# A problem with fractions

A. There is great pressure on teachers to get the highest possible grade in Sats. A technique can be hammered into a child so that they regurgitate the answer with no real understanding. However, if the context changes or they don't practise it for some time they may have problems. Always look to the longer term - difficult to do when schools are judged by results, but a deeper understanding and greater flexibility does lead to better results in the long term.

Just in case some pupils have for any reason missed out on the building blocks for understanding converting fractions to decimals and vice versa, I would begin using the place-value grid and work on changing decimals to fractions using 0.1 = 1Z10, 0.01 = 1Z100 and 0.001 = 1Z1000 .

Next, use fractions with one digit after the decimal point. Begin with 0.3, 0.7 and 0.9. Then use some that require cancelling to get the simplest equivalent fraction, such as 0.5. They might tell you straight away it is a half. If so, ask them to explain why: (0.5 = = 12 ). Some useful revision of equivalent fractions and cancelling! Next, ask about 0.2 (0.2 = = 1Z5), and so on.

Now introduce some mixed-number equivalents such as 2.4.

Then I move on to fractions with two digits after the decimal point, such as the straightforward 0.03 or 0.07, and those where the simplest equivalent fraction has to be found, such as 0.05.

The next stage is to look at fractions containing tenths and hundredths, and how these combine to give the fraction in hundredths. For example 0.13, which is one tenth plus three hundredths. To add them, the bottom numbers have to be the same, so both are changed into hundredths. Ask the pupils at each stage what has to be done to add the two fractions together. Ask them if they can see the connection between 13Z100 and 0.13. They might suggest themselves that, because the decimal fraction ends at the hundredths, you just put the numbers above the 100.

After that, you can look at fractions that need the simplest fraction to be found, such as 0.25 or 0.24. This is important because it makes changing fractions to decimals easier to understand.

Now look at changing fractions to decimals. Once again, it is useful to have a place-value chart available for pupils to write in. Begin with those fractions that are in tenths. Ask them how you would write 7Z10 on the chart. Discuss the fraction 2Z5, asking if this can be made into tenths = 4Z10. This is revision of equivalent fractions.

Include other examples where the denominator is a factor of either 10 or 100.

Introducing top-heavy fractions , say 17Z10 , can add interest. When I try this, pupils like to put the 17 under the tenths (in the same square on the place-value grid). Ask them to write this fraction as a sum of fractions, for example 5Z10 + 12Z10; leading them, through questioning, to 10Z10 + 7Z10 = 1 + 7Z10. So 1.7 is the equivalent decimal fraction.

Recently, I taught a Year 6 boy this topic via the internet using i-teach.

We were both using headsets and a webcam, and there was a whiteboard that we could both write on.

We began with long division, the topic for our previous lesson. A PowerPoint presentation of the lesson was pre-loaded to lead the learning, but we did occasionally digress!

You can see (and hear) the lesson by going to www.mathagonyaunt.co.uk and clicking on i-teach, then archive. If you would like a copy of the PowerPoint presentation then please email me.

* The i-teach website is at www.i-teach.com

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