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Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Addition Subtraction Multiplication Stage E Stage E Stage E HTU + TU, then HTU + HTU. Cross 10s, 100s boundary. Add least significant figures first. Check for mental approach first before written method. HTU – TU, then HTU – HTU Extend to simple decimals with or without exchange from pence to pounds. Ensure that all calculation is checked before started for any other possible ‘tricky’ bits. Ensure that the setting out is accurate. Know table facts up to 12 x 12. Partitioning / distributive law Pupils to explain the effect of multiplying by 10 and 100 Addition to be done mentally. Continue to partition TU x U 754 – 86 = 668 23 x 8 Record steps in brackets then move to working without. Double lines for answer. + 625 48 13 (5+8) 60 (20 + 40) 600 (600 + 0) 673 Take away -6 Record using grid notation. Support the grid by using multiplication sentence. X ← -80 ________________________ 668 674 754 20 8 Use Multiplication grid itp to support teaching the grid method. Find the difference Plot landmarks on number line first. +14 +600 http://www.taw.org.uk/lic/itp/mult_grid.html +54 Stage E Know by heart multiplication facts up to 12 x 12. Relate fractions to division. ¼ means ÷ 4 Know ÷ 4 is the same as halve and halve again. Approximate answer first using multiplication facts Recognise that division is noncommutative. Know that a number cannot be divided by 0. Divide any integer up to 1000 by 10 3 23 x 8 = 184 205 + 176 11 70 300 381 Division “900 ÷ 10 = 90 because the digits move one place to the right” Reinforce finding of remainders on the number line (adding on or subtracting) 21 ÷ 5 “What do I know? I know that 61 is not a multiple of 5, so there will be a remainder.” ____________________________ 86 100 700 754 10 x 5 2x5 ___________________________ 0 50 60 61 22 Yr 4 to 5 age appropriate. + 356 97 13 140 300 453 Add mentally from top or bottom. Simple decimals £ and pence notation (fix the decimal point) To use the money target boards to extend decimal notation http://nsonline.org.uk/node/47820 £ 0.45 0.55 + 0.32 0.12 1.20 1.32 (fix the decimal point) Decision making to include the use of the calculator William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Complimentary addition - Short multiplication for TU x U 754 86 14 (100) 600 (700) 54 (754) 668 Most significant digit first. 23 x 7 140 (20 x 7) 21 (3 x 7) 161 Simple decimals: Fix the decimal point. Move to least significant digit. £ 8.95 - 4.38 .62 (5.00) 3.00 (8.00) .95 (8.95) 4.57 Decomposition Record remainders in fraction or decimal notation when appropriate 61 ÷ 5 = 12 r 1 12 r 1/5 12 r 0.2 Continue to use partitioning/rearranging method. 69 ÷ 3 = 23 x 7 21 ( 3 x 7) 140 (20 x 7) 161 60 ÷ 3 = 20 9÷3 =3 69 ÷ 3 = 33 Move to extending using bigger numbers on grid. 96 ÷ 6 754 700 and 50 and 4 - 86 80 and 6 Use chunking method for TU by U division 60 36 ↓ ↓ 10 6 Exchange 96 ÷ 6 = 16 140 80 60 (because 6 ÷ 3 = 2 ) “What do I know? 6 x 10 = 60” “ It’s tricky to take 6 from 4 and 80 from 50 because it becomes a negative answer” 754 600 - 86 600 12 lots of 5 and a remainder of 1 which can be seen on the number line. 61 ÷ 5 = 12 r 1 4 6 6 =668 23 Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Decomposition £ 8.95 = -4.38 £ 8 . 90 4 . 30 Underline the non-divisor. 6x6 5 8 ____________________________ 0 36 96 “ 5 takeaway 8 is tricky because it becomes a negative answer” For children who are secure on the number line, begin to move to vertical takeaway chunking method – relating to subtracting chunks along a number line: Exchange 8.95 = -4.38 8 . 80 4 . 30 4 . 50 10 x 6 15 8 7 = £4.57 96 ÷ 6 = Insist the answer is written in the original algorithm if given a space or in a number sentence if given an = sign 96 - 60 36 - 36 0 (10 x 6) ( 6 x 6) Placing the answers back into the original number sentence. 