ACARA v9 CONTENT DESCRIPTION “solve problems involving division, choosing efficient strategies and using digital tools where appropriate; interpret any remainder according to the context and express results as a whole number, decimal or fraction”
Builds on multiplication facts and place value, and on the multiplication of the previous unit. Year 5 divides to solve problems, choosing efficient strategies, using a calculator where it helps, and dealing sensibly with any remainder. A remainder can be left as a whole-number remainder, written as a decimal, or written as a fraction, and the context of the problem decides which form, and whether to round up or down, makes sense.
Dividing by partitioning
One efficient way to divide is to partition the number by place value and divide each part. To work out eighty-four divided by four, split eighty-four into eighty and four: eighty divided by four is twenty, four divided by four is one, and twenty plus one is twenty-one. Partitioning turns a hard division into a few easy ones using known facts, then adds the results. Dividing is the reverse of multiplying, so the same facts that build the multiplication tables also answer division questions quickly.
Dividing by partitioning
Split by place value, divide each part, then add.
Divide 84 by 4 by partitioning.
Division with a remainder
Not every division comes out evenly, and what is left over is the remainder. Seventeen divided by five gives three, because five groups of three is fifteen, with two left over, written as three remainder two. Arranging seventeen objects into groups of five makes this clear: three full groups form, and two objects remain that cannot fill a fourth group. The remainder is always smaller than the number being divided by, because if it were as large, another whole group could be made. Recognising and recording the remainder is the first step; deciding what to do with it comes next.
Division with a remainder
Full groups in blue; the remainder in gold.
Share 17 into groups of 5.
Interpreting the remainder
What a remainder means depends on the problem, so it must be interpreted in context. If twenty-three children travel in cars holding four each, five cars carry twenty and three children are still waiting, so a sixth car is needed: the answer rounds up. If twenty-three lollies are shared equally among four children, each child gets five and three are left over, so the answer is five with some remaining: it rounds down. The same calculation, twenty-three divided by four, gives different sensible answers depending on what the numbers stand for. Reading the question carefully decides whether to round up, round down, or share the remainder out.
Interpreting the remainder
The context decides: round up, round down, or share.
Read the context to decide what to do with the remainder.
Whole number, decimal or fraction
A remainder can also be written as part of an exact answer, as a decimal or a fraction. Seventeen divided by five is three remainder two, and that two left over, shared into five, is two fifths, so the exact answer is three and two fifths, or three point four as a decimal. Which form to use depends on the context: a remainder suits whole objects, a decimal suits money or measurement, and a fraction suits an exact share. The whole-number remainder, the decimal and the fraction are three ways of writing the same result, and moving between them shows a full understanding of the division.
Whole number, decimal or fraction
One result, three ways to write it.
Write 17 / 5 as a remainder, a decimal and a fraction.
Solving division problems
Division solves many everyday problems: sharing a quantity equally, splitting into groups of a fixed size, or finding a rate. The steps are the same each time: decide that division is needed, choose an efficient strategy or a calculator, carry it out, and then interpret any remainder in the context of the problem. Checking the answer against an estimate guards against mistakes, since a division answer should be close to a rounded one. Setting the problem out clearly, with the numbers and the operation, helps avoid slips and makes the remainder easy to handle.
Solving division problems
Choose a strategy, divide, then check.
Divide, then check against an estimate.
Dividing with confidence
Dividing larger numbers confidently means putting these steps together: divide by partitioning or with a calculator, find any remainder, and then express the result in the form the problem needs, as a whole-number remainder, a decimal or a fraction, rounding up or down where the context calls for it. The link between division and multiplication, and a quick estimate to check, keep the work reliable. With these habits a child can solve division problems of many kinds, ready for the modelling and the larger calculations of later years.
Quick self-check
1. To divide 84 by 4 by partitioning, you work out...
2. 17 divided by 5 gives...
3. 23 children travel in cars holding 4 each. How many cars are needed?
4. The remainder when 17 is divided by 5, written as a fraction, makes the answer...