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Numeracy: decide what the numbers represent

Numeracy involves choosing a useful method as well as carrying it out. These mixed-level examples move from a fraction of a group to a mean and an angle calculation. Each question shows its suggested year.

Adaptigo is an independent learning platform, not affiliated with or endorsed by ACARA. These original NAPLAN-style examples are not official test questions or results.

What to notice

Identify the whole before calculating a fraction. For a mean, count the observations as well as adding their values. With angles, use the relationship that belongs to the shape in the question.

What to do

Draw a small model or jot down the quantities. Label units and intermediate values. Estimate the size of a sensible answer, then calculate and compare the result with that estimate.

Why it works

Models connect symbols to meaning. A fraction model shows equal shares; a chart organises observations. An estimate can catch an answer that is larger than the whole or an average outside the observed range.

Work through an example

Three quarters of 16 counters are blue. How many are blue?

Three of four equal parts
A whole divided into four equal parts, with three parts marked.
  1. Split 16 into four equal groups: each quarter contains 4 counters.
  2. Choose three of those groups: 3 × 4 = 12 blue counters.
  3. 12 is below 16 and above half of 16, as three quarters should be.

A common mistake

Dividing by the denominator finds one equal share, not always the requested fraction. Read the numerator to decide how many shares to take.

A strategy to try

Check the meaning of the result before inspecting the options. A mean should lie between the smallest and largest values. Triangle angles should total 180 degrees. These checks test the answer using a second relationship.

Try it now

Try three questions

No account is needed. These examples do not change saved learning progress. Choose an answer and check it for an explanation; you can try again.

Year 5 · Numeracy

1. Three quarters of 20 seedlings have flowers. How many seedlings have flowers?
Help: a starting point

The whole group contains 20 seedlings. Divide it into four equal groups.

Help: the next step

Take three of those equal groups.

Year 7 · Numeracy

2. The chart shows laps swum in three sessions. What is the mean number of laps per session?
0Mon6Wed8Fri10
Laps per session: Monday 6, Wednesday 8, Friday 10. All bars start at zero.
Help: a starting point

Find the total laps across Monday, Wednesday and Friday.

Help: the next step

Share that total equally across the three sessions.

Year 9 · Numeracy

3. Two interior angles of a triangle are 45° and 65°. What is the third interior angle?
Help: a starting point

Recall the total of the interior angles in a triangle.

Help: the next step

Add the two known angles, then subtract their sum from that total.

For parents and carers

Use the year labels as starting points, not a ranking of ability. If the fraction example is difficult, the linked guide uses more concrete models. For an older learner, ask why the chosen operation fits the context. This is a small sample of number, statistics and geometry, not a claim to cover every numeracy skill or reproduce a full test.

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