Mathematical Reasoning and Problem Solving
What Mathematical Reasoning and Problem Solving covers
This domain tests multi-step word problems, estimation, pattern and logic puzzles, and the ability to explain why an answer is reasonable. The mathematics may come from number, geometry, or data, but the mark depends on selecting the right operations, keeping track of units, and answering the question actually asked.
Core rules
- Read twice: first for the story, second for the quantities and the question. Underline what is given and what must be found.
- Break a multi-step problem into labelled steps; write an equation or number sentence for each step.
- Use estimation to predict the size of the answer before calculating; then check that the exact answer is close.
- Keep units with every quantity and convert before combining. A rate compares two different units, such as km per hour or cost per item.
- For “which is cheaper” or “best buy” problems, compare unit prices: total cost ÷ number of items.
- For logic puzzles, make a table or list; eliminate possibilities rather than guessing.
Worked example
A shop sells pens in packs of 5 for $12 and singles for $3 each. Maya needs 23 pens. What is the least she can pay? Packs needed: 23 ÷ 5 = 4 remainder 3, so 4 packs give 20 pens and 3 singles are needed. Cost = 4 × $12 + 3 × $3 = $48 + $9 = $57. Check whether 5 packs ($60) is cheaper: it gives 25 pens but costs more, so $57 is the least for at least 23 pens. If the question asked for exactly 23 pens, the same combination works.
Traps that cost marks
Answering a sub-step and stopping. Using the wrong unit, such as mixing dollars and cents or minutes and hours. Rounding too early in a multi-step calculation and carrying the error forward. Solving for a quantity that is not the one requested-for example, finding the discount instead of the final price. Assuming all items can be split when the context requires whole packs. Always restate the question in one sentence and check that your final number answers it.