96 ÷ 6 = 16 24 Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Interactive Teaching Programs that could support a range of teaching methods, suitable for calculating at Stage E. Addition Subtraction Multiplication Division Bead sticks Add subtract 1, 10, 100, 1000 Complements Counting on Counting stick Data handling Counting stick further options Counting Counting on Doubling & halving guidance) Difference Number spinners Doubling & halving guidance) Function Blocks Number line Twenty cards Place value Tell time Moving digits Decimal target board Function Blocks Make numbers Make numbers guidance Place value Midpoint guidance Money problems Patterns of Make numbers Make numbers guidance Number spinners Guess my number Guess my number guidance (PDF) Midpoint half way between Counting stick further options Doubling and halving Doubling and halving Number facts Tell time Twenty cards Calculate percentages Twenty cards Grouping Converting measures Grouping Multiplication array Converting units of measure Multiplication array Number line Counting stick Number line Converting units of measure Function Blocks Counting stick further options Function Blocks Counting stick Doubling and halving Multiplication board Counting stick Data handling Number line Number facts Add subtract 1, 10, 100, 1000 Twenty cards Counting Function Blocks Moving digits Midpoint half way between Multiplication board Multiplication facts Doubling & halving guidance) Facts and place value Multiplication facts Number dials Guess my number Guess my number guidance (PDF) Number dials Make numbers Make numbers guidance Multiplication grid Place value dots Money problems Multiplication tables Sum Product Difference Sum Product Difference Guidance (PDF) Multiplication & division facts 2-6 Order numbers on a number line Patterns of calculations Moving digits Moving digits Calculate percentages Converting measures Counting stick further options Doubling and halving Doubling & halving guidance) Facts and place value Multiplication grid Multiplication tables Multiplication & division facts mixed 25 Make numbers Make numbers guidance Multiplication & division facts 2-6 Remainders Multiplication & division facts mixed Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 calculations Target practice Multiplication & division trios Place value charts & partitioning tool Place value chart & partitioning tool guidance (PDF) Multiplication & division with partitioning Multiplication grid Multiplication grid guidance (PDF) Place value dots Sum Product Difference Sum Product Difference Guidance (PDF) Multiplication & division trios Multiplication & division with partitioning Place value dots Prime factors Target practice Place value charts & partitioning tool Place value chart & partitioning tool guidance (PDF) Target practice Timed number bonds Place value dots Prime factors Which number where Target practice Which number where 26 Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Addition Subtraction Stage F Stage F HTU + HTU, then ThHTU + ThHTU. Approximate using the most significant digit, rounding skills. Check using the inverse. Refer to the carried digit as a ten or a hundred. Decision making -appropriate teaching/use of the calculator. Consolidate decomposition. (HTU – HTU) (ThHTU – ThHTU) (THHTU – HTU) Pupils taught to cross out the numbers and replace them with the exchanged number. Consolidate decimals Check answers through inverse and equivalent calculations. 587 + 475 12 150 900 1062 587 + 475 1062 11 Multiplication Stage F Know all multiplication facts to 12 x 12. Approximate first, appropriate use of the calculator HTU and U, TU x TU to be introduced with the grid method first. HTU x U TU x TU 346 x 9 Continue to consolidate rearranging with Diennes. X 300 1 ten to carry over. 80 add 70 equals 150 and the one ten to carry makes 160. That’s 6 tens and 100 to carry over. 500 add 400 equals 900 and the one hundred to carry makes 1000” 40 6 9 346 x 9 = 3114 Addition to be done mentally or across followed by column addition 28 x 27 X 20 27 20 What do I know? 3 x7 = 21. 210 14 ↓ ↓ 30 2 224 ÷ 7 = 32 Column addition one ten from 50 which leaves 40 and makes 14 in the units. 40 to subtract 80 is tricky. I will rearrange one hundred from 700 and make 140. 600 to subtract 200 is 400. 14 subtract 6 equals 8. 140 subtract 80 equals 60 and 600 subtract 200 equals 400.” Know all multiplication facts to 12 x 12 Use the relationship between multiplication and division Extend chunking method to include HTU by U, with an integer remainder Dividing up to 10,000 by 10/100 Check with inverse operation. Use of calculator. 224÷ 7 Teach checking strategy “4 to subtract 6 is tricky. I will rearrange Stage F Partitioning method when numbers are easy. 754 = 600 140 14 - 286 200 80 6 400 60 8 = 468 “ 7 add 5 equals 12. That’s 2 units and Division 8 Relate fractions to division and calculate fractions of amounts. http://www.teachfind.com/nationalstrategies/unit-3-ict-resources-1 William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Yr 4 to 5 age appropriate. Short method column subtraction: 7648 + 1486 14 120 1000 8000 9134 7648 + 1486 9134 111 12.45 7.36 + 24.50 11 1.20 13.00 30.00 44.31 Carry below the line under appropriate column Language must be in the context of place value. - 754 286 468 Use the number line to find remainders and express the quotient as a fraction or decimal. 