Calculation Policy Fractions

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1 Calculation Policy Fractions This policy is to be used in conjunction with the calculation policy to enable children to become fluent in fractions and ready to calculate them by Year 5. It has been devised to meet the requirements of the National Curriculum 05, for the teaching and learning of mathematics. It is designed to give pupils a consistent and smooth progression of learning fractions across the school, using concrete experiences and representations to develop an understanding of the underlying mathematical concepts. The policy builds progressively on from the content and methods established in the Early Years Foundation Stage, who follow the Development Matters EYFS document. In line with the National Curriculum 05, the calculation policy is organised according to year groups, addressing the age related expectations. However, it is vital that pupils are taught at the stage that they are ready for, being moved onto the next stage as soon as the concept or method is secure, or working at a lower stage until they are secure to move on. When planning, it is important that you consider the following to enable children to make cognitive connections and be effective learner s of mathematics: -the use of concrete resources (representations) to support conceptual understanding or pictures and images such as number lines and 00 squares to support mental imagery -the language that will be modelled and used -the symbols that will be used -Real-life contexts which are meaningful and will support understanding and provide opportunities to use and apply -problem solving approaches which will help children to recognise when to use certain operations and methods when faced with problems The Connections Model: Using and Applying (AT) opportunities must be a priority within maths lessons. It is important to distinguish between children knowing facts and children using methods to get to an answer, using the facts they know. 'Knowledge-led curriculum' with three forms of knowledge:

2 Factual: I know that... Procedural: I know how... Conceptual: I know why... Encourage children to be using the language of I know that/how/why... Year Representations to support the learning of objectives in bold Understand halves of shapes and sets of objects as two equal parts Group and share objects equally and relate to halves Understand halves of shapes and sets of objects as two equal parts Understand one-half as one of two equal parts Understand the word fraction as equal parts of a whole Group and share objects equally and relate to halves Understand one-half as one of two equal parts Understand the word fraction as equal parts of a whole Understand quarters of shapes and sets of objects as four equal parts Understand one-quarter as one of four equal parts Understand quarters of shapes and sets of objects as four equal parts

3 Understand one-quarter as one of four equal parts One-quarter of the whole is blue

4 Counting: Pupils should count in fractions up to 0, starting from any number and using the ½ and ¼ equivalence on the number line. Year Representations to support the learning of objectives in bold Find halves and quarters of lengths and quantities practically Read, write and understand ½ Read, write and understand ¼ Know that two-quarters are equivalent to one-half Find halves and quarters of lengths and quantities practically Read, write and understand ½ whole whole Read, write and understand ¼ Know that two-quarters are equivalent to one- half Find three-quarters of a set of objects or shape Recognise unitary fractions ½, /3, ¼, /5 of shapes whole split

5 into equal parts (denominator) part is shaded (numerator) whole is split into equal parts (denominator) part is shaded (numerator) Find three-quarters of a set of objects or shape 3 Recognise unitary fractions ½, /3, ¼, /5 of shapes

6 Year 3 Representations to support the learning of objectives in bold

7 Counting: Count up and down in tenths. Find fractions of quantities practically unitary fractions Find fractions of quantities practically unitary fractions 5 of 0 Understand how to calculate unitary fractions of quantities by dividing Find ¼, /, ¾ and / of shapes, lengths and objects Understand the numerator and denominator in proper fractions (3/, /3, /5 ), Understand how to calculate non-unitary fractions of quantities Understand equivalence of fractions through practical activities Compare and order fractions with the same denominator Add and subtract fractions with the same denominator up to whole Problem Solving: Solve problems that involve all of the above. of 0 3 of 9

8 Understand how to calculate unitary fractions of quantities by dividing 7 of 7 of 7 =? = 7 into 7 groups beads divided (numerator) group? (denominator) 7 How many beads are there in How many 7s are in? 7 How many 7s are in? Find ¼, /, ¾ and / of shapes, lengths and objects

9 3 Understand the numerator and denominator in proper fractions (3/, /3, /5 ), 5 whole is split into 5 equal parts (denominator) parts are shaded (numerator) 3 8 Denominator = = whole = total 3 counters = whole 7 split into 7 equal groups Numerator = how many parts are in the group. 3 groups out of the 7 = 3 7

10 Understand how to calculate non-unitary fractions of quantities of of 7 = = A 7 groups) Numerator = 3 (3 9 (8 9 = ) = 8 9 A x 3 =? 3 7 Understand equivalence of fractions through practical activities

11 Folding strips Fraction wall using individual cards Compare and order fractions with the same denominator 3 Add and subtract fractions with the same denominator up to whole 5 = whole = whole 5 5 lots of a lots of a 5 = whole Understand that the denominator = whole lots of a = whole - 3 = lots of a - 3 lots of a = quarter of a whole

