OC maths practice: keep the units in a word problem

Say what the answer must measure

Before calculating, decide whether the answer should be a number of objects, a price, a time or a distance. Write that unit beside the unknown. This provides a simple check on the calculations you choose.

The word “each” often connects two quantities. For example, pencils per packet links a number of packets to a number of pencils. Keep that relationship visible rather than combining every number in the question.

Solve a packing problem in two stages

Original problem: a class has six packets of eight pencils and gives three pencils to each student. The total is six packets × eight pencils per packet = 48 pencils. Those 48 pencils supply 16 students with three each.

Multiplying six by three first does not follow the given relationship. The intermediate unit helps: packet counts must be converted to pencil counts before dividing by pencils per student.

Check what a remainder means

If there were 50 pencils instead, 16 students could still receive three each, with two pencils left. A fractional student would not answer a question about complete allocations.

Do not round automatically. Decide whether the task asks for complete groups, the amount left or enough containers for everything. The same division can lead to different reported answers when the requested quantity changes.

Use a changed quantity to check the method

Change the packet count or the allocation and solve again without the worked answer. Then explain why each operation is used. This is more informative than reproducing the original numbers.

Use the current official OC student resources for the named test’s presentation. These examples teach a numerical method; they do not predict a particular paper or provide a placement judgement.

Try it yourself

Five packets contain nine pencils each. Each learner receives four pencils. How many learners receive a complete set, and how many pencils remain?

References

• NSW Department of Education: student resources