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Cirencester Primary School Fractions Policy Updated March 2017 “Fair’s Fair!” – Whatever you do to the top, you do to the bottom. -ELG: Solve problems including doubling, halving & sharing practically using objects -Exceeding: Solve problems including doubling, halving & sharing using actual numbers. 6 objects ... 6 YR Half of 6 = 3 ... -Recognise, find and name a half as one of two equal parts of an object, shape or quantity -Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity Give shapes and chn find half Half & half again Fractions are fair Y1 Chn to chop shapes in half Link to concrete that ½ is also ÷ 2 8÷2=4 ¼ of 8 = ½ of 8 = 4 ½ of 4 = 2 Therefore ¼ of 8 = 2 -Recognise, find, name and write fractions ⅓, ¼, ²⁄₄, ¾ of a length, shape, set of objects or quantity -Write simple fractions eg ½ of 6 = 3 and recognise the equivalence of two quarters and one half Shape ½ of 12 = Shade in half of the grid 6 parts of the grid are shaded, so ½ of 12 = 6 Quantity ¼ of 12: Divide by denominator. So 12 ÷ 4 = 3 Use a fraction wall to show the equivalence of two quarters and one half 1 Whole Y2 ½ ¼ Length Use string, fold in half to find half and again to find quarter Partition number. Eg ½ of 48cm Half of 40 = 20 Half of 8 = 4 20 + 4 = 24cm Chn can find ¼ and use repeated addition to find 2 , 3 and 4 4 4 4 ½ ¼ ¼ ¼ -Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing onedigit numbers or quantities by 10 U Y3 1 DP . . . . . . . . . . Tnths 1 2 3 4 -Recognise, find and write fractions of a discrete set of objects: unit fractions and nonunit fractions with small denominators -Recognise and use fractions as numbers: unit fractions and nonunit fractions with small denominators -Recognise and show, using diagrams, equivalent fractions with small denominators See Y2 quantity ¼ of 12 Shade in ¼ Shade in ½ Divide by the D Multiply by the N -Add and subtract fractions with the same denominator within one whole (eg ⅗ + ⅕ = ⅘) -Compare and order unit fractions with the same denominator Add N’s together 1 + 2 As D is the same, chn need to look at N only and order depending on size. 4 4 1+2=3 See Y5 smaller equivalent fractions Leave denominator as it is. Therefore 4 3 6 4 7 8 9 1.0 ÷ 10 = 0.1 Relate to money: £ and p £1.10 = 1 and 1 = 110p 10 Do the same for subtraction but take away N’s instead, leaving the D as it is! 2 3 4 4 4 4 -Solve problems that involve all of the above - - - - Recognise and sf how, using diagrams, families of common equivalent fractions Count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten Recognise and write decimal equivalents to ¼, ½, ¾ Recognise and write decimal equivalents of any number of tenths or hundredths 1 = = 2 x5 x5 5 10 1 is shaded 10 Y4 5 is shaded 10 Ensure pupils are shown a wide range of shapes and visual ways to represent fractions U DP . . . . . . . . . . Tenths 0 Hundredths 1 0 2 0 0 3 4 0 5 0 6 0 7 0 8 0 9 1 0 N ÷ D will give you fraction to decimal DP 1 4 1.00 ÷ 4 = 0.25 . . . Tnths 7 Hths Tenths 7 7 Thths Adding Subtracting decimals to 1/100 0.02 + 3. 5 = ¼ of 8 = ¾ of 8 = 1 Hundredths 1 7 Thousandth 1.0 ÷ 100= 0.01 Relate to money: £ and p £1.01 = 1 and 1 = 110p 100 Fractions of quantities Therefore 0.7 = 7 tenths = 7 10 If you have a digit in the 100th column that is not a 0 then it represents 100ths e.g. in 0.71, the 7 represents tenths and the 1 represents hundredths Mixed Numbers 13 / 15 + 9 / 15 = Adding and subtracting fractions, where the denominator is the same -Solve simple measure and money problems involving fractions/decima -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 Finding a fraction of a number ÷ by D X answer by N 5 7 + 2 7 3 12 1 12 2 8 of 72 72 ÷ 8 = 9 9 X 2 = 18 Therefore 2 of 72 = 18 8 -Read and write decimal numbers as fractions [eg 0.71 = 71/100] Recognise the value of the digits: tenths, hundredths or thousandths Place over appropriate denominator [D for down, D being the bottom of the fraction] DP . . . Tnths 7 Hths Tenths 7 7 Thths N Numerator