1. Addition Subtraction Multiplication Division
CPA for parents
Addition
Subtraction
Multiplication
Division

2. Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’
Expectations
Combining two parts to make a whole (part whole model).
Starting at the bigger number and counting on (using cubes).
Regrouping to make 10 using tens frame.
Key symbols
+ =

3. Year 1 Addition and subtraction
read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
represent and use number bonds and related subtraction facts within 20
add and subtract one-digit and two-digit numbers to 20, including zero
solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ☐ – 9.

4. Addition: reception/year 1

5. - = Subtraction:reception/year 1 Key vocabulary Take away Less than
The difference
Subtract
Minus
Fewer
Decrease
Expectations
Taking away ones
Counting back
Finding the difference
Part whole model
Make 10 using the ten frame
Key symbols
- =

6. Subtraction:reception/year 1

7. Subtraction:reception/year 1

8. Addition: year 2 Expectations
Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’
Expectations
Adding three single digits.
Use of base 10 to
combine two numbers.
Key symbols
+ =
Addition: year 2

9. Year 2 Addition and subtraction
solve problems with addition and subtraction:
using concrete objects and pictorial representations, including those involving numbers, quantities and measures
applying their increasing knowledge of mental and written methods
recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
a two-digit number and ones
a two-digit number and tens
two two-digit numbers
adding three one-digit numbers
show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.

10. Addition: year 2

11. - = Subtraction: year 2 Key vocabulary Take away Less than
The difference
Subtract
Minus
Fewer
Decrease
Expectations
Counting back
Finding the difference
Part whole model
Make 10
Use the base of 10
Key symbols
- =

12. Subtraction: year 2

13. Addition: year 3 Expectations
Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’
Expectations
Column method- regrouping.
Using place value counters (up to 3 digits).
Key symbols
+ =
Addition: year 3

14. Year 3 Addition and subtraction
add and subtract numbers mentally, including: a three-digit number and ones a three-digit number and tens a three-digit number and hundreds add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction estimate the answer to a calculation and use inverse operations to check answers solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction.

15. Addition: year 3

16. - = Subtraction: year 3 Key vocabulary Take away Less than
The difference
Subtract
Minus
Fewer
Decrease
Expectations
Column method with regrouping (up to 3 digits using place value counters)
Key symbols
- =

17. Subtraction: year 3

18. Addition: year 4 Expectations
Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’
Expectations
Column method- regrouping (up to 4 digits).
Key symbols
+ =
Addition: year 4

19. Year 4 Addition and subtraction
add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
estimate and use inverse operations to check answers to a calculation
solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

20. Addition: year 4

21. - = Subtraction: year 4 Key vocabulary Expectations Take away
Less than
The difference
Subtract
Minus
Fewer
Decrease
Expectations
Column method with regrouping (up to 4 digits)
Key symbols
- =

22. Subtraction: year 4

23. Addition: year 5 Expectations
Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’
Expectations
Column method- regrouping (up to 4 digits).
Use of place value counters for adding decimals.
Key symbols
+ = .
Addition: year 5

24. Year 5 Addition and subtraction
add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)
add and subtract numbers mentally with increasingly large numbers
use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy
solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

25. Addition: year 5

26. - = . Subtraction: year 5 Key vocabulary Expectations Take away
Less than
The difference
Subtract
Minus
Fewer
Decrease
Expectations
Column method with regrouping
Abstract for whole numbers
Start with place value counters for decimals- with the same amount of decimal places.
Key symbols
- =

27. Subtraction: year 5

28. Addition: year 6 Expectations
Key vocabulary Sum, total Parts and wholes Plus, add Altogether More ‘is equal to’ ‘is the same as’
Expectations
Column method- regrouping (up to 4 digits).
Abstract methods.
Place value counters to be used for adding decimal numbers.
Key symbols
+ = .
Addition: year 6

29. Year 6 Addition and subtraction
perform mental calculations, including with mixed operations and large numbers
use their knowledge of the order of operations to carry out calculations involving the four operations
solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
solve problems involving addition, subtraction, multiplication and division
use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

30. Addition: year 6

31. - = . Subtraction: year 6 Key vocabulary Expectations Take away
Less than
The difference
Subtract
Minus
Fewer
Decrease
Integer
Decimal
Expectations
Column method with regrouping
Abstract methods
Place value counters
for decimals - with different amounts of decimal places.
Key symbols
- =

