MULTIPLICATION AND DIVISION
Year 1
Multiplication and Division facts
 count in multiples of twos, fives and tens (copied from Number and Place Value)
Mental Calculations
 count in multiples of twos, fives and tens (copied from Number and Place Value)
Problem Solving
 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
MULTIPLICATION - Year 1
5 groups
of 2
6 lots of 5
5 pairs
5 lots of 2 or
2 lots of 5
4 lots of 2
or
2 lots of 4
DIVISION - Year 1
Solve problems involving both sharing and grouping:
Sharing 12 cakes equally between 3
How many groups of 3 are in 15?
How many groups of 4 can be made with 12 stars?
MULTIPLICATION AND DIVISION
Year 2
Multiplication and Division facts
 count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward
(copied from Number and Place Value)
 recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including
recognising odd and even numbers
 Know that doubling is multiplying by 2 and halving is divided by 2
 I know significant doubles (eg 10 + 10, 50+ 50=, 50p+50p= ) involving doubling multiples of 5
upto 50
Mental Calculations
 show that multiplication of two numbers can be done in any order (commutative) and division of
one number by another cannot
Written Calculations
 calculate mathematical statements for multiplication and division within the multiplication tables
and write them using the multiplication (×), division (÷) and equals (=) signs
Inverse Operations, Estimating and Checking
 Understand that division is the inverse of multiplication
Problem Solving
 solve problems involving multiplication and division, using materials, arrays, repeated addition,
mental methods, and multiplication and division facts, including problems in contexts
MULTIPLICATION - Year 2
Use arrays to show commutative property of
multiplication
Relate multiplication to scaling
DIVISION – Year 2
How many 10ps are in 50p?
Introducing that division is
the inverse of multiplication
Grouping using a number line: Children to see
the link between multiplication and division
and begin to recall division facts.
Children understand that halving means “divided by 2”.
MULTIPLICATION AND DIVISION
Year 3
Multiplication and Division facts
 count from 0 in multiples of 4, 8, 50 and 100 (copied from Number and Place Value)
 recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables
Mental Calculations
 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 (appears also in Written Methods)
o Through doubling, they connect the 2, 4 and 8 multiplication tables.
o Pupils develop efficient mental methods, for example, using commutativity and associativity
(for example, 4 × 12 × 5 = 4 × 5 × 12 = 20 × 12 = 240)
o Children use existing knowledge to find related facts:
For example, using 3 × 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3 to derive related facts (for example, 30
× 2 = 60, 60 ÷ 3 = 20 and 20 = 60 ÷ 3).
Written Calculations
 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 (appears also in Mental Methods)
Inverse Operations, Estimating and Checking
 estimate the answer to a calculation and use inverse operations to check answers (copied from
Addition and Subtraction)
Problem Solving
 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
MULTIPLICATION - Year 3
Children continue to learn from concrete resources and other models and images to develop conceptual
understanding. (See Years 1 and 2)
Children represent calculations as arrays, repeated addition and use number lines to calculate.
Through doubling, they connect the 2, 4 and 8 multiplication tables.
Pupils develop efficient mental methods, for example, using commutativity and associativity (for example, 4 ×
12 × 5 = 4 × 5 × 12 = 20 × 12 = 240)
Children use existing knowledge to find related facts:
If 3 x 2 = 6 then 3 x 20 = 60
Children continue to relate multiplication
to scaling contexts.
DIVISION – Year 3
Children continue to learn from concrete resources and other models and images to develop conceptual
understanding. (See Years 1 and 2)
Children use existing knowledge to find related facts:
For example, using 3 × 2 = 6, 6 ÷ 3 = 2 and 2 = 6 ÷ 3) to derive related facts (for example, 30 × 2 = 60, 60 ÷ 3 =
20 and 20 = 60 ÷ 3).
Children continue to use number lines to find groups of numbers including remainders:
16 ÷ 3 = 5 r1
0
3
6
9
12
15 16
MULTIPLICATION AND DIVISION
Year 4
Multiplication and Division facts
 count in multiples of 6, 7, 9, 25 and 1000 (copied from Number and Place Value)
 recall multiplication and division facts for multiplication tables up to 12 × 12
 Doubles and halves of numbers up to 50
Mental Calculations
 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 (appears also in Properties
of Numbers)
 understand the impact on place value when a number is multiplied or divided by 10 and 100
 Halve whole numbers including odd numbers
 Know that x 4 is doubling twice and x8 is doubling three times
Written Calculations
 multiply two-digit and three-digit numbers by a one-digit number using grid method
Properties of Numbers – Multiples, Factors, Primes, Square and Cube numbers
 recognise and use factor pairs and commutativity in mental calculations (repeated)
Inverse Operations, Estimating and Checking
 estimate and use inverse operations to check answers to a calculation
Problem Solving
 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
MULTIPLICATION - Year 4
Children continue to learn from concrete resources and other models and images to develop conceptual
understanding. (See Years 1 and 2)
Children use mental strategies to find products and missing numbers.
