# A Progression in Fractions worth considering

Thanks to Caroline Clissold for this month's maths blog which explores how children can progress in Fractions from Year 1 to Year 6.

I spent the summer mulling over the national curriculum requirements for fractions – as one does! I compared the way we teach fractions to the way they teach it in Singapore. In Singapore, children add and subtract fractions with the same denominator and explore equivalences in Year 2. I believe that we should be doing that as and when the opportunity arises, which it does in Year 1.

I feel sorry for Year 5 and 6 teachers who seem to spend a great deal of time playing catch up with areas of fractions that should have been mastered in previous years instead of focussing on the requirements for their years.

I find the progression for fractions in Years 3 and 4 quite weak. Children are expected to spend far too long adding and subtracting fractions with the same denominator which seems quite unproductive when they could be adding and subtracting fractions with the same denominator in Years 1 and 2.

Here is a suggested progression that would be worth considering.

In Year 1, children are required to recognise, find and name halves and quarters. Using strips of paper, they could keep one whole, fold a second in half and a third into quarters. If they then examine these, they will notice that two halves are equivalent to one whole, four quarters are equivalent to one whole and two quarters are equivalent to one half. This is the early stage of equivalent fractions. They could cut the parts up and arrange them to make addition and subtraction statements.  You could begin to sow the seeds for mixed numbers and improper fractions when counting in halves, for example, In Year 2, the children could count in thirds. We are not teaching improper and mixed numbers, just sowing the seeds and letting children know that they exist!

In Year 2, the children could be exploring other fractions with the same denominator and not be restricted to halves, quarters and thirds. Give them cubes, ask them to make a bar of four of the same colour. What is the fraction of each part? From their experience in Year 1, they should be able to tell you that each is ¼. Ask them to substitute one cube with another of a different colour. What addition and subtraction number statements can they make? Now do this with three cubes, then five, six, seven and eight. Ask them to make addition and subtraction statements, for example, They could also use cubes to work on adding fractions that are less than one, for example,
3/8 + 2/8 = 5/8. Expect them always to record the other commutative and inverse facts that they can make from their first statement. This is based on the approach they take in Singapore and it is so sensible.

They could begin to explore equivalences using cubes. In each model we can see that half the cubes are pink, so ½ is equivalent to 2/4, 3/6 and 4/8. The whole is different each time but the fraction that are pink is the same. In Year 3 they could move on to adding and subtracting fractions within multiples of the same denominator within one, for example halves, quarters and eighths and thirds, sixths and twelfths. This could be carried out through fractions walls, for example, From this they can see that, for example, ½ + ¼ + 2/8 = 1.
The children could explore equivalences between these fractions and begin to discover the generalisation that they can multiply or divide the numerator and denominator by the same number to give an equivalent fraction.
The children could count in different fractions in order to keep the idea of mixed numbers and improper fractions familiar.

In Year 4, children could add and subtract fractions with multiples of the same denominator but this time that are greater than one. For addition, they will need to change improper fractions to mixed numbers. They are already familiar with these, so now is the time to discover how to convert from on to the other.

In following this route, by the time the children reach Year 5, they will be confident at adding and subtracting fractions and be ready to move onto adding and subtracting other fractions by finding common denominators. They will also have time to master multiplying fractions by whole numbers and percentages.

In Year 6, there will be no catch up! Children will be able to really focus on multiplying fractions by fractions and dividing fractions by whole numbers.

Now wouldn’t that be wonderful!!

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Mathematics, Maths

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