## Langrish calculation progression document

Vicky Boulain Langrish calculation progression document This document shows the progression of mental and written calculations for all four operati...
Author: Ethan Lloyd
Vicky Boulain

Langrish calculation progression document

This document shows the progression of mental and written calculations for all four operations in Langrish Primary School. It is important children become confident MATHLETES using mental and written strategies to explain their thinking and solve problems. Before beginning to record in a written format children must have had significant mental and practical work. They need to learn and refine written methods of recording. They also need to use and apply what they have learnt when working on problem solving tasks. When children have learnt a new method of recording a written calculation it is vital they practise, reinforce, consolidate, use and apply it to mathematical learning and NOT simply move onto the next method of recording. Written methods are TOOLS to enable children to record their thinking in an organised way.

Vicky Boulain

Langrish mental calculation progression document .

Vicky Boulain

Year R  I can recognise numbers from 

 I can read and write numbers

Year 2  I can read and write numbers

1-20.

from 1 to 20 in digits and

from 0 to 100 in digits and

I can write numbers from 1-

words.

words.

20. 

I can count back from 20-1.

I can count in 2s to 20.

I can count in 10’s to 100.

I can say 1 more or 1 less than any number to 20.

Year 1

I can say my number bonds to 10.

 I can say my number bonds to 10 and 20.  I can count to and across 100, forwards and backwards.  I can count in 2s, 5s and 10s to 100.  I can add 10 to any number up to 50.  I know doubles of numbers up to 10+10.  I can say the number that is 1 more or 1 less to numbers to 100.  I can recognise odd and even numbers.

 I can count in steps of 2, 3 and 5 from 0 forwards and backwards.  I can count in 10s from any number forward and backwards.  I can say my number bonds in multiples of 10 to 100.  I know my 2x tables.  I know my 5x tables.  I know my 10x tables.  I can add or subtract mentally a two digit and ones.  I can add or subtract mentally a two digit number and tens.  I can add or subtract mentally two 2 digit numbers.

Vicky Boulain

Year 3  I can read and write numbers from 0 to 1000 in digits and words.  I can count in steps of 4, 8, 50 and 100 from 0, forwards and backwards.  I can count in 10s or 100s from any number forward and backwards.  I can count up and down in tenths.  I can compare and order numbers to 1000.

Year 4  I can read and write numbers from 0 to 1000 in digits and words.  I can count in steps of 6, 7, 9 and 25 from 0, forwards and backwards.  I can count in 1000s from any number forward and backwards.  I can count backwards through 0 to include negative numbers

 I know my 3x tables.

 I can count up and down in hundredths.

 I know my 4x tables.

 I can compare and order numbers to 1000.

 I know my 8x tables.

 I know all of my times tables up to 12x12

 I can add or subtract mentally a three digit

 I can multiply and divide mentally.

and ones.  I can add or subtract mentally a three digit number and tens.  I can add or subtract mentally a three digit number and hundreds.

 I can multiply 3 numbers to together.  I can recognise factor pairs.  I can work out doubles and halves of two-digit numbers.  I can read Roman numerals to 100 (I to C).

Vicky Boulain

Year 5  I can read and write numbers to 1000,000 in digits and words  I can count forwards or backwards in steps of powers of 10 for any given number up to 1000,000  I can count forwards and backwards with positive and negative whole numbers through 0.  I can use my times tables facts to multiply multiples of 10 and 100.

Year 6  I can read, write, order and compare numbers up to 10,000,000  I can multiply and divide decimals mentally by 10, 100 or 1000 up to three decimal places. 

I can order positive and negative numbers.

I can add and subtract positive numbers.

 I can mentally calculate with mixed operations

 I know all my square numbers to 12 x 12.  I know some cube numbers.

and large numbers. 

 I know prime numbers to 100.  I can read, write, order and compare numbers with up to three decimal places.  I know the equivalence between a simple fraction and a decimal.  I can give a simple fraction as a percentage.  I can multiply and divide numbers mentally drawing upon

I can find fractions of quantities with a numerator larger than one.

I can add near multiples of 10, 100 and 1000.

I can subtract near multiples of 10, 100 and 1000.

I can add a pair of decimal numbers with up to 2 decimal places.

known facts.  I can multiply and divide decimals by 10, 100 and 1000  I can add and subtract numbers mentally with increasingly large numbers. can read Roman numerals to 1000 (M) and recognise years written in Roman numerals  I know factor pairs of numbers to 100. Vicky Boulain

Langrish written calculation progression document

Vicky Boulain

Addition Year R Pictorial representations of calculations – children are encouraged to combine 2 sets into 1.