12 Counting: Count up and down in hundredths. Year Representations to support the learning of objectives in bold Identify pairs of fractions that total Recognise that hundredths arise when dividing an object by 00 whole whole Compare numbers with the same number of decimal places up to d.p. Round decimals with d.p. to the nearest whole number. Identify pairs of fractions that total Use of fraction cards Work out equivalent fractions using diagrams Work out equivalent fractions using diagrams

13 Recognise and write decimal equivalents of any number of tenths or hundredths. Recognise and write decimal equivalents to ¼, ½, ¾ 5 Find the effect of dividing a or digit number by 0, 00, identifying the value of digits in the answer as ones, tenths and hundredths Problem Solving: Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number. Solve simple measure and money problems involving fractions and decimals to d.p What is the same? What is different? Look at the relationships. Build on reasoning and algebraic idea. Year 5 Representations to support the learning of objectives in bold

14 Counting: Continue to develop and embed. Use mixed numbers and improper fractions Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents. Use mixed numbers and improper fractions 3 = 5 7 = 5 Add and subtract improper fractions with the same denominator Compare and order mixed numbers and improper fractions with the same denominator Read, write, order and compare numbers with up to 3 d.p. Round decimals with d.p. to the nearest whole number and to d.p. Read and write decimal numbers as fractions Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents Recognise the per cent symbol (%) and understand that the per cent relates to number of parts per hundred, and write percentages as a fraction with denominator 00 as a decimal fraction Explore patterns of equivalent fractions Multiply proper fractions and mixed numbers by whole numbers Solve problems involving numbers up to 3 d.p. Solve problems which require knowing percentage and decimal equivalence of ½, ¼, /5, /5, /5 and

15 those with a denominator of a multiple of 0 or 5 Add and subtract improper fractions with the same denominator = 5 = 5 = 3 wholes 5 = whole Compare and order mixed numbers and improper fractions with the same denominator

16 Explore patterns of equivalent fractions ? 6 5 6? Multiply proper fractions and mixed numbers by whole numbers x ½ x =

17 6 ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ x ½ = +6 = 8 x ½=8 Year 6 Representations to support the learning of objectives in bold

18 Counting: Continue to develop and embed. Use common multiples to show equivalent fractions Identify the value of each digit in numbers given to 3 d.p. Solve problems which require answers to be rounded to specified degrees of accuracy Associate a fraction with a division and calculate decimal fraction equivalents (e.g ) for a simple fraction (e.g.3/8) Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts Use common multiples to show equivalent fractions Use common factors to simplify fractions Compare and order fractions by converting them to fractions with a common denominator Add and subtract fractions with different denominators Multiply proper fractions and mixed numbers by whole numbers Divide proper fractions and mixed numbers by whole numbers Multiply digit numbers with up to d.p. by whole numbers 3 Multilply both the numerator and denominator by = 3 6 Or 3 Multilply both the numerator and denominator by 5 = 0 3 5

19 Multiply and divide numbers by 0, 00 and 000 where the answers are up to 3 d.p. Identify the value of each digit to 3 d.p. and multiply and divide numbers by 0, 00 and 000 where the answers are up to 3 d.p. Use written division methods in cases where the answer has up to d.p. Problem Solving: provide a wide range of problem solving opportunities involving fractions, decimals and percentages Use common factors to simplify fractions 6 Find the smallest number, other than, which is a factor of 8 both the numerator and denominator. (3) Find the smallest number, other than, which is a factor of both the numerator and denominator. (3) 9 The smallest number, other than, which is a factor of both the numerator and denominator is 3 Simplify both the numerator and denominator by dividing each by = 8 6 Simplify both the numerator and denominator by dividing each by = 3

20 Compare and order fractions by converting them to fractions with a common denominator 8 Find the smallest number, other than, which is a factor of both the denominators. Both denominators are divisible by =?? = Whatever you do to the denominator you do to the numerator. / Whatever you do to the bottom, you do to the top = 3 3

21 7 8 = Compare 3 3 also use: < > = Compare 8 also use: < > = Add and subtract fractions with different denominators First, find the common denominator. Build on children s knowledge of arrays x = common denominator = = 5 0?? 0 0 Whatever you do to the denominator you do to the numerator. / Whatever you do to the bottom, you do to the top. = 0 0

22 x x 5 = = x x = Subtract fractions with different denominators First, find the common denominator. Build on children s knowledge of arrays x = common denominator = 0-3 = 5 0?? = 0

23 0 0 Whatever you do to the denominator you do to the numerator. / Whatever you do to the bottom, you do to the top. 0 3 x x 5 3 = = x x 5-0 = Multiply proper fractions and mixed numbers by whole numbers x ½ x =

24 6 ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ ½ x ½ = +6 = 8 x ½=8 Divide proper fractions by whole numbers /3 divided by = /6 whole split into thirds third divided by = /6

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