Progression through the teaching of

calculation Year 5 - 6

Aim of ProgressionMaths has changed!!

The maths work your child is doing at school may look very different to the kind of ‘sums’ you remember. This is because children are encouraged to work mentally, where possible, using personal jottings to help support their thinking.

‘Formal’ calculations are introduced from Year 3 onwards. Even then children are encouraged to use these methods for calculations they cannot solve in their heads.

Calculation

When faced with a problem, we want children to ask themselves….

• Can I do this in my head?• Could I do this in my head using

drawings or jottings to help me?• Do I need to use a written method?• Should I use a calculator?

Addition +THE FOLLOWING ARE STANDARDS THAT WE EXPECT

THE MAJORITY OF CHILDREN TO ACHIEVE.Year 5

Following formal addition methods with carrying above the line being introduced at Year 4, children should at Year 5 should then extend the carrying method to numbers with at least four digits.

• 587 3587

+ 475 + 675 1 1_ 1 1 1___

1062 4262

Addition +Using similar methods, children will:• Add several numbers with different

numbers of digits• Begin to add two or more decimal fractions

with up to three digits and the same number of decimal points

• Know that decimal points should line up under each other, particularly when adding or subtracting mixed amounts, e.g 3.2m – 280cm

Addition +• Year 6Children should extend the carrying method to number with any

number of digits. 7648 6584+ 1486 + 5848 1 11_ 111_

9134 12432

Using similar methods, children will:• Add several numbers with different numbers of digits• Begin to add two or more decimal fractions with up to four

digits and either one or two decimal places• Know that decimal points should line up under each other,

particularly when adding or subtracting mixed amounts, e.g 401.2 + 26.85 + 0.71

Subtraction -• Year 5The teaching of subtraction continues from Year 4 where an expanded

method will have been introduced.This expanded method uses partitioning

Step 1: 754 = 700 + 50 + 4 - 286 200 + 80 + 6

Step 2: 700 + 40 + 14 (adjusting from T to U) - 200 + 80 + 6

Step 3: 600 + 140 + 14 (adjusting from H to T) - 200 + 80 + 6 400 + 60 + 8 = 468

Subtraction -

Decomposition 614 1

754 (as in your booklet, as the borrowing between the tens

- 286 and the hundreds takes place, the 5 and the 7 will be

468 crossed out)

Children should:• Be able to subtract numbers with different numbers of digits• Begin to find the number between two decimal fractions with

up to three digits and the same number of decimal places• Know that decimal points should line up under each other.

Subtraction -• Year 6If children are able by the end of year 5 to cope withdecomposition then they will continue with this method into Year 6 513 1 6467 - 2684 3783

Children should:• Be able to subtract numbers with different numbers of digits• Be able to subtract two or more decimal fractions with up to three

digits and either one or two decimal places• Know that decimal points should line up under each other.

Multiplication XYear 5As in Year 4, Year 5 children when being introduced to multiplication will

be using the Grid Method

Year 5 children will begin with HTU x U369 x 9Children are expected to approximate first369 x 9 is approximately 370 x 10 – 3700 x 300 60 9 2700 9 + 540 81 1 1___

3321

2700 540 81

Multiplication XTU x TU

72 x 38

Again children are expected to approximate first

72 x 38 is approximately 70 x 40 = 2800

x 70 2 2100

30 + 560

8 60

16 1____

2736

2100 60

560 16

Multiplication XUsing similar methods, children will be expected to multiply decimals with one decimal place. They should know that decimal points line up under each other.

e.g 4.9 x 3Approximating first4.9 x 3 is approximately 5 x 3 = 15

x 4 0.9 12 3 + 2.7 14.7

12 2.7

Year 6ThHTU x U4346 x 8Approximate first4346 x 8 is approximately 4346 x 10 = 43460

x 4000 300 40 8 32000 8 + 2400 320 48 34768

Multiplication X

32000 2400 320 48

Multiplication XYear 6HTU x TU

372 x 24Approximate first372 x 24 is approximately 400 x 25 = 10000

X 300 70 2 600020 + 14004 1200 280 40 8 _ 1__

8928

6000 1400 40

600 140 8

Multiplication xUsing similar methods, Year 6 pupils will be expected to multiply decimals with up to two decimal places by a single digit and then by two digits.

4.92 x 3

Approximate first

4.92 x 3 is approximately 5 x 3 = 15

X 4 0.9 0.02 12

3 + 0.7

_0.06

12.76

12 2.7 0.06

Multiplication XYear 6

For the higher attainers who have grasped the concept of multiplication in Year 5, the short method of multiplication will be taught.

365

x 9 5 4_

3285

Division Year 5

In Year 4, a method of division called ‘Chunking’ will be introduced as a written method.This method is carried over into Year 5 where children will use the method to solve short division questions such as

TU U Example: 196 6 32 r 4 6 ) 196 - 180 (30x) 16 - 12 (2x) 4Answer: 32 reminder 4 or 32r4

Division Year 6 Children will continue to use this method into Year 6 where they will extend it to solving HTU U and HTU TU

HTU TU Example: 972 36 27 36 ) 972 - 360 (10x) 612 - 360 (10x) 252 - 180 (5x) 72 - 72 (2x)Answer 27

Division Year 6Division using the ‘chunking’ method will be extended to solving division with decimals up to two decimal places.87.5 7 12.5 7 )87.5 - 70.0 (10X) 17.5 - 14.0 (2X) 3.5 - 3.5 (0.5X) 0

Answer: 12.5

Division A short method of division will be introduced to those children who can fully understand the chunking method. This will only be used for division of HTU by U or TU by U. 4 1369 9 = 3

9)369

By the end of Year 6, all children will have a range of calculation methods, mental and written. Selection will depend upon the numbers involved.

Children should not be made to go onto the next stage if:* they are not ready* they are not confident

Children should be encouraged to approximate their answers before calcualting and should be encouraged to check their answers after calculation.

Children should also be encouraged to consider first before they attempt the question, whether a mental calculation would be appropriate.

Time for you to have a go!!Try to use the methods explained tonight to solve each of the following questions:

1. 1654 + 465 =2. 6854 - 798 =3. 965 30 =4. 374 X 24 =