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Four Rules of Maths In seven stages

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Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division

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Addition Stage 1 (Reception) Practical activities and discussions Practical activities and discussions Finding one more than a number from 1 to 10 Finding one more than a number from 1 to 10 Using vocabulary associated with addition Using vocabulary associated with addition

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Addition Stage 2 (Year 1) Begin to use the + and = sign to record mental calculations Begin to use the + and = sign to record mental calculations Know by heart all number bonds to 10 Know by heart all number bonds to 10 Use knowledge to know that addition can be done in any order to do mental calculations more efficiently Use knowledge to know that addition can be done in any order to do mental calculations more efficiently

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Addition Stage 3 (Year 2 ) Adding three single digit numbers mentally Adding three single digit numbers mentally Know by heart all number bonds to 20 Know by heart all number bonds to 20 Use +and = to record mental calculations Use +and = to record mental calculations Use number line to make informal jottings Use number line to make informal jottings Use partitioning to reflect mental methods 47 + 78 =40 + 70 + 7 + 8 Use partitioning to reflect mental methods 47 + 78 =40 + 70 + 7 + 8

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Addition Stage 4 (Year 3) Using informal pencil and paper methods (jottings) and introducing vertical addition Using informal pencil and paper methods (jottings) and introducing vertical addition Adding TU and TU, moving into HTU using jottings (most significant digit first) Adding TU and TU, moving into HTU using jottings (most significant digit first) 83 83 + 42 ---- ---- 120 120 + 5 ---- ---- 125 125

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Addition Stage 5 (Year 4) Vertical format least significant digit first extends to bigger numbers Vertical format least significant digit first extends to bigger numbers 368 368 + 493 ----- ----- 11 11 150 150 + 700 ----- ----- 861 861

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Addition Stage 6 (Year 5) Children using the compact layout, involving carrying Children using the compact layout, involving carrying 368 368 + 491 ----- ----- 859 859 Extending to decimals Extending to decimals

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Addition Stage 7 (Year 6) Compact addition using carrying for thousands, hundreds, tens and units, and decimals Compact addition using carrying for thousands, hundreds, tens and units, and decimals Consolidation of Stage 6 Consolidation of Stage 6

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Subtraction Stage 1 (Reception) Practical activities and discussion Practical activities and discussion Finding one less than a number from 1 to 10 Finding one less than a number from 1 to 10 Begin to relate subtraction to taking away Begin to relate subtraction to taking away

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Subtraction Stage 2 (Year 1) Begin to use the - and = sign to record mental calculations Begin to use the - and = sign to record mental calculations Know by heart all subtraction facts to 10 Know by heart all subtraction facts to 10

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Subtraction Stage 3 (Year 2 ) Know by heart all subtraction facts to 20 Know by heart all subtraction facts to 20

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Subtraction Stage 4 (Year 3) Using informal pencil and paper methods (jottings) Using informal pencil and paper methods (jottings) Use a number line to record complimentary addition Use a number line to record complimentary addition 84 – 56 +4 +20 +4 =28 +4 +20 +4 =28 56 60 80 84 56 60 80 84

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Subtraction Stage 5 (Year 4) 563 - 248 500 + 60 + 3 500 + 60 + 3 - 200 + 40 + 8 --------------- --------------- 500 + 50 + 13 500 + 50 + 13 - 200 + 40 + 8 - 200 + 40 + 8 ---------------- ---------------- 300 + 10 + 5 300 + 10 + 5

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Subtraction Stage 5 (Year 4) Cont……. 50 10+ 50 10+ 500 + 60 + 3 500 + 60 + 3 - 200 + 40 + 8 --------------- --------------- 300 + 10 + 5 300 + 10 + 5

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Subtraction Stage 6 (Year 5) Decomposition extended to decimals and larger numbers Decomposition extended to decimals and larger numbers Contracted recording at decomposition Contracted recording at decomposition 5 10+ 5 10+ 3 10+ 3 10+ 6476 6476-2684 ------- ------- 3792 3792

