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National Curriculum: Fractions (including decimals and percentages) Year 6 - Making Connections

Created on 15 October 2013 by ncetm_administrator
Updated on 18 December 2013 by ncetm_administrator

Making Connections

Teachers should use every relevant subject to develop pupils’ mathematical fluency. Confidence in numeracy and other mathematical skills is a precondition of success across the national curriculum.

Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics.

(National Curriculum in England Framework Document, September 2013, p9

Connections within Mathematics

There are many connections and these need to be discussed with pupils. They need to see that fractions are numbers in their own right, and can, thus, be placed on a number line. They need to understand how fractions are linked to division – using both sharing and grouping. Also the link to multiplication and finding factors, and that fractions express a relationship between 2 groups, e.g. 3 out of these 4, the proportion.

Making connections to this topic in adjacent year groups

Year 5

  • compare and order fractions whose denominators are all multiples of the same number
  • identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
  • recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 25 + 45 = 65 = 1 15
  • add and subtract fractions with the same denominator and denominators that are multiples of the same number
  • multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
  • read and write decimal numbers as fractions [for example, 0.71 = 71/100]
  • recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
  • round decimals with two decimal places to the nearest whole number and to one decimal place
  • read, write, order and compare numbers with up to three decimal places
  • solve problems involving number up to three decimal places
  • recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal
  • solve problems which require knowing percentage and decimal equivalents of ½, ¼, 15, 25, 45 and those fractions with a denominator of a multiple of 10 or 25.

Key Stage 3

  • work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 72 or 0.375 and 38 )
  • define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%
  • interpret fractions and percentages as operators
  • express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
  • use ratio notation, including reduction to simplest form
  • divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
  • understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
  • relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions
  • solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics
  • solve problems involving direct and inverse proportion, including graphical and algebraic representations

Cross-curricular and real life connections

Learners will encounter fractions in many different real life contexts:

  • When shopping, children can compare prices presented in decimal form. Consider reductions in price when the reduction is given as a fraction (e.g. ‘one third off’) or percentage (‘20% off today’). Sharing the cost of a total bill equally in a restaurant provides a useful context in which to practise estimation of fractions as well as calculating.
  • Fractions skills can be also emphasised when focusing on measurement. Journey times and fuel consumption can be estimated and calculated (e.g. what fraction of the journey do we have remaining?) Measurement of area and perimeter is strongly linked to work with fractions, ratio and proportion; what proportion of the playground needs to be set aside for ball games?
  • When interpreting and evaluating data children will need to use their fraction knowledge. E.g. Half a million people are earning 20% below the minimum wage
  • Issue 11 of the NCETM Primary Magazine provides wonderful links to the work of artist Mondrian, with a focus on fractions and decimal work.

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