St Joseph’s Calculation Guidance
Formal Method for Addition/Subtraction
Pupils will be taught to use the formal written method of columnar addition and
subtraction throughout Key Stage 2. The following expectations are:




In Year 3, children will be expected to add and subtract numbers up to 3 digits
with formal written methods.
In Year 4, children will be expected to add and subtract numbers up to 4 digits
with formal written methods.
In Year 5, children will be expected to add and subtract numbers with more
than 4 digits with formal written methods.
In Year 6, children will be expected to add and subtract numbers with more
than 4 digits and apply this skill to adding and subtracting decimal numbers up
to two places with formal written methods.
1
1
1
Formal Method for Multiplication
Pupils will be taught to use the formal written methods of multiplication throughout
Key Stage 2. The following expectations are:




In Year 3, children will be expected to use short multiplication to multiply twodigit number by one-digit number.
In Year 4, children will be expected to use short multiplication to multiply twodigit and three-digit number by one-digit number.
In Year 5, children will be expected to use short multiplication to multiply up to
4 digits numbers by one-digit number and to use long multiplication to multiply
up to 4 digits by two-digit number.
In Year 6, children will be expected to use long multiplication to multiply multidigit numbers up to 4 digits by a two-digit whole number.
2
2
2
1
1
2
4
2
2
Formal Method for Division
Pupils will be taught to use the formal written methods of division throughout Key
Stage 2. The following expectations are:




In Year 3, children will be expected to recognise inverse facts connecting
multiplication and division together.
In Year 4, children will be expected to recall all multiplication and division facts
and be able to divide mentally using know and derived facts.
In Year 5, children will be expected to use short division to divide numbers up
to 4 digits by a one-digit number.
In Year 6, children will be expected to use long division to divide numbers up
to 4 digits by a two-digit number, interpreting remainders according to the
context (two decimal places).
0
0
4
4
0
(15x20)
(15x8)
Remainder given as a
whole number.
Remainder given as a
fraction and simplified.
Remainder given as a
decimal.
3
Written Methods for Adding/Subtracting Fractions
Pupils will be taught to use the written methods for adding and subtracting fractions
throughout Key Stage 2. The following expectations are:

In Year 3, children will be expected to add and subtract fractions with the
same denominator, within one whole.
For example,

5 + 1= 6
6 - 2 = 4 =1
7
8
7
7
8
8
2
In Year 4, children will be expected to add and subtract fractions with the
same denominator, beyond one whole.
For example,
1
5 + 4=
7

7
3 2
2
7
6 -
2 =
8
8
1 1
4=
1
8
2
In Year 5, children will be expected to add and subtract fractions with the
same denominator and denominators that are multiples of the same number.
Children will be taught to simplify, where possible.
For example,
2 - 3 = 4–3=1
3 6
6 6 6
1 + 4= 2+4=6=3
4
8 8 8 8 4

In Year 6, children will be expected to add and subtract fractions with different
denominators and mixed numbers, using the concept of equivalent fractions.
For example,
3 2 3 2 5 6 6
2+
4=
4
6
1-
4=
3
5
6+
12
5-
6 3 6 3
15
8 =
14 =
2 =
1
12
12
12
6
12 =
15
5 3
20 -
12 =
15
15
2
8
15
4
Written Methods for Multiplying/Dividing Fractions
Pupils will be taught to use the written methods for multiplying and dividing fractions
throughout Key Stage 2. The following expectations are:




In Year 3, children will be expected to recognise fractions in the context of
parts of a whole, numbers, measurements, a shape, and unit fractions as a
division of a quantity.
In Year 4, children will be expected to solve problems involving increasingly
harder fractions to divide quantities, including non-unit fractions where the
answer is a whole number.
In Year 5, children will be expected to multiply proper fractions and mixed
numbers by whole numbers, supported by materials and diagrams.
In Year 6, children will be expected to multiply simple pairs of proper fractions,
writing the answer in its simplest form. Be able to divide proper fractions by
whole numbers.
Examples;
1 x 1 = (1 x 1) = 1
2 x 3 = (2 x 3) = 6 = 3 = 1
4
3
1÷
3
1÷
3
2
(4 x 2)
2
2
=
8
1
4÷
= 1
(3 x 2)
6
5
=1÷2= 1x1=1
3
1
3
4
2
6
(3 x 4) 12 6
8
4÷
5
=
4
2
= 4 =1
(5 x 8)
8
40 10
=4÷ 8= 4x1=4=1
5
1
5 8
40 10
5