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Four Rules of MathsFour Rules of Maths
In seven stagesIn seven stages
Four RulesFour Rules
AdditionAddition SubtractionSubtraction
MultiplicationMultiplication divisiondivision
Addition Stage 1 (Reception)Addition Stage 1 (Reception)
Practical activities and discussionsPractical activities and discussions Finding one more than a number Finding one more than a number
from 1 to 10from 1 to 10 Using vocabulary associated with Using vocabulary associated with
additionaddition
Addition Stage 2 (Year 1)Addition Stage 2 (Year 1)
Begin to use the + and = sign to Begin to use the + and = sign to record mental calculationsrecord mental calculations
Know by heart all number bonds to Know by heart all number bonds to 1010
Use knowledge to know that addition Use knowledge to know that addition can be done in any order to do can be done in any order to do mental calculations more efficientlymental calculations more efficiently
Addition Stage 3 (Year 2 )Addition Stage 3 (Year 2 )
Adding three single digit numbers Adding three single digit numbers mentallymentally
Know by heart all number bonds to 20Know by heart all number bonds to 20 Use +and = to record mental calculationsUse +and = to record mental calculations Use number line to make informal jottingsUse number line to make informal jottings Use partitioning to reflect mental methods Use partitioning to reflect mental methods
47 + 78 =40 + 70 + 7 + 847 + 78 =40 + 70 + 7 + 8
Addition Stage 4 (Year 3)Addition Stage 4 (Year 3) Using informal pencil and paper methods Using informal pencil and paper methods
(jottings) and introducing vertical addition(jottings) and introducing vertical addition Adding TU and TU, moving into HTU using jottings Adding TU and TU, moving into HTU using jottings
(most significant digit first)(most significant digit first) 8833+ + 4422 -------- 120120+ + 55 -------- 125125
Addition Stage 5 (Year 4)Addition Stage 5 (Year 4) Vertical format least significant digit first extends Vertical format least significant digit first extends
to bigger numbersto bigger numbers
336688+ + 449933 ---------- 1111 150150+ + 700700 ---------- 861861
Addition Stage 6 (Year 5)Addition Stage 6 (Year 5)
Children using the compact layout, Children using the compact layout, involving carryinginvolving carrying
368368+ 491+ 491 ---------- 859859
Extending to decimalsExtending to decimals
Addition Stage 7 (Year 6)Addition Stage 7 (Year 6)
Compact addition using carrying for Compact addition using carrying for thousands, hundreds, tens and units, thousands, hundreds, tens and units, and decimalsand decimals
Consolidation of Stage 6Consolidation of Stage 6
Subtraction Stage 1 (Reception)Subtraction Stage 1 (Reception)
Practical activities and discussionPractical activities and discussion Finding one less than a number from Finding one less than a number from
1 to 101 to 10 Begin to relate subtraction to “taking Begin to relate subtraction to “taking
away”away”
Subtraction Stage 2 (Year 1)Subtraction Stage 2 (Year 1)
Begin to use the - and = sign to Begin to use the - and = sign to record mental calculationsrecord mental calculations
Know by heart all subtraction facts to Know by heart all subtraction facts to 1010
Subtraction Stage 3 (Year 2 )Subtraction Stage 3 (Year 2 )
Know by heart all subtraction facts to Know by heart all subtraction facts to 2020
Subtraction Stage 4 (Year 3)Subtraction Stage 4 (Year 3) Using informal pencil and paper Using informal pencil and paper
methods (jottings) methods (jottings) Use a number line to record Use a number line to record
complimentary additioncomplimentary addition
84 – 5684 – 56
+4 +20 +4 =28+4 +20 +4 =28
56 60 80 8456 60 80 84
Subtraction Stage 5 (Year 4)Subtraction Stage 5 (Year 4)
563 - 248563 - 248
500 + 60 + 500 + 60 + 33- 200 + 40 + - 200 + 40 + 88
------------------------------
500 + 500 + 50 + 1350 + 13 - 200 + 40 + 8- 200 + 40 + 8 -------------------------------- 300 + 10 + 5300 + 10 + 5
Subtraction Stage 5 (Year 4)Subtraction Stage 5 (Year 4)
Cont…….Cont……. 5050 10+10+
500 + 60 + 3500 + 60 + 3
- 200 + 40 + 8- 200 + 40 + 8
------------------------------
300 + 10 + 5300 + 10 + 5
Subtraction Stage 6 (Year 5)Subtraction Stage 6 (Year 5)
Decomposition extended to decimals and Decomposition extended to decimals and larger numberslarger numbers
Contracted recording at decompositionContracted recording at decomposition
