Comparing fractions (part 2)



Comparing fractions - how many segments?

How do you compare fractions with different denominators? Comparing fractions is a nightmare for pupils and teachers. This is a very difficult subject to teach and probably an even worse topic to learn. Put this on an examination paper and you will separate the wheat from the chaff, and mostly it will be chaff. How can we be more successful and not have to teach it year after year to the same pupils.

Possibly the root of the problem is fractions are hard to understand. Read the quote below does it ring any bells?

“It has been said that ‘fractions’ have been responsible for putting more people off mathematics than any other single topic.  In fact the very word fraction has been known to make strong men wince!”

(Nuffield Maths 3 Teachers’ Handbook: Longman 1991)

Starting the journey

Here is one way that I have adopted which has proved successful, it involves using a graphical method. The pupils draw the fractions in equal size grids, then compare. You have to guide them with the size of the fractions.

It does of course rely on them being able to employ the strategy outlined in my previous blog which has the gripping title Comparing fractions (part 1).

So for example they are asked to compare 4/5 with 2/3. Which of these two fractions is bigger? Give them two grids like those below which are 3 x 5.

If they have been given enough practice and help with the previous work they should be able to produce grids which look like this.

They should be able to spot that 4/5 is bigger than 2/3 simply by counting the squares. I suggest you do a number of questions like this. This practice is vital and will form the basis of further discussion.

Moving forward

Of course it my not be possible to draw grids every time. We may want to use a numerical method but we can now link the two, graphical and numerical. Using the example above point out we have used grids that are 3x5 and surprise, surprise that matches the values of the two denominators.

Chose another example you have given them, say compare 3/5 and 4/7, the grids they used to compare these should have been 5x7, and point out that the dimensions match the denominators. After several examples they should get the idea.

Destination

Inform the pupils that this is no coincidence. The denominators have to be the same just like the grids were the same. Using the first question you can now demonstrate that the denominators can match the dimensions of the grid. So

4 x 3 = 12        2 x 5 = 10

5 x 3    15        3 x 5     15

The link between the grid fractions shown diagrammatically and how we compare fractions numerically is made. The visual is really important for lot of kids, they cannot jump straight to the numbers, this approach also establishes the only way we can compare fractions, by using equivalent denominators.

Does anyone else have another way of comparing fractions? If so we not leave a comment.

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