D Denominator 3X½ Multiply whole number by numerator 3X1=3 Leave denominator as it is = 2 3 Therefore ____ 2 1 Hundredths 1 -Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams 7 Thousandth 7 tenths therefore 7/10 71 hundredths therefore 71/100 717 thousandths therefore 717/10002 7X4¼ Multiply the two whole numbers 7 X 4 = 28 Multiply whole number by numerator 7X¼= # 7 = 4 Therefore 28 Y5 1¾ + 1 ¾ = 29 ¾ -Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths ‘Fairs Fair’: whatever you do to D you must do to N Smaller equivalent fractions Find a number you could divide both the N and D of the fraction by. 8 ____ 80 ÷ by 8 ÷ by 8 1 Therefore 10 Larger equivalent fractions Multiply both the N and D by the same number X by 2 6 ____ 18 X by 2 -Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements >1 as a mixed number [eg ⅖ + ⅘ = 1⅕] -Add and subtract fractions If both denominators in the fraction are the same: -Compare and order fractions whose denominators are all multiples of the same number Improper fraction to mixed number Add N’s together Find LCD 12 ____ 8 0 1 r4 8 1 12 12 ÷ 8 = 1 r 4 The remainder is recorded as a fraction 4 Therefore 1 ___ 8 Mixed number to improper fraction 4 5 ___ 2/5 of 25 8 Multiply whole number by D 5 X 8 = 40 Add on your numerator 40 + 4 = 44 Leave denominator as it is 2/3 of 66 Therefore Fractions of Quantities 1/5 of 20 Therefore 12 36 44 _____ 8 1 2 ____ + ____ 4 4 1+2=3 Leave denominator as it is 3 Therefore ____ 4 If both denominators in the fraction are ifferent: d Find a LCD [lowest common denominator: a number that will appear in both the D times table] 1 2 ____ + ____ 4 8 LCD = 8 Leave a fraction alone if it already has the LCD X by 2 1 ____ 4 2 ____ 8 X by 2 ‘Fairs fair’ whatever you do to D you must do to N Now add N Therefore 2 4 2 ____ + ____ = ____ 8 8 8 ‘Fairs fair’ whatever you do to D you must do to N Once D is the same for all fractions, use the value of the N to compare and order the size Which is larger? 1 2 ____ or ____ 4 8 LCD = 8 Leave a fraction alone if it already has the LCD X by 2 1 ____ 4 2 ____ 8 X by 2 ‘Fairs fair’ whatever you do to D you must do to N They are therefore equal. -Solve problems which require knowing percentage and decimal equivalents of ½, ¼, ⅕, ⅖, ⅘ and those fractions with a denominator of a multiple of 10 or 25 -Associate a fraction with division to calculate decimal fraction equivalents (eg 0.375) for a simple fraction [eg ⅜] 3 8 3÷8 0. 3 7 5 Y6 .30 Find LCD ‘Fairs fair’ whatever you do to D you must do to N N÷D 8 3 -Compare and order fractions, including fractions >1 6 0 40 Therefore 3 = 0.375 8 Once D is the same for all fractions, use the value of the N to compare and order the size Which is larger? 1 2 ____ or ____ 4 8 LCD = 8 Leave a fraction alone if it already has the LCD X by 2 1 ____ 4 2 ___ 8 X by 2 ‘Fairs fair’ whatever you do to D you must do to N They are therefore equal. -Multiply simple pairs of proper fractions, writing the answer in its simplest form [eg ¼ x ½ = ⅛] -Divide proper fractions by whole numbers [eg ⅓ ÷ 2 = ⅙ ] -Use common factors to simplify fractions; use common multiples to express fractions in the same denomination ½ 4/8 NXN Multiply the denominator by the whole number To simplify: Find LCD = 4 DXD 2X3=6 Numerator stays the same ¼x½ 1X1=1 4X2=8 1 Therefore = 1 8 6 -Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions Fairs Fair! Whatever you do to D you must do to N 4 ÷4 1 12 ÷4 3 To express fraction in same denomination multiply both D and N by a whole number 1 X4 4 2 X4 8 Add and subtract fractions with different denominators and mixed numbers: See Y5 Add and subtract mixed numbers, 34 8 - 1 2 4 1. Change both fractions into improper fractions 2. Make denominator the same by finding LCD 3. Simply add/subtract numerators and denominators 4. Change back to mixed fraction if appropriate -Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts F 1 _ 10 D 0.1 % 10 F to D you do N÷D % to D you ÷10 D to % you X10 Chn must know 1 3 2 3 0.33 33% 0.66 66%