Download - Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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Page 1: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

Four Rules of MathsFour Rules of Maths

In seven stagesIn seven stages

Page 2: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

Four RulesFour Rules

AdditionAddition SubtractionSubtraction

MultiplicationMultiplication divisiondivision

Page 3: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 4: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 5: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 6: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 7: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 8: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 9: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 10: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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”

Page 11: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 12: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 13: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 14: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 15: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 16: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 17: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

Subtraction Stage 7 (Year 6)Subtraction Stage 7 (Year 6)

Consolidation of stage 5Consolidation of stage 5 Contracted recording of decimalsContracted recording of decimals

Page 18: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 19: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 20: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 21: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 22: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 23: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 24: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 25: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 26: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 27: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 28: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 29: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

Division Stage 4 (Year 3)Division Stage 4 (Year 3)

Use the Use the ÷÷ and = signs, recording and = signs, recording horizontallyhorizontally

Page 30: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 31: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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

Page 32: Four Rules of Maths In seven stages. Four Rules Addition Addition Subtraction Subtraction Multiplication Multiplication division division.

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