Mathematical Reasoning: Selective Test Practice & Examples

Mathematical Reasoning draws entirely on the NSW curriculum up to Year 6, but questions apply those ideas in unfamiliar, multi-step situations. The strands your child should be comfortable with are:

• Number and operations — place value, factors and multiples, order of operations, and mental strategies for large numbers.
• Fractions, decimals and percentages — converting between them, finding fractions of quantities, and simple percentage increase or decrease.
• Ratio and proportion — sharing in a given ratio and scaling recipes, maps or mixtures up and down.
• Measurement — length, area, perimeter, volume, mass, time, and unit conversions.
• Geometry — properties of 2D shapes and 3D solids, angles, symmetry, and simple coordinate work.
• Data — reading and interpreting tables, graphs and simple averages.
• Multi-step word problems — combining two or three of the above in a single question, which is where most of the difficulty lives.

These are original FunThinkers questions written at Selective difficulty — one each for ratio, percentages, measurement and geometry, rate and speed, and number patterns. Each has five options. Work them out on paper first, then reveal the answer.

There is no calculator and no dictionary in the Mathematical Reasoning section. Your child writes their working on paper with a pencil, so neat, organised working is worth practising in its own right — a tidy layout makes it far easier to spot a slip before choosing an answer.

Two habits pay off under these conditions. The first is estimation: before working a problem out exactly, form a rough sense of the answer, so an obviously wrong option can be ruled out and a careless mistake gets caught. The second is elimination: because every question has five options, testing or excluding options is sometimes faster than solving from scratch — for example, checking which option divides evenly, or which is the only one in a sensible range.

The maths is 35 questions in 40 minutes, which is roughly 68 seconds per question on average. That average is the trap: a few hard questions will take much longer, so your child cannot afford to burn two or three minutes on any single one early on.

The reliable strategy is skip and return. Answer the questions that come quickly, flag anything that stalls, and move on — then come back with whatever time is left. Because it is multiple choice with no penalty for guessing, every question should have an answer marked before time runs out, even if a few are educated guesses. The goal in practice is to build the instinct for when to commit and when to move on, so real test time is spent on the questions your child can actually win.