Year 1 Children will use a number track to add numbers together using jumps of 1.

4

+

5

=

9

As children are introduced to numbers as digits these can be included. Children will start to understand that numbers can be added together in any order and that it is often easiest to add the smaller number onto the bigger number.

2

3

5

Children will be introduced to the (addition) + sign and the (same as) = sign.

Children will progress onto using a blank number line to add on the smaller number to the larger number in jumps of 1.

12 + 2

+ 3

=

5

This is then refined and written without the use of pictures. However, children would still be using concrete apparatus for their working out of the calculation.

2 3

+ +

3 4

= =

5 = +1

12

17 +1

13

+1

14

+1

15

+1

16

17

5 7 Vicky Boulain

Year 3

In Year 2 children will initially continue to work on blank number lines. Children will look at bridging to 10 whilst adding on a blank number line. This will help build their confidence not only in written methods but also mental methods.

36

+

7

=

43

+4

Children will begin the year by consolidating their use of the partitioning method for addition. Progression in Year 3 addition looks to apply the partitioning method into vertical written methods – expanded column method.

463 + 514 = 977

+3

400 + 60 + 3 36

+ 500 + 10 + 4

43

40

900 + 70 + 7

= 977

Once children are confident with bridging to 10 they will move onto use a blank number line to add numbers by partitioning into tens and units.

36

+

7

=

43

+10

+10

35

45

+4

55

59

Children will then begin more formal written calculations by adding through partitioning numbers which they should now be confident with.

124 100 20 4

+ + +

+

143

100 40 3

=

= 200 = 60 =7

267

= 267 Vicky Boulain

Year 4 Compact method for column addition.

351 + 425 = 776 3 5 1 + 4 2 5

Compact method for column addition – 4 digit numbers and numbers with 2 decimal places.

Year 6 Consolidation of Key Stage 2 written addition methods.

th h t u + th h t u = t u . ts hs + t u . ts hs =

7 7 6 6 5. 14 + 2 3 .63 Children will be adding 3 digit numbers

8 8.7 7

htu+htu=

Vicky Boulain

Subtraction Year R Children are introduced to subtraction with the use of apparatus and objects. They begin with a set of objects and experiment with taking some away and counting how many are left.

Year 1 Children will use a number track to subtract 2 numbers using jumps of 1. Children will understand that when subtracting you move from the right to the left on number tracks or number lines.

10

-

5

=

5

Pictorial representations of calculations – children are encouraged to take away the amounts to find the number left.

=4 Children will then progress on to being introduced to the (subtraction) - sign and the (same as) = sign.

8

-

3

=

5

This would then be refined and written without the use of pictures. However, children would still be using concrete apparatus for their working out of the calculation.

3 6

-

2 4

= =

Children will start to understand that numbers can be subtracted from each other but that you must start off with the bigger number and subtract the smaller number.

1 2

Children will progress onto using a blank number line to subtract the smaller number from the bigger number in jumps of 1.

18 -

5 =

13

-1

13

-1

14

-1

15

-1

16

-1

17

18

Vicky Boulain

Subtraction Year 2

Year 3

In Year 2 children will continue to work on blank number lines. Children will look at bridging to 10 whilst subtracting on a blank number line. This will help build their confidence not only in written methods but also mental methods.

46

-

9

=

37

-3

Progression in Year 3 subtraction looks to apply the partitioning method into vertical written methods – expanded column method.

823 - 451 = 372

-6

37

Children will begin the year by consolidating their use of the partitioning method for subtraction.

700 120 800 + 20 + 3

46

40

- 400 + 50 + 1 300 + 70 + 2

= 372

Once children are confident with bridging to 10 they will then move onto using a blank number line to subtract numbers by partitioning them into tens and units.

Finding the difference

83

In year 3 children will also be introduced to the concept of finding the difference.

-

22

-10

-2

61

= 61

63

Children are encouraged to count up from the smaller number to the bigger number when the difference is small.

-10

73

83

58 – 47 = 11 +3

47

+8

50

58 Vicky Boulain

Subtraction Year 5

Year 4 Compact method for column subtraction.

826 - 578 = 248 7 11 16 8 2 6

Year 6

Compact method for column subtraction – 4 Consolidation of Key Stage 2 written digit numbers and numbers with 2 decimal subtraction methods. places.

th h t u - th h t u = t u . ts hs - t u . ts hs =

- 5 7 8 2 4 8

3 5. 65 - 2 3 . 1 3

Children will be subtracting 3 digit numbers

1 2 . 5 2

htu-htu= Finding the difference Children will continue to use the method of finding the difference and counting on where the numbers are appropriate. (Counting up from the smaller number to the bigger number).

