A brief summary of some of the most important fraction concepts to be taught in Year 4. Fractions Children should be able to understand the meaning of and be able to spell and read these words: Fraction, half, quarter, eighth, third,  sixth,  fifth,  tenth,  twentieth. The reading of fractions is important and 1/10 for instance should be read as 'one tenth'. Other simple fractions should be recognised such as 3/4  and 4/5. Following on from previous work on fractions, children should understand the relationship between fractions of different sizes, for example that one half is more than one quarter, but less than three quarters. As an extension, they should know that a mixed number lies between the two whole numbers on either side, for example that 4 and 3/4  is between 4 and 5.  They should be able to see whether familiar fractions involving quarters and eighths are smaller or more than one half. Equivalent fractions. The key to understanding fractions is equivalent fractions.  With a good understanding of the idea of equivalence and one or two further ideas, most problems in fractions may be solved easily and quickly. This idea will be introduced this year and developed further in subsequent sets of worksheets. Equivalent fractions are fractions that look different, but have the same value, e.g.  3/6  and 1/2. Children should be able to establish equivalence by sorting a number of items into different groups and should know some simple equivalencies such as 4/6  equals  2/3 . Children should be able to see whether simple fractions are more or less that one half. They can do this by putting the fractions on a  0 to 1 number line. When using fractions with young children, they should be written with a horizontal line rathere than a sloping line. Decimal fractions By the end of Year 4 children are expected to be able to read and write decimal fractions to two decimal places and understand the importance of the decimal point. Children will begin to work to two decimal places when using familiar measurements, especially money and metric length. Part of this is recognising in money, for example, that the first number after the point is tenths, which can be thought of as the number of 10p coins. Practical work on this, using real coins, is always very helpful. Avoid only using one figure after the decimal point in the context of money because £4.5 means four pounds fifty and not four pounds and five pence (£4.05).  In a similar way 5.5 m means 5 metres and 50 cm ( not 5 m and  5 cm). Number lines are again important in helping children read and order simple decimal fractions eg numbers between 1 and 2. Calculators may be used, but only as a tool to display the results of mental arithmetic e.g. in one step change 5.32 to 5.39 . In questions such as this the calculator is of no help if the child does not understand place value. Much of this work will also reinforce the language of mathematics - less than, more than, count on, count back etc. Some of the hardest work involves adding or subtracting using mixed units e.g. 1.4 litres + 300 millilitres. Children will need a secure grasp of the decimal system in order to answer these correctly. The relationship between fractions and decimal fractions is a crucial one to develop. Initially, this will be with simple fractions such as 1/2 and 1/4 as well as tenths. Again, the calculator can be used, with the fraction e.g. 7/10 being seen as a division calculation:  7 divided by 10 = 0.7 Games such as snap, or matching cards, are very good ways of building this relationship. Ratio Children should be familiar with the following vocabulary: In every,  for every. Children should be able to handle problems involving simple ratio and proportion and know that 2 in every 5 means 4 in every 10 etc. They should be able to construct simple patterns in which, for example, every fourth square is coloured. A good introduction to ratio is to use a ‘feely bag’ with a number of cubes in it of  two different colours. Children take out one cube at a time, up to a total of about 10. They record the ratio of the cubes taken out e.g.             red:blue    3:7 Before taking any out try to predict the outcome. Change the number of one colour of cubes etc. Go to fractions and ratio concepts