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Subtraction Stage 7 (Year 6) Consolidation of stage 5 Consolidation of stage 5 Contracted recording of decimals Contracted recording of decimals

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Multiplication Stage 1 (Reception) Working at a practical level to gain experience of doubling and become familiar with the appropriate language Working at a practical level to gain experience of doubling and become familiar with the appropriate language

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Multiplication Stage 2 (Year 1) Know by heart addition doubles to at least 5 Know by heart addition doubles to at least 5

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Multiplication Stage 3 (Year 2) Understand multiplication as repeated addition Understand multiplication as repeated addition Know by heart the multiplication facts for the 10 and 2 multiplication tables Know by heart the multiplication facts for the 10 and 2 multiplication tables

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Multiplication Stage 4 (Year 3) Mental methods using partitioning Mental methods using partitioning 38 x 7 = (30 x 7) + (8 x 7) 38 x 7 = (30 x 7) + (8 x 7) Introduction of grid layout to show expanded working out Introduction of grid layout to show expanded working out Know by heart the multiplication facts for the 10, 2, 5, 3 and 4 times tables Know by heart the multiplication facts for the 10, 2, 5, 3 and 4 times tables x308 721056266

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Multiplication Stage 5 (Year 4) Grid method extended to bigger numbers Grid method extended to bigger numbers 56 x 27 56 x 27 Know by heart the multiplication facts up to 10 x 10 Know by heart the multiplication facts up to 10 x 10 x506 2010001201120 735042392 1512

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Multiplication Stage 6 (Year 5) Grid method extended to bigger numbers and decimals Grid method extended to bigger numbers and decimals 23.5 x 12 23.5 x 12 x2030.5 10200305235 24061 47 47 282

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Multiplication Stage 6 (Year 5) Cont……………. Introduction of vertical format linked to grid method Introduction of vertical format linked to grid method 38 38 x 7 x 7 ----- ----- 210 (30 x 7) 210 (30 x 7) + 56 ( 8 x 7) + 56 ( 8 x 7) ------ ------ 266 266 Vertical format using decimals and larger numbers Vertical format using decimals and larger numbers

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Multiplication Stage 7 (Year 6) Consolidation of stage 6 Consolidation of stage 6 Contracted vertical multiplication, e.g. Contracted vertical multiplication, e.g. 38 38 X 7 X 7 ----- ----- 266 266

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Division Stage 1 (Reception) Working at a practical level to gain experience of sharing and become familiar with the appropriate language Working at a practical level to gain experience of sharing and become familiar with the appropriate language

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Division Stage 2 (Year 1) Separate a given number of objects into equal groups and record results informally Separate a given number of objects into equal groups and record results informally

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Division Stage 3 (Year 2) Understanding division as grouping, repeated subtraction or sharing, and recording informally Understanding division as grouping, repeated subtraction or sharing, and recording informally

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Division Stage 4 (Year 3) Use the ÷ and = signs, recording horizontally Use the ÷ and = signs, recording horizontally

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Division Stage 5 (Year 4) Begin to use standard written methods, e.g. 96 ÷ 6 Begin to use standard written methods, e.g. 96 ÷ 6 96 96 - 60 (6 x 10) - 60 (6 x 10) ----- ----- 36 36 - 36 (6 x 6) + - 36 (6 x 6) + ----- ----- ----- ----- 00 16 00 16

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Division Stage 6 (Year 5) Use standard written methods using multiples of 10, e.g. 196 ÷ 6 Use standard written methods using multiples of 10, e.g. 196 ÷ 6 196 196 - 180 (6 x 30) - 180 (6 x 30) ----- ----- 16 16 - 12 (6 x 2) + - 12 (6 x 2) + ----- ---- ----- ---- 4 32 remainder 4 4 32 remainder 4

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Division Stage 7 (Year 6) Consolidation of stage 6 Consolidation of stage 6 Contraction of formal method Contraction of formal method 196 196 - 180 30 - 180 30 ----- ----- 16 16 - 12 2 + - 12 2 + ----- ---- ----- ---- 4 32 remainder 4 4 32 remainder 4

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