Find the difference between 4 and 9 = 5

Children are encouraged to select their own method for this. Vicky Boulain

Multiplication Year R

Year 1 Children will be looking at ‘lots of’ and will be using practical apparatus to make ‘lots of’

Cars come in packs of 2s How many cars do I have if I have 3 packs?

No formal recording of number sentences in books.

Vicky Boulain

Multiplication Year 2

Year 3

In Year 2 children will start to look at how they can describe multiplication pictorially by using arrays.

Children will begin the year applying their use of the partitioning method for multiplication.

3 X 4 = 12

12 x 4 = 48 10 x 4 = 40 2 x 4 =8 40 + 8 = 48

Towards the end of Year 3 children will start to use the grid method for multiplication Children will then progress onto using repeated addition to show multiplication on a blank number line.

12 x 3 = 36

4 X 2 =8 3 +2

0

+2

+2

2

4

+2

6

8

10

2

30

6

= 36

Children will work on multiplying 2 digit by 1 digit numbers.

Vicky Boulain

Multiplication Year 5

Year 4 Continue using grid method to multiply 2 digit numbers together.

t u xt u=

Year 6

Children will continue to use the grid method to multiply numbers with 2 decimal points.

6.13 X 81 =

72 x 12 = 864 6

70

2

10

700

20

= 726

2

140

4

= 144 = 870

Children will progress to using grid method to multiply numbers with 1 decimal place.

0.13 4

80

1

480

6

10.4

0.13

Short multiplication using column method – 3 digit numbers by 1 digit number.

h t u x u . ths = 365 X 1.3 =

= 486 = 10.53 =496.53

Long multiplication using column method – 3 digit numbers by 1 digit number.

3 6 5 X

1.3

1 0 9 5 3 6 5 0 4 7 4.5 I

h t u xu= 346 x 9 =

5.3 X 72 = 381.6 70

2

5

350

10

= 360

0.3

21

0.6

= 21.6

3 4 6

=381.6

X

9

54 3 6 0 2 7 0 0 3 1 1 4 I

Vicky Boulain

Division Year R

Year 1 Children will be looking at ‘sharing’ and will be using practical apparatus to make ‘groups’ of objects

I have 4 sweets.

I share them with my 2 friends.

How many sweets does each child get?

Vicky Boulain

Division Year 2

Year 3

In Year 2 children will start to look at how they can divide by sharing equally. Children start by sharing physical objects and then record this pictorially.

8 ÷ 4 = 2

Children will consolidate their learning using repeated addition to show division on a blank number line with remainders.

46 ÷ 6 = 7 r4 +6 1 1 0

Children then move on to using repeated addition to show division on a blank number line.

12 ÷ 6 = 2 +6

+6

+6

+6

+6

2

3

4

5

6

7

12

6

18

24

30

(3 x 10)

6

0

(3 x 2)

10

10 30

2 60

15 ÷ 6 = 2 r3 +6

+6

0

+3

2

1 6

42

36

(3 x 10)

12

Children will then use repeated addition to show division on a blank number line with remainders.

12

+4

Children will then move on to chunking numbers together on a blank number line to work out division problems in a more time efficient way.

2

0

+6

66 ÷ 3 = 22

+6

1

+6

15 Vicky Boulain

66

46

Division Year 5

Year 4 Children will continue to consolidate the use of the chunking method on a blank number line using bigger numbers and division problems with remainders.

Chunking method for division – This is where you use your tables knowledge to support division such as 3 digit numbers by 1 digit number with remainders.

738 ÷ 7 = 105 r3

htu÷u=

(7 x 100)

224 ÷ 5 = 45 r 4

(7 x 5) +3

5

100 0

700

735

738

224 200 (40x5) 24 20 (4x5) 4 Short (bus stop division) 3 digit number by 1 digit number with remainders.

Year 6 Long division for numbers with more place values such as 3 digit numbers divided by 2 digit numbers with remainders.

htu÷tu= 697 ÷ 17 = 0 4 1 17) 6 9 7 0 2 3

Children will also continue to consolidate their use of the short (bus stop method) as they become more confident.

htu÷u= 871 ÷ 12 = 0 7 2r7 12) 8 7 1 Vicky Boulain

Vocabulary for 4 operations

Vicky Boulain