5 10+5 10+
3 10+ 3 10+
64766476
-2684-2684
--------------
37923792
Subtraction Stage 7 (Year 6)Subtraction Stage 7 (Year 6)
Consolidation of stage 5Consolidation of stage 5 Contracted recording of decimalsContracted recording of decimals
Multiplication Stage 1 (Reception)Multiplication Stage 1 (Reception)
Working at a practical level to gain Working at a practical level to gain experience of doubling and become experience of doubling and become familiar with the appropriate familiar with the appropriate languagelanguage
Multiplication Stage 2 (Year 1)Multiplication Stage 2 (Year 1)
Know by heart addition doubles to at Know by heart addition doubles to at least 5least 5
Multiplication Stage 3 (Year 2)Multiplication Stage 3 (Year 2)
Understand multiplication as Understand multiplication as repeated additionrepeated addition
Know by heart the multiplication Know by heart the multiplication facts for the 10 and 2 multiplication facts for the 10 and 2 multiplication tablestables
Multiplication Stage 4 (Year 3)Multiplication Stage 4 (Year 3) Mental methods using partitioningMental methods using partitioning
3388 x x 77 = ( = (3030 x x 77) + () + (88 x x 77)) Introduction of grid layout to show expanded working outIntroduction of grid layout to show expanded working out
Know by heart the multiplication facts for the 10, 2, 5, 3 and 4 times tablesKnow by heart the multiplication facts for the 10, 2, 5, 3 and 4 times tables
xx 3030 88
77 210210 5656 266266
Multiplication Stage 5 (Year 4)Multiplication Stage 5 (Year 4)
Grid method extended to bigger numbersGrid method extended to bigger numbers
5656 x x 2727
Know by heart the multiplication facts up to 10 Know by heart the multiplication facts up to 10 x 10x 10
xx 5050 66
2020 10001000 120120 11201120
77 350350 4242 392392
15121512
Multiplication Stage 6 (Year 5)Multiplication Stage 6 (Year 5)
Grid method extended to bigger numbers and Grid method extended to bigger numbers and decimalsdecimals
23.523.5 x x 1212
xx 2020 33 0.50.5
1010 200200 3030 55 235235
22 4040 66 11 4747
282282
Multiplication Stage 6 (Year 5)Multiplication Stage 6 (Year 5)Cont…………….Cont…………….
Introduction of vertical format linked to grid methodIntroduction of vertical format linked to grid method 3388 x 7x 7 ---------- 210 (30 x 7)210 (30 x 7) + + 56 ( 8 x 7)56 ( 8 x 7) ------------ 266266
Vertical format using decimals and larger numbersVertical format using decimals and larger numbers
Multiplication Stage 7 (Year 6)Multiplication Stage 7 (Year 6) Consolidation of stage 6Consolidation of stage 6
Contracted vertical multiplication, e.g.Contracted vertical multiplication, e.g.
3838
X 7X 7
----------
266266
Division Stage 1 (Reception)Division Stage 1 (Reception)
Working at a practical level to gain Working at a practical level to gain experience of sharing and become experience of sharing and become familiar with the appropriate familiar with the appropriate languagelanguage
Division Stage 2 (Year 1)Division Stage 2 (Year 1)
Separate a given number of objects Separate a given number of objects into equal groups and record results into equal groups and record results informallyinformally
Division Stage 3 (Year 2)Division Stage 3 (Year 2)
Understanding division as grouping, Understanding division as grouping, repeated subtraction or sharing, and repeated subtraction or sharing, and recording informallyrecording informally
Division Stage 4 (Year 3)Division Stage 4 (Year 3)
Use the Use the ÷÷ and = signs, recording and = signs, recording horizontallyhorizontally
Division Stage 5 (Year 4)Division Stage 5 (Year 4) Begin to use standard written methods, Begin to use standard written methods,
e.g. 96 e.g. 96 ÷ ÷ 66
9696 - 60 (- 60 (66 x x 1010)) ---------- 3636 - 36 (- 36 (66 x x 66) ) ++ ----- ----- ---------- 00 00 1616
Division Stage 6 (Year 5)Division Stage 6 (Year 5)
Use standard written methods using Use standard written methods using multiples of 10, e.g. 196 multiples of 10, e.g. 196 ÷ ÷ 66
196196 - 180 (- 180 (66 x x 3030)) ---------- 1616 - 12 (- 12 (66 x x 22) ) ++ ----- --------- ---- 4 4 32 remainder 432 remainder 4
Division Stage 7 (Year 6)Division Stage 7 (Year 6) Consolidation of stage 6Consolidation of stage 6 Contraction of formal methodContraction of formal method
196196 - 180 - 180 3030 ---------- 1616 - 12 - 12 22 ++ ----- --------- ---- 4 4 32 remainder 432 remainder 4
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