Primary 6 Maths: PSLE Problem-Solving

The hardest PSLE Maths questions test heuristics: assumption method, working backwards, spotting patterns. What they look like and how to practise them without tears.

Most schools typically cover this topic in Term 3, around week 5 — though every school sets its own sequence.

Every PSLE Maths paper ends with a handful of questions that don't belong to any single topic. They're the problem-solving questions — the ones tuition centres build entire courses around — and they test heuristics: the assumption (supposition) method, working backwards, drawing systematic lists, spotting number patterns, and restructuring unfamiliar problems into familiar ones.

Two honest facts for parents. First: these questions are a minority of the paper — the bulk of PSLE marks still come from solid topic mastery, which is why chasing heuristics before the foundations are secure is backwards. Second: heuristics can be learned. They look like flashes of insight; they're actually a small library of reusable moves.

The heuristics that matter most

• The assumption method. "30 animals, 84 legs" — assume all are chickens, count the shortfall, convert. Once a child has the template, a whole family of questions opens up.
• Working backwards. When a problem describes a chain of changes and gives you the end state, start from the end and reverse each step.
• Systematic listing. Not glamorous, but the difference between a list and a systematic list (fixed order, no gaps, no repeats) is the difference between 1 mark and full marks.
• Before-after with an unchanged total. The advanced sibling of the P5 comparison model — often the last question on the paper.

The mistakes to watch for

• Diving into calculation before reading twice. The hardest questions embed the key constraint in an unassuming sentence. Strong problem-solvers read, restate, then compute.
• Abandoning a method after one failed attempt. The assumption method in particular feels wrong the first time ("but they're not all chickens!"). Children need to trust the template through the discomfort.
• No check step. Every heuristic produces an answer that can be verified against the original story in under a minute. Top scorers always spend that minute.

Example question — the assumption method

How to practise this topic

Heuristics stick when they're practised as templates across many surface stories — chickens and goats today, cars and motorcycles tomorrow — so the child learns to see the structure underneath. Practise one heuristic at a time, then mix them so the real skill (choosing the right move) gets exercised. And keep perspective: if topic-level gaps exist in fractions or ratio, close those first — they're worth more marks.

What this topic covers

In the MOE syllabus, Primary 6 PSLE Problem-Solving (P6-M-12) includes:

• Model drawing (advanced/comparison and before-after)
• Guess and check heuristic
• Working backwards heuristic
• Making suppositions (supposition method)
• Before-and-after concept
• Simultaneous equations concept
• Challenging multi-step word problems
• Number pattern recognition
• Systematic listing
• Excess and shortage

Before this topic

These topics feed into PSLE Problem-Solving — if this one wobbles, check them first: Primary 5 Word Problems · Primary 6 Fractions · Primary 6 Decimals · Primary 6 Percentage · Primary 6 Ratio · Primary 6 Algebra.