Data questions in ACER Scholarship Maths

A data question gives information to read: a bar chart, a table of results, or a situation involving chance. Then it asks what the information shows.

In our ACER-style questions the data comes from an experiment or an event. Think of paper helicopters dropped at a target, plants grown in sun and shade, a kayak race timed at checkpoints. The test's aim is mathematical ability rather than school achievement; in our data questions, your child interprets new numbers rather than recalling a definition.

Read the situation, find the maths, check: with data, the reading takes longest and the rest follows from it.

These are our own, matched to the level of ACER's Level 1 Mathematics and running from easier to harder. None is from an ACER paper. Each one shows the answer and the working; read every heading with your child first.

Some questions give several statements and ask which is supported. That means the numbers in front of your child prove it, not that it is probably true in real life.

The way through is to test every statement. For each, find the numbers it talks about and check them.

In the plant question, the tempting statement sounds right because the shady plants look much shorter. But working out the actual comparison shows it fails. The correct statement is the one that survives the numbers.

This is close to what Humanities asks of a text: judge a claim against the evidence on the page. The Humanities sample questions show the same habit.

Chance questions reward listing. When every outcome is equally likely, the probability is the number of outcomes that fit divided by the number of outcomes altogether.

The trap is listing totals instead of outcomes. For a nest of chicks, the possible numbers of females look like a short list of equally likely results, but they aren't: some totals can happen in more ways than others. Writing every order out, such as F and M in each position, shows the real count.

A tidy list in a fixed order is quicker than it sounds, and it is the check as well as the method. It uses the same counting as number questions.

Each slip below matches a wrong option in the worked examples. As you read the working, ask your child which numbers that option uses and what each stands for.

• Picking the biggest bar or number. The question may ask for a fraction or a rate, not the largest count.
• Mixing up hits and misses. A count of drops inside the circle is not a count of drops outside.
• Choosing the longest stretch as the fastest. Speed depends on distance and time together.
• Treating totals as equally likely. List the outcomes, not the totals.
• Choosing what seems true. Supported means the data proves it.

Reading takes time, and with 32–36 multiple-choice questions in 40 minutes that time has to come from somewhere. A table question can be fast if your child reads the headings once, carefully, rather than skimming and rereading.

Comparing rates or fractions has to be done by hand, because ACER does not allow rulers, books or papers, calculators, watches or mobile phones. Changing everything to the same base, such as per hour or out of the same total, keeps it manageable. Speed tables like the kayak race overlap with measurement.

Use real data. Weather records, sports results and timetables are full of tables. Ask your child for a true statement and a tempting false one about the same table, and which numbers tell them apart.

For chance, toss coins or roll dice and record the results, then compare them with a full list of outcomes. Talking about why some totals turn up more than others builds the listing habit.

Four examples show the method. Practice test 1 has a full Mathematics section on ACER's time, and its results by skill show whether data questions are costing marks.

In the app, the data lesson has an Interactive version and Notes, and skill drills give more table and chart questions. Data questions sit with the other kinds on the ACER Maths sample questions page.