Calculations in mathematics Things are different now!

Calculations in mathematicsCalculations in mathematics

Things are different now!Things are different now!

additionaddition

Year 3Year 3

Partitioning method is used – for examplePartitioning method is used – for example

37 + 24 = 6137 + 24 = 61

30 + 20 = 5030 + 20 = 50

7 + 4 = 117 + 4 = 11

Addition Addition

Year 4Year 4Partitioning used for Partitioning used for increasingly large increasingly large numbers –egnumbers –eg

2417 + 3524 = 59412417 + 3524 = 5941

2000 + 3000 = 50002000 + 3000 = 5000 400 + 500 = 900400 + 500 = 900 10 + 20 = 3010 + 20 = 30 7 + 4 = 117 + 4 = 11

Year 4 continuedYear 4 continuedVertical layout Vertical layout introduced – egintroduced – eg

47+ 368+47+ 368+ 7676 493493

110 700110 700 13 13 150 150 123 123 11 11 861861

AdditionAddition

Year 5 & Year 6Year 5 & Year 6

As for year 4 but extended to include As for year 4 but extended to include decimals with partitioning – egdecimals with partitioning – eg

7.6 + 5.8 = 13.47.6 + 5.8 = 13.4

7 + 5 = 127 + 5 = 12

0.6 + 0.8 = 1.40.6 + 0.8 = 1.4

AdditionAddition

Y6Y6More able children introduced to compact and efficient More able children introduced to compact and efficient method at the appropriate time – egmethod at the appropriate time – eg

1 7 9 + 2 1 . 7 +1 7 9 + 2 1 . 7 +

2211 3 31 1 66 2 22 211 . 5 . 5

4 1 54 1 5 4 4 . 24 4 . 2

SubtractionSubtraction

Year 3Year 3

Empty number line method is used – egEmpty number line method is used – eg

95 - 33 = 6295 - 33 = 62

7 7 50 50 55

33______________________________9533______________________________95

40 90 40 90

SubtractionSubtraction

Years 4 – 6Years 4 – 6The empty number line The empty number line continues to be used in these continues to be used in these year groups. year groups.

The children are encouraged The children are encouraged to develop increasingly refined to develop increasingly refined and efficient methods of using and efficient methods of using the number line.the number line.

SubtractionSubtraction

Year 6Year 6

Compact and efficient method introduced at appropriate Compact and efficient method introduced at appropriate time for more able children – egtime for more able children – eg

6 66 6

4 7 4 7 116 – 5 7 . 6 – 5 7 . 112 -2 -

1 3 91 3 9 3 4 . 53 4 . 5

3 3 73 3 7 2 2 . 7 2 2 . 7

Multiplication Multiplication

Year 3Year 3Arrays are used to develop understanding.Arrays are used to develop understanding.

Children begin to use partitioning – egChildren begin to use partitioning – eg

16 x 5 = 8016 x 5 = 80

10 x 5 = 5010 x 5 = 50

6 x 5 = 306 x 5 = 30

Multiplication Multiplication

Year 4Year 4

Children continue to partition but grid method is Children continue to partition but grid method is introduced – egintroduced – eg

6 x 32 = 1926 x 32 = 192 X 30 2 X 30 2

6 180 126 180 12

Multiplication Multiplication

Years 5 & 6 Years 5 & 6

Grid method used with larger numbers and Grid method used with larger numbers and decimals – egdecimals – eg

27 x 15 = 40527 x 15 = 405 1.23 x 45 = 55.351.23 x 45 = 55.35

X 20 7 X 20 7 X 1 0.2 0.03X 1 0.2 0.03

10 200 70 = 270 10 200 70 = 270 40 40 8 1.240 40 8 1.2 49.249.2

5 100 35 = 135 5 100 35 = 135 5 5 1 0.15 6.155 5 1 0.15 6.15

405 405 55.3555.35

MultiplicationMultiplication

More compact method for grid introduced where More compact method for grid introduced where appropriate:appropriate:

26 x 3726 x 37

20 x 30 = 60020 x 30 = 600 20 x 7 = 14020 x 7 = 140 6 x 30 = 1806 x 30 = 180 6 x 7 = 426 x 7 = 42 962962

MultiplicationMultiplication

Y6 Y6

Compact and efficient method introduced when Compact and efficient method introduced when appropriate for more able children – egappropriate for more able children – eg

3 2 x 2 4 x 4 . 8 x3 2 x 2 4 x 4 . 8 x

11 6 6 2 22 2 22 3 3

1 9 21 9 2 4 8 4 8 14 . 414 . 4

4411 8 0 8 0

5 2 85 2 8

DivisionDivision

Year 3 and 4Year 3 and 4Chunking method used along with visual model Chunking method used along with visual model including remainders – egincluding remainders – eg

16 16 ÷ ÷ 4 = 44 = 4 36 36 ÷ ÷ 10 = 3 Rem 610 = 3 Rem 6

…….. . . . . . . . . . .. . . . . . . . . . ……. . . . . . . . . . . .. . . . . . . . . . …….. . . . . . . . . . .. . . . . . . . . .

…….. . . . . . . . . . . . .

DivisionDivision

Years 4, 5 & 6Years 4, 5 & 6

These methods can also be used with a number These methods can also be used with a number line – egline – eg

120 120 ÷ ÷ 9 = 13 rem 39 = 13 rem 3

0____________________________90_____117__1200____________________________90_____117__120

10x9 3x910x9 3x9

Division Division

Year 4, 5 & 6Year 4, 5 & 6The concept of chunking is still used but The concept of chunking is still used but method becomes numerical rather than method becomes numerical rather than pictorial. Several strategies are used, all pictorial. Several strategies are used, all of which rely on good knowledge of of which rely on good knowledge of times tables!times tables!

2. 2. 265 265 ÷ ÷ 13 = 20 rem 513 = 20 rem 5

13 265 13 265 130130 (10 x 13) (10 x 13) 135 -135 - 130 130 (10 x 13) (10 x 13) 55

93 93 ÷ ÷ 6 = 15 rem 3 (16.5)6 = 15 rem 3 (16.5)

I know that 10 x 6 = 60I know that 10 x 6 = 60 and 5 x 6 = 30 and 5 x 6 = 30 so 15 x 6 = 90so 15 x 6 = 90

Useful websitesUseful websiteswww.supermathsworld.comOuter space-related activities on wide range of topics – annoying music though!Outer space-related activities on wide range of topics – annoying music though!www.educationcity.comLog-in: 815western Log-in: 815western Password: schoolPassword: schoolGo to ‘Curriculum Map’Go to ‘Curriculum Map’MathsMathsChoose year group then specific maths areaChoose year group then specific maths areawww.bbc.co.uk/schoolradio/maths/mathschallenge.shtmlwww.bbc.co.uk/schoolradio/maths/mathschallenge.shtmlDownload radio programmes containing a variety of mental maths questionsDownload radio programmes containing a variety of mental maths questionswww.subtangent.comwww.subtangent.comMore able children – investigative challengesMore able children – investigative challengesnrich.maths.org/publicnrich.maths.org/publicGo to ‘Stage 1 and 2’ down left-hand side for the latest mathematical challenges, graded Go to ‘Stage 1 and 2’ down left-hand side for the latest mathematical challenges, graded

by difficulty with stars.by difficulty with stars.woodlands-junior.kent.sch.uk/mathswoodlands-junior.kent.sch.uk/mathsAllsorts of interactive activities. Well indexed.Allsorts of interactive activities. Well indexed.