222 ÷ 5 7 Column addition 28 X 27 = 756 “What do I know? 222 is not a multiple of 5” 4x5 £2.73 x 3 40 x 5 £ ____________________________ 0 2 22 222 £2.73 x 3 = 273p x 3 “When I have a number left which is smaller than the divisor I know it’s a remainder.” x 200 44 r 2 70 3 3 600 210 9 273p x 3 = 819p = £8.19 (Continue to use ITP multiplication) http://www.taw.org.uk/lic/itp/mult_grid.html 28 or 44 2 5 or 44.4 Use vertical chunking method if secure on number line. 196 ÷ 6 is approximately 30 because 6 x 30 = 180 196 180 (30 x 6) 16 12 (2 x 6) 4 196 ÷ 6 = 32 r 4 or - 32 2 3 Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Division of numbers involving decimals using chunking method. 87.5 ÷ 7 = 87.5 ÷ 7 is approximately 12 (12 x 7 = 84) 87.5 - 70.0 17.5 14.0 3.5 3.5 0.0 (10 x 7) (2 x 7) (0.5 x 7) 87.5 ÷ 7 = 12.5 Underlining non divisor. Answers written as part of a number sentence (Overcoming Barriers Level 4 to Level 5 typical questions) Work out 575 ÷ 25, explaining your method. Peter says that, if you want to divide a number by 12, you can divide it by 4 then by 3. Is he right? Explain how you know. Work out 768 ÷ 12 using Peter's method and using another method. Do you get the same answer? How many 35p packets of stickers can I 29 Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 buy with £5? Explain how you know. Coaches have 56 seats for passengers. How many coaches are needed to take 275 people on a trip? Complete this calculation: 943 ÷ 41 = 2 Work out whether or not 29 is a factor of 811. 30 Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Interactive Teaching Programs that could support a range of teaching methods, suitable for calculating at Stage F. Addition Subtraction Multiplication Division Bead sticks Add subtract 1, 10, 100, 1000 Counting Counting on Counting Data handling Counting on Counting stick Difference Data handling Counting stick further options Multiplication array Number line Counting stick further options Converting units of measure Counting stick Function Blocks Function Blocks Counting stick Multiplication board Counting stick further options Multiplication facts Doubling and halving Multiplication facts Make numbers Make numbers guidance Number dials Doubling & halving guidance) Remainders Twenty cards Facts and place value Number dials Midpoint half way between Moving digits Find the multiple Moving digits Multiplication grid Guess my number Guess my number guidance (PDF) Twenty cards Make numbers Make numbers guidance Multiplication tables Number spinners Function Blocks Number facts Decimal target board Number facts Place value Find the multiple Place value Tell time Guess my number Guess my number guidance (PDF) Tell time Make numbers Make numbers guidance Twenty cards Moving digits Order numbers on a number line Patterns of calculations Calculate percentages Number line Multiplication board Doubling & halving guidance) Midpoint guidance Converting units of measure Doubling and halving Number spinners Midpoint half way between Multiplication array Doubling & halving guidance) Number line Twenty cards Grouping Function Blocks Doubling and halving Moving digits Calculate percentages Counting stick further options Number line Function Blocks Grouping Counting stick Complements Function Blocks Add subtract 1, 10, 100, 1000 Multiplication tables Fractions Place value dots Multiplication & division trios Sum Product Difference Sum Product Difference Guidance (PDF) Multiplication & division with partitioning Patterns of calculations Doubling and halving Doubling & halving guidance) Facts and place value Find the multiple Multiplication grid Make numbers Make numbers guidance Multiplication & division trios Multiplication & division with partitioning Place value dots 31 Yr 4 to 5 age appropriate. William Reynolds Primary School Calculation Policy Stages E & F Yr 4 – Consolidate Level 3 Start Level 4. Yr 5 – Revise Level 3 Mainly Level 4 Target practice Multiplication grid Multiplication grid guidance (PDF) Place value charts & partitioning tool Place value chart & partitioning tool guidance (PDF) Prime factors Target practice Place value charts & partitioning tool Place value chart & partitioning tool guidance (PDF) Place value dots Sum Product Difference Sum Product Difference Guidance (PDF) Place value dots Prime factors Target practice Target practice Which number where Timed number bonds Which number where 32