Calculations – years 1-6

Dear Parents/CarersOver recent months several parents have asked us to explain the way we teach calculations in maths. In order to help you support your child we are sending out guidance which is adapted from the school calculations policy. This is in line with Government recommendations.The booklet is organised into three sections:Year 1 and 2Year 3 and 4Year 5 and 6

Most children will perform calculations in line with their relevant phase of learning. Some children, however, will naturally progress more slowly or more quickly. Those progressing more quickly will be extended onto the type of calculations shown for the next year group when their teacher feels they are ready and vice versa. If you require further information about typical progression in a year group this can be found in the national guidelines website:http://nationalstrategies.standards.dcsf.gov.uk/search/primary/results/nav:49930

Year 1 /Year 2

Addition : horizontal format e.g. 7 + 3 = 10

23 + 12 = 3520 +10 =303 + 2 = 530 + 5 = 35

Subtraction: Horizontal format again. Children encouraged to use a number line to find the difference between two numbers when apparatus not appropriate:

9 – 4 = 5 +1 +1 +1 +1 +1____________________________________________________________________________________4 5 6 7 8 9

They move onto larger numbers when ready, counting to the next multiple of 10 first. eg. 41-26 +4 +10 +1_________________________________________________________________________________26 30 40 41

10 +4 +1 = 15

Multiplication and division

Introduced as “groups of” (arrays) and repeated addition/subtraction.

4 groups of 2 4 x 2 = 8

Number lines are used too:

eg 3jumps of 5 to make 15. 3 x 5 = 15

+ 5 +5 +5

____________________________________

0 5 10 15

______________________________________________________________________________________

Division shown as counting in groups backwards.

Division is introduced in terms of sharing and is linked very closely to the multiplication facts the children are becoming familiar with:

8 ÷ 2 = 4

or on a number line: 8 ÷ 2 = 4 jumps -2 -2 -2 -2 ________________________________________________________0 2 4 6 8

Year 3 and 4

Addition – children develop partitioning using a horizontal method in Y3/4, partitioning into HTUEg 36 + 42 = 7830 + 40 = 706 + 2 = 870 + 8 = 78

They move towards standard written methods:

39+ 56 80 15 95

Subtraction – continue to use the number line method – counting up from the smaller number to the larger number as well as backwards using efficient jumps:

57 – 29 = 28 +1 +10 +10 +7_________________________________________________________________________29 30 40 50 57

Multiplication – start with horizontal format

Eg 8 x 4 = 32

Continue to show as jumps on a number line

+4 +4 +4 +4 _____________________________________________ 4 + 4 + 4 + 4 = 16

18 x 3

10 x 3 = 308 x 3 = 2430 + 24 = 54

Move onto grid method: x 40 343 x 6 6 240 18

240 + 18 = 258

Division – horizontal format with informal jottings:

Eg 27 divided by 3 = 9

37 divided by 6 = 6 r1

+6 +6 +6 +6 +6 +6 r1 _______________________________________________________________0 6 12 18 24 30 36 37

Year 5 and 6Addition – children are taught to choose an efficient method for solving their calculations: mental, written or calculator:

Methods include partitioning and standard written methods, including carrying. Addition of decimals – up to 2 decimal places. When ready, the number of digits and decimal places is extended.

Eg 2468 2468 + 4927 + 4927 6000 (2000+4000) 7395 1300 (400+900) 80 (60 +20) 15 (8 + 7) 7395

16 . 25 16 . 25 + 25. 03 + 25 . 08 30 . 00 41 . 28 11 . 00 0. 20 0. 08 41 .28

Subtraction

Y5 continue to use the number line method where they count up to the larger number (this is linked to mental maths skills)

Y6 move onto standard decomposition, after the SATs

eg 376 – 149

+1 +50 +100 +76_______________________________________________________________________149 150 200 300 376

100 + 76 + 50 + 1 = 227

or 376 – 149 = 227

149 +1 376150 _ 149 +50 1 ( 50) 50 ( 200) 100 ( 300) 76 ( 376)200 227 +100

300

+76

376

Multiplication

Grid method

246 x 4 = 984

x 200 40 6 800 + 160 4 800 160 24 24 984

24 x 13

x 20 4

10 200 40 = 240 3 60 12 = 72 312 short multiplication by partitioning

24 246X 13 x 4 12 (3x4) 24 (4x6) 60 (3x20) 160 (4x40) 40 (10x4) 800 (4x200) 200 (10x20) 984 312

The multiplication of decimals is included. The grid method is used first followed by short multiplication partitioning.

12 . 5 x 6 = 75 12 . 5 x 6 60 (6x10) 12 (6x2) x 10 2 0.5 60 3 (6x0.5) 12 75 6 60 12 3 3 75

Moving onto long multiplication:

124 264X 16 x 4 744 (6x124) 10561240 (10x124)1984

Division

The “chunking” method is used – “chunks” of the multiple are taken away – this reinforces the use and application of times table facts.

125 divided by 4 = 31 r1

125 (10 lots of 4) 40 85 (10 lots of 4) 40 45 (10 lots of 4) 40 5 (1 lot of 4) 4 1

Add up how many 4s there were: 10+10+10+1 = 31 r1

The children move onto efficient chunking when ready – this is where they begin to take away larger “chunks” of the multiple, making this method faster.

125 divided by 4 = 31 r1

125 (30x4) 120 - 5 (1x4) 4 - 31 r 1