The New National Curriculum for Mathematics aims to ensure that all

pupils:

• become fluent  - confident and accurate in their maths skills

• reason mathematically - can talk about their work and explain their thinking

• can solve problems - can apply their knowledge in different contexts

Addition

Addition in Year 1

•Focussing on what ‘equals’ means 2 = 2

=

3 =

Represent and use number bonds to 20

Use a range of concrete objects

• Add one digit and two digit numbers – use objects, number lines, counting on

• Solve problems using concrete objects and representations

• Identify ‘one more’How many different ways can you make 5?

My plant measures 16cm.Tomorrow it will be 5cm taller.How tall will it be tomorrow?Show me how you know youranswer is correct.

Addition in Year 2

• Add numbers using objects, pictorial representations and mentally

2 digit number and ones 2 digit number and tens 2 two digit numbers

32 + 22=

24 + 13 =20 + 10 = 304 + 3 = 730 + 7 =

Partitioning

Re-partitioning numbers

Introduction to columns

• Recall and use addition and subtraction facts to 20 and derive and use related facts to 100

• Demonstrate thecommutative law of addition

I know that 7 + 3 = 10. So27 + 3 makes 30. To checkthis, I can partition 27 into20 and 7 .20+7+ 3= 20+10= 30

=+ +

Commutative

12 + 30 = 30 + 12

? + 25 = 25 + 41

Addition Year 3

Mental calculationAdd numbers mentally, including:• a three‐digit number and ones• a three‐digit number and tens• a three digit number and hundreds• Partition all numbers and recombine,

start with TO + TO then HTO + TO

Written calculationAdd numbers with up to three digits, using formal

written (columnar) methods

Addition Year 4

Mental calculations• Practise mental methods with

increasingly large numbers• Consolidate partitioning and re‐

partitioning• Use compensation for adding too

much/little and adjusting

Mental calculation

• I know that 63 + 29 is

• the same as 63 + 30 –1

I know that 63 + 29 isthe same as 63 + 30 –1

55 + 37 =55 + 30 + 7 = 92

43

Written calculationsAdd numbers with up to four digits, using

the formal written (columnar) method

262 + 145 =

Addition Year 5• Add numbers mentally with increasingly large

numbers, e.g. 12 462 + 2300 = 14 762• Mentally add tenths, and one‐digit numbers and

tenths• Add decimals, including a mix of whole numbers

and decimals, decimals with different numbers of places, and complements of 1 (e.g. 0.83 +

0.17 = 1)1.9km + 1.3km =

Written calculationAdd whole numbers with more than four digits, using the formal written

(columnar) method

• Add fractions with the same denominator and denominators that are multiples of the

same number

Addition Year 6

Mental calculations• Perform mental calculations,

including with mixed operations and large numbers (more complex calculations)

• Children use representation of choice• Consolidate partitioning and re‐

partitioning• Use compensation for adding too

much/little and adjusting• Refer back to pictorial and physical

representations when needed.

Adding Fractions

• Add fractions with different denominators and mixed numbers, using the concept of equivalent fractions

Find the common denominator:

2/5 + 3/8 =

5 and 8 are both factors of 40.

16/40 + 15/40 = 31/40

Mental Strategies

Putting the largest number first:• 5 + 36 is the same as 36 + 5. Start at 36 and count on

in ones• 30 + 60 is the same as 60 + 30. Start at 60 and count on

in tens

Partitioning:• 14 + 25 = (10 + 4) + (20 + 5)• (10 + 20) = 30• (4 + 5) = 9• The answer is 39

Compensation:• 17 + 9 = 17 + 10 – 1 = 26• 26 + 11 = 26 + 10 + 1 = 37

Doubles or near doubles:• 8 + 8 = 16

so 8 + 9 = 8 + 8 + 1 = 17

Bridging through 10, 20 etc• 8 + 7 = (8 + 2) + 5

10 + 5 = 15• 15 + 9 = (15 + 5) + 4

20 + 4 = 24

Addition

27

• 8 + 5

• 25 + 42

• 25 + 27

• 25 + 49

• 127 + 113

• 145 +127

• 3537 + 2946

How would you solve these?• Number line

• Partitioning

• Diennes

• Place value counters

• Column addition

• 100 square

• Compensation

• Pictures