Mathematical Reasoning: Choosing a Strategy
What the questions demand
Mathematical reasoning questions test whether you can select and apply a method, not just calculate. Topics include number and place value, fractions, decimals and percentages, ratio and rate, patterns and algebra, measurement, geometry, and data interpretation. Many items are word problems where the arithmetic is easy but the setup is the challenge.
Concepts to understand
- Operations and order: know how multiplication, division, and brackets interact before substituting numbers.
- Proportional thinking: ratio, rate, and percentage questions usually reduce to finding a unit value first.
- Patterns: identify the rule, then express it in words or a simple formula before extending it.
- Geometry facts: angle sums, area and perimeter relationships, and properties of triangles and quadrilaterals.
- Data: read tables and graphs carefully, checking axes, units, and totals.
Traps to watch
- Answering the wrong quantity: the question asks for the remainder, not the total.
- Forgetting to convert units, such as minutes to hours or centimetres to metres.
- Assuming a shape's dimensions change proportionally when only one changes.
- Choosing an answer because it looks familiar rather than because it fits.
Worked example
A recipe for 6 people needs 450 g of rice. How much for 10 people? Find the unit value: 450 ÷ 6 = 75 g per person. Multiply: 75 × 10 = 750 g. The trap answer is often 450 ÷ 10 or a guess based on doubling.
Rule of thumb
Write down what is given, what is asked, and the unit of the answer before calculating. Estimate first so an unreasonable result stands out.