Four Rules of Maths

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.
• 50 10
• 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
•