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Fractions teaching

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Introduction

Maths Assignment Fractions form part of the Number and the Number System strand in the Framework for the National Numeracy Strategy (NNS). They form part of a wider topic of fractions, decimals, percentages, ratio and proportion. Work on this topic begins in the foundation stage, and progresses across Key Stages one and two, becoming more broad and deep as it does so. Teaching in this area must consider this progression, accounting for different ages and ability levels, so the progression is steady and new concepts are introduced that build on others which are secure. In doing this, teaching must also be aware of the possible misconceptions which may arise in children, so they are anticipated and planning is used to either overcome or avoid them. Details of how fractions are reflected in the foundation stage, Key Stages one and two curriculum and the NNS can be found in Appendix 1 and 2. The five strands of the NNS are highly interconnected and aim to provide children with the confidence and flexibility to use and apply mathematical principles. The topic of fractions is integrated with all of the strands. It forms part of the Number and the Number system strand, as part of a wider understanding of fractions, decimals, ratio and proportion. ...read more.

Middle

Children also begin to position halves on a number line as a means of comparing fractions with whole numbers. Their work in this direction complements other areas in telling the time and movement through turns. Work in Year three develops fraction vocabulary to include thirds and tenths and extends their equivalence knowledge to include tenths, quarters and halves up to a whole. Pictorial representation is now more complex and shows a step towards problem solving, including the concept of estimating fractions from practical examples. Number lines are used to show ordering of simple fractions as is counting in halves, quarters, etc. In Key Stage two the topic of fractions is extended to using fraction notation and recognising equivalence, recognising the equivalence between decimals and fractions, ordering familiar fractions, finding fractions of numbers and quantities and recognising the equivalence between percentages, fractions and decimals in Years five and six. In recognising equivalence in Year four, pictorial representation is still used, but becomes a tool to aid rather than a puzzle. Fraction walls are useful at this stage. The concept of equivalence is more abstract in years five and six children develop the idea of twentieths, hundredths and thousandths. They learn the vocabulary of numerator and denominator and begin to generalise the idea of equivalence as being both numerator and denominator multiplied by a common factor. ...read more.

Conclusion

One possible misconception that may arise in dealing with fractions is the child not attending to the size of the denominator as being the division of the unit and the numerator as the number of the parts. This may become particularly apparent towards the end of Key Stage two, when children begin to order fractions with different denominators. Swan (2001) describes a method of multiple representations of the fraction to use as tools to help children to grasp the concept. In this, a set of cards with the relevant fraction on are used, along with pictures of the fractions as a shaded part of equal squares and cards of the fractions marked along a number line. The children work in groups to put the corresponding representations with the right fractions and then go about ordering them. Through practical group work and peer discussion the misconceptions are confronted and new reasoning created. A plenary could be used to reflect on the different methods children used to order the cards and which representation they found most useful. Fractions teaching is a highly complex and sophisticated topic to teach effectively in primary schools. Teachers should be aware of the links the topic has with others, the progression that is expected of the children across the year groups and the possible misconceptions and strategies to correct them in order to encourage children to be able to use fractions with fluency and confidence. ...read more.

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