Children then move on to using grid method for multiplying two and three digit numbers by one number
14 x 6
Estimation: 10 x 6 = 60
x
10
4
6
60
24
60 + 24 = 84
234 x 6
Estimation: 200 x 6 = 1200
1200 + 180 + 24 = 1404 using column addition if necessary
1
x
200
30
4
6
1200
180
24
1200
180
24
_____
1404
DIVISION – Year 4
Children continue to learn from concrete
resources and other models and images to develop conceptual
1
understanding. (See Years 1 and 2)
Children use mental strategies to find products and missing numbers.
Children begin to chunk on a number line: ( 2 or 3 digit number by a 1 digit number)
96 ÷ 3 = 32
MULTIPLICATION AND DIVISION
Year 5
Multiplication and Division facts
 count forwards or backwards in steps of powers of 10 for any given number up to 1,000,000
(copied from Number and Place Value)
Mental Calculations
 multiply and divide numbers mentally drawing upon known facts including decimals
o 0.6 x 7 = 4.2 because 6 x 7 = 42
o 3.5 ÷ 5 = 0.7 because 35 ÷ 5 = 7
 multiply and divide whole numbers and those involving decimals by 10, 100 and 1000
 Know that TU x 5 is TU x 10 and then divided by 2 (18 x 5 = (18 x 10) ÷ 2)
 Know that TU x 9 is TU x 10 then subtract TU (18 x 9 = (18 x 10) – 18 = 162)
 Round and compensate for near pounds (£4.99 x 3 = £5 x 3 – 3p = £14.97)
 Use knowledge of doubles and halves of whole numbers to find doubles and halves of decimal
numbers (2.3 + 2.3 = 4.6 because 23+23=46; Half of 5.8 is 2.7 because half of 58 is 27)
Written Calculations
 multiply numbers up to 4 digits by a one- or two-digit number using a formal written method
 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
Properties of Numbers – Multiples, Factors, Primes, Square and Cube numbers
 identify multiples and factors, including finding all factor pairs of a number, and common factors of two
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
 recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)
Inverse Operations, Estimating and Checking
 estimate and use inverse operations to check answers to a calculation
Problem Solving
 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
MULTIPLICATION - Year 5
Children continue to learn from concrete resources and other models and images to develop conceptual
understanding. (See Years 1 and 2)
Children use mental strategies to find products and missing numbers.
Children practise using grid method for multiplying two and three digit numbers by one number as Year 4
Short Multiplication:
Use grid method to lead on to short multiplication. Children need to see the continuity in method and
appreciate its efficiency.
327 x 4 =
Estimation: 300 x 4 = 1200
Leading on to 4 digit numbers:
3652 x 8 =
Estimation: 4000 x 8 = 32,000
Use and apply this method in the context of money and measures as well.
DIVISION – Year 5
Children continue to learn from concrete resources and other models and images to develop conceptual
understanding. (See Years 1 and 2)
Children use short division (bus stop method) to calculate 2 and 3
digit numbers with1 digit number
Children see the link between chunking on a number line with
short division:
96 ÷ 3 = 32
Continue with short division with
“carrying”:
Short division with remainder answers:
MULTIPLICATION AND DIVISION
Year 6
Multiplication and Division facts
 As Year 5
Mental Calculations
 perform mental calculations, including with mixed operations and large numbers
 associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple
fraction (e.g. 3/8)
(copied from Fractions)
Written Calculations
 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 one-digit whole number using the formal written method of short
division where appropriate for the context
 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
 use written division methods in cases where the answer has up to two decimal places (copied from
Fractions (including decimals))
Properties of Numbers – Multiples, Factors, Primes, Square and Cube numbers
 identify common factors, common multiples and prime numbers
 use common factors to simplify fractions; use common multiples to express fractions in the same
denomination
(copied from Fractions)
 calculate, estimate and compare volume of cubes and cuboids using standard units, including
centimetre cubed (cm3) and cubic metres (m3), and extending to other units such as mm3 and km3
(copied from Measures)
Order of Operations
 use their knowledge of the order of operations to carry out calculations involving the four operations
Inverse Operations, Estimating and Checking
 use estimation to check answers to calculations and determine, in the context of a problem, levels of
accuracy
Problem Solving
 solve problems involving addition, subtraction, multiplication and division
 solve problems involving similar shapes where the scale factor is known or can be found
(copied from Ratio and Proportion)
MULTIPLICATION - Year 6
Children continue to learn from concrete resources and other models and images to develop conceptual
understanding. (See Years 1 and 2)
Children practise short multiplication as in Year 5
Use grid multiplication to introduce long multiplication:
18 x 13 =
Estimation: 20 x 10 = 200
1234 x 16 =
Estimation: 1200 x 20 = 24,000
Use short and long multiplication to multiply numbers with up to 2 decimal places:
3.19 x 8 =
Estimation: 3 x 8 = 24
Use and apply this method in the context of money and measures as well.
DIVISION – Year 6
Children continue to learn from concrete resources and other models and images to develop conceptual
understanding. (See Years 1 and 2)
Children practice short division as in Year 5
Extend short division to include converting remainders to decimals (only to those who are ready):
Introduce long division to those who are ready: