Calculation Policy
Division – Years 4-6
Division
Obj
Gui
Year 4
Vid
Ex
Obj
Gui
Year 5
Vid
Ex
Divide up to 3 digit numbers by a single digit (without remainders initially)
Pupils must be secure with the process of short division for dividing 2-digit numbers by a single digit (see
steps in Y3), and must understand how to calculate remainders, using this to ‘carry’ remainders within
the calculation process (see example)
Dividing a 3 digit number by a one digit number.
When the answer for the first column is zero (e.g. how many groups of 5 can be made from 1
hundred?), children could initially write a zero above to acknowledge its place, in this example,
with the hundred being exchanged for 10 tens as it moves to the tens column.
Real life contexts need to be used routinely to help pupils gain a full understanding, and the ability to recognise the place of
division and how to apply it to problems. Include money and measure contexts when confident.
As a teaching
tool only by the
end of Year 4.
Obj
Gui
Year 6
Vid
Ex
Divide at least 4 digit numbers by both single digit and
2 digit numbers (including decimal numbers and
quantities)
Short division with remainders:
Pupils should continue to use the short division method,
but with numbers to at least 4 digits. They should
understand how to express remainders as fractions,
decimals, whole number remainders or rounded
numbers. Real life problem solving contexts need to be
the starting point, where pupils have to consider the
most appropriate way to express the remainder.
Calculating a decimal remainder: In the example below,
rather than expressing the remainder as r 1, a decimal
for the calculation ‘how many groups of 8 can be made
point is added after the units because there is still a
from 17 ones?’ there is a remainder of 1. A zero is
remainder, and the one remainder is carried onto zeros
placed after the decimal point in the tenths column and
after the decimal point (to show there was no decimal
the 1 remainder is exchanged for 10 tenths. The
value in the original number). Keep dividing to an
calculation is then ‘how many groups of 8 can be made
appropriate degree of accuracy for the problem being
out of 10 tenths? This process can continue by adding
solved.
zeros in the following decimal columns to
accommodate remainders as necessary.
Divide up to 4 digits by a single digit, including those with
remainders.
Now that pupils are introduced to examples that give rise to
remainder answers, division needs to have a real life problem
solving context, where pupils consider the meaning of the
remainder and how to express it, i.e. as a fraction, a decimal, or
as a rounded number or value, depending upon the context of
the problem.
The answer to 5309 ÷ 8 could be expressed as 663 and 5 eighths,
663r5 as a decimal or rounded as appropriate.
Remainders can be used in Year 4 but decimals and
fractions should be used by Year 5 (see example in Y6
section)
Division
Children should also be taught to use the long division
method. A detailed explanation of how to carry out this
method is included on the next page.
Division
The National Curriculum in England. ©Crown Copyright 2013
Year 4 objectives
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Division
The National Curriculum in England. ©Crown Copyright 2013
Year 4 guidance
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Division
The National Curriculum in England. ©Crown Copyright 2013
Year 5 objectives
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Division
The National Curriculum in England. ©Crown Copyright 2013
Year 5 guidance
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Division
The National Curriculum in England. ©Crown Copyright 2013
Year 6 objectives
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Division
The National Curriculum in England. ©Crown Copyright 2013
Year 6 guidance
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Division