FLIXTON JUNIOR SCHOOL
Calculations Policy
Division
Written: September 2015
Next Review: July 2017
DIVISION
Year Group Expectations
Year 3
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Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a
known or related fact, calculate mentally, use a jotting, written method)
Understand that division is the inverse of multiplication and vice versa
Understand how division statements can be represented using arrays
Understand division as sharing and grouping and use each appropriately
Recall and use division facts for the 3, 4 and 8 multiplication tables
Derive and use doubles of all numbers to 100 and corresponding halves
Write and calculate mathematical statements for division using the multiplication tables that they
know, including for two-digit numbers divided by one-digit numbers using mental methods,
progressing to formal written methods
Use estimation to check answers to calculations and determine, in the context of a problem, an
appropriate degree of accuracy
Solve problems, including missing number problems, involving division (and interpreting
remainders), including positive integer scaling problems and correspondence problems in which n
objects are connected to m objects
Year 4
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Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a
known or related fact, calculate mentally, use a jotting, written method)
Recognise and use factor pairs and commutativity in mental calculations
Recall division facts for multiplication tables up to 12 × 12
Use partitioning to double or halve any number, including decimals to one decimal place
Use place value, known and derived facts to divide mentally
Divide numbers up to 3 digits by a one-digit number using the formal written method of short
division and interpret remainders appropriately for the context
Use estimation and inverse to check answers to calculations and determine, in the context of a
problem, an appropriate degree of accuracy
Solve problems involving division (including interpreting remainders), integer scaling problems
and harder correspondence problems such as n objects are connected to m objects
Year 5
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Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a
known or related fact, calculate mentally, use a jotting, written method)
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
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Recognise and use square numbers and cube numbers, and the notation for squared ( ) and
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cubed ( )
Use partitioning to double any number, including decimals to two decimal places
Divide numbers mentally drawing upon known facts
Solve problems involving division including using their knowledge of factors and multiples,
squares and cubes
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
Use estimation and inverse to check answers to calculations and determine, in the context of a
problem, an appropriate degree of accuracy
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
Year 6
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Choose an appropriate strategy to solve a calculation based upon the numbers involved (recall a
known or related fact, calculate mentally, use a jotting, written method)
Identify common factors, common multiples and prime numbers
Use partitioning to double or halve any number
Perform mental calculations, including with mixed operations and large numbers
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
Use written division methods in cases where the answer has up to two decimal places
Use estimation and inverse to check answers to calculations and determine, in the context of a
problem, an appropriate degree of accuracy
Use their knowledge of the order of operations to carry out calculations involving the four
operations
Solve problems involving addition, subtraction, multiplication and division
STAGE ONE
The Empty Number Line:
Use an empty number line to jump backwards to make the link with repeated
subtraction
STAGE TWO
Bar Models
Draw a bar model to visualize the calculation
30 ÷ 6 =
STAGE THREE
Vertical number line
Use a vertical number line in preparation for developing chunking.
Link to repeated subtraction.
Repeatedly subtract individual groups of the divisor.
Subtracting multiples of the divisor (initially 10 groups and individual groups, then 10 groups
and other multiples in line with tables knowledge.
STAGE FOUR
Chunking
Continue to develop use of grouping (repeated subtraction) to be able to subtract
multiples of the divisor, moving on to the use of the chunking method.
When developing their understanding of chunking children should utilize a key facts
box as shown below. This enables an efficient recall of table facts and will help them
in identifying the largest group they can subtract in one chunk. Any remainders
should be shown as integers, e.g.
Children should be able to use this method to divide a three digit number by a single
digit number. To make this method more efficient, the key facts box should be
extended to include 4x and 20x etc.
Children may continue to use a key facts box for as long as they find it useful. Using
their knowledge of linked table facts they should be encouraged to use higher
multiples of the divisor as shown above.
To develop the chunking method further, it should be extended to include dividing a
four-digit number by a two-digit number, e.g.
In addition children should also be able to use the chunking method and solve
calculations interpreting the remainder as a decimal up to two decimal places.
This should first be demonstrated using a simple calculation such as 13 ÷ 4 to show
the remainder initially as a fraction.
Using practical equipment, children can see that for 13 ÷ 4, the answer is 3
remainder 1, or put another way, there are three whole groups and a remainder of 1.
This remainder is one part towards a full group of four, so is ¼.
To show the remainder as a fraction, it becomes the numerator where the
denominator is the divisor.
To show the remainder as a decimal relies on the children’s knowledge of decimal
fraction equivalents. For decimals with no more than 2 decimal places, they should
be able to identify:
STAGE FIVE
Formal short method
Introduce using table facts that the children already know:
Introduce remainders
Formal method using partitioning
This will lead to
And with remainders