32. Subtraction: year 6

33. Multiplication and division

34. Year 1 multiplication and division
solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

35. x = Multiplication: reception/year 1 Key vocabulary Double Times
Multiply by
The product of
Groups of
Lots of
Equal groups
(Area)
Expectations
Recognising and making equal groups.
Doubling.
Counting in multiples Use cubes, Numicon and other objects in the classroom
Key symbols
x =

36. Multiplication: reception/year 1

37. ÷ = / Division: reception/year 1 Key vocabulary Share Group Divide
Divided by
Half
Expectations
Sharing objects into groups
Division as grouping (e.g. I have 12 sweets and put them in groups of 3, how many groups?)
Use cubes and draw round the same number of cubes at a time.
Key symbols
÷ = /

38. Division: reception/year 1

39. Year 2 Multiplication and division
recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts.

40. x = Multiplication: year 2 Key vocabulary Double Times Multiply by
The product of
Groups of
Lots of
Equal groups
(Area)
Expectations
Arrays- showing commutative multiplication
Key symbols
x =

41. Multiplication: year 2

42. ÷ = / Division: year 2 Key vocabulary Share Group Divide Divided by
Half
Expectations
Division as grouping
Division within arrays- linking to multiplication
Repeated subtraction
Key symbols
÷ = /

43. Division: year 2

44. Year 3 Multiplication and division
recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods
solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.

45. x = Multiplication: year 3 Key vocabulary Double Times Multiply by
The product of
Groups of
Lots of
Equal groups
(Area)
Expectations
Arrays
2d × 1d using base 10
Key symbols
x =

46. Multiplication: year 3

47. ÷ = / Division: year 3 Key vocabulary Share Group Divide Divided by
Half
Expectations
Division with a remainder-using lollipop sticks, times tables facts and repeated subtraction.
2d divided by 1d using base 10 or place value counters
Key symbols
÷ = /

48. Division: year 3

49. Year 4 Multiplication and division
recall multiplication and division facts for multiplication tables up to 12 × 12
use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
recognise and use factor pairs and commutativity in mental calculations
multiply two-digit and three-digit numbers by a one-digit number using formal written layout
solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.

50. x = Multiplication: year 4 Key vocabulary Double Times Multiply by
The product of
Groups of
Lots of
Equal groups
(Area)
Expectations
Column multiplication- introduced with place value counters.
(2 and 3-digit multiplied by 1-digit).
Key symbols
x =

51. Multiplication: year 4

52. ÷ = / Division: year 4 Key vocabulary Share Group Divide Divided by
Half
Expectations
Division with a remainder.
Short division (up to 3 digits by 1 digit- concrete and pictorial).
Key symbols
÷ = /

53. Division: year 4
Year 4
Year 5

54. Year 5 Multiplication and division
identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers
know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers
establish whether a number up to 100 is prime and recall prime numbers up to 19
multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers
multiply and divide numbers mentally, drawing upon known facts
divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context
multiply and divide whole numbers and those involving decimals by 10, 100 and 1,000
recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes
solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign
solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates

55. x = Multiplication: year 5 Key vocabulary Double Times Multiply by
The product of
Groups of
Lots of
Equal groups
(Area)
Expectations
Column multiplication
Abstract only but might need a repeat of year 4 first (up to 4 digit numbers multiplied by 1 or 2 digit numbers)
Key symbols
x =

56. Multiplication: year 5
Year4
Year 5

57. ÷ = / Division: year 5 Key vocabulary Share Group Divide Divided by
Half
Expectations
Short division
(up to 4 digits by a 1 digit number including remainders)
Key symbols
÷ = /

58. Division: year 5

59. Year 6 Multiplication and division
multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
perform mental calculations, including with mixed operations and large numbers
identify common factors, common multiples and prime numbers
use their knowledge of the order of operations to carry out calculations involving the four operations
solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
solve problems involving addition, subtraction, multiplication and division
use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

60. x = Multiplication: year 6 Key vocabulary Double Times Multiply by
The product of
Groups of
Lots of
Equal groups
(Area)
Expectations
Column multiplication.
Abstract methods (multi-digit up to 4 digits by a 2 digit number).
Key symbols
x =

61. Multiplication: year 6

62. ÷ = / Division: year 6 Key vocabulary Share Group Divide Divided by
Half
Expectations
Short division.
Long division with place value counters (up to 4 digits by a 2 digit number).
Children should exchange into the tenths and hundredths column too.
Key symbols
÷ = /

63. Year 6 also do short division as per year 5
Division: year 6
Year 6 also do short division as per year 5