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Four Rules of Maths

Four Rules of Maths. In seven stages. Four Rules. Addition Subtraction Multiplication division. Addition Stage 1 (Reception). Practical activities and discussions Finding one more than a number from 1 to 10 Using vocabulary associated with addition. Addition Stage 2 (Year 1).

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Four Rules of Maths

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  1. Four Rules of Maths In seven stages

  2. Four Rules • Addition • Subtraction • Multiplication • division

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

  4. Addition Stage 2 (Year 1) • Begin to use the + and = sign to record mental calculations • 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

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

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

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

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

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

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

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

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

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

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

  15. Subtraction Stage 5 (Year 4) Cont……. 5010+ 500 + 60 + 3 - 200 + 40 + 8 --------------- 300 + 10 + 5

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

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

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

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

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

  21. Multiplication Stage 4 (Year 3) • Mental methods using partitioning 38 x 7 = (30 x 7) + (8 x 7) • 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

  22. Multiplication Stage 5 (Year 4) • Grid method extended to bigger numbers 56 x 27 • Know by heart the multiplication facts up to 10 x 10

  23. Multiplication Stage 6 (Year 5) • Grid method extended to bigger numbers and decimals 23.5 x 12

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

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

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

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

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

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

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

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

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

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