How your child
learns to calculate:
Division
Children need to understand division in two ways:
-
sharing equally (e.g. sharing out 6 sweets between 3 children)
grouping (e.g. making groups of 2 from a total of 6)
Year 1:
- Children are able to count back in ones, twos, fives and tens.
- Children can share objects into groups and count how many are in each
group.
Skills needed to be able to solve division calculations:
-
be able to count back in steps of equal size (especially tens)
be able to halve
know their multiplication facts (times tables) and know that these are
also division facts (how many 8s are in 24?)
Solving division, using sharing equally
Solving division, using repeated subtraction
As for multiplication and repeated addition, this is the first step when moving
to a written method. Children see that division is linked to subtraction and that
the same amount is being taken away more than one time.
Children use a number line and starting with the total, repeat taking away the
divisor (the number which is divided into the total) until they have nothing left:
The answer is in the number of jumps needed (so in this diagram it is 4).
Solving division, using chunking on a number line
When moving on to larger numbers, children use key facts from their times
tables to support their working. This allows them to become more efficient
with repeated subtraction by chunking groups together:
Starting with 98, 10 groups of 7 have been chunked together all at once and
counted back, leaving 28 on the number line. This speeds up the process of
solving division. Children are ready for this method when they have secure
times table knowledge and counting back skills.
The answer is in how many groups of 7 have been made, which in this
diagram is 14.
The number line method can also be used to solve problems with remainders,
and with bigger numbers.
Solving division, using chunking with a written method
When children are ready to move away from the number line, they use a
written vertical method:
It works exactly the same as the number line: Key facts are recorded and then
chunks of the divisor are taken away at the same time. The notes in the
brackets are important because they explain how many groups have been
taken away. This is where the final answer will be found. In this question, we
can see that 18 groups of 13 were taken away until there was nothing left.
The ability to solve subtraction mentally, and times table knowledge are
necessary to be able to use this method.
Becoming more efficient
Here, with good times table knowledge, 30 groups of 6 are taken away
altogether. If children know that 3 x 6 is 18, they can know that 30 x 6 is 180
and so become more efficient with their working out.
When 4 is left, no more groups of 6 can be taken away, so this is the
remainder.
Important note:
All children are different and should be allowed to choose the method that
they feel most comfortable and confident with. Some children will always find
the number line method the best way of working out calculations. This method
will work for any size of numbers and with problems with remainders in the
answer, so does not stop them from progressing in their maths work.