it to kids in secondary but only as a cheat, a last resort to those who need all the marks they can get on their GCSEs.

I'd refuse to let my child be forced into using it, tbh.

17leftfeet:

Your DC probably doesn't go to my DD1's school but we've also hit upon the GRID ONLY teaching approach.

Our solution has been conspiracy. Many parents have resorted to teaching our children how to do things using other methods at home (and our fraction method would be to find lowest common denominator - LCD and then add fractions with same denominator and simplify if necessary). Once the child understands one or more methods of getting to the answer they can then 'fudge' the grid method.

It's ridiculous - but at some schools you have to show you can do the 'grid method' first before you're actually allowed to do more streamlined methods. I can somewhat see the point (they're forcing you to think through the problem systematically and breaking it down into many small steps - but the odd thing about maths is that the more calculations you do the more likely a small error will creep in somewhere and ultimately the answer you arrive at will be wrong).

So 17 my advice is teach either your method or that of TeenandTween (which is useful if a common denominator is not immediately obvious) - and then once your child is good at arriving at correct answers for adding fractions - have them do it again with the grid (which is simply another way of looking at the same problem) until they get to the point where the grid more or less makes sense. Satisfy the teacher you can do the grid method - and you'll breeze through the streamlined LCD method. (Same applies for long multiplication/ division (although this tends to be handled through 'chunking').

if you need resources math drills has all sorts of free fractions worksheets here: www.math-drills.com/fractions2.shtml#adding

HTH