If your child has come home saying “teacher says use a heuristic”, you are not alone in wondering what that means. PSLE maths heuristics are simply problem-solving strategies: structured ways of attacking a word problem when the method is not obvious. Singapore’s primary maths syllabus has long placed problem solving at its centre, and heuristics are the toolkit pupils build from Primary 3 onwards to handle the longer, multi-step questions in the later papers.
This guide walks through the heuristics parents most often see on worksheets, what each one looks like in practice, and how you can support your child at home without re-teaching everything the school does differently from how you learnt it.
What Heuristics Are and Why Schools Teach Them
A heuristic is not a formula. A formula tells you exactly what to do; a heuristic suggests a way to start thinking. In a typical problem sum, the numbers are given but the path from question to answer is hidden. Heuristics give children a short menu of approaches to try when they feel stuck.
Teachers usually group them loosely into four kinds:
- Representing the problem: drawing a diagram, model or table so the relationships become visible.
- Making a calculated guess: guess and check, or looking for a pattern.
- Walking through the process: acting it out, working backwards, before and after.
- Changing the problem: simplifying it, solving part of it first, or making a supposition.
Exact labels vary between textbooks and schools, so do not worry if your child’s worksheet uses a slightly different name. The underlying ideas are the same. For the official syllabus, check the Ministry of Education (MOE) website; for exam format details, check the Singapore Examinations and Assessment Board (SEAB).
The Main PSLE Maths Heuristics, One by One
Draw a Model
The bar model is the best known strategy and gets a full treatment in our guide to teaching the bar model method for primary maths problem sums. In short, children draw rectangles to represent quantities, then compare, split or join them. Many of the other heuristics below work alongside a model rather than replacing it.
Guess and Check
The child makes a sensible guess, tests it against the conditions in the question, then adjusts. The key is to record each attempt in a neat table so the guesses get closer rather than random.
Example: “There are 20 chickens and goats on a farm with 56 legs in total. How many goats are there?” A child might guess 10 goats (40 legs) plus 10 chickens (20 legs), giving 60 legs. That is too many, so try fewer goats. Eight goats and 12 chickens give 32 + 24 = 56. Done.
Guess and check is a good entry point because almost every child can start it. Its weakness is speed, which is why older pupils are often nudged towards supposition for the same type of question.
Supposition (Assumption Method)
Supposition is the faster cousin of guess and check. Using the same farm question, assume all 20 animals are chickens. That gives 40 legs, which is 16 short of 56. Each goat swapped in adds 2 legs, so 16 ÷ 2 = 8 goats. Parents who learnt simultaneous equations will recognise this as the same logic, just without algebra.
Working Backwards
When a question describes a series of changes and gives you only the final amount, start from the end and undo each step. “Mei spent half her money on a book, then $6 on lunch, and had $9 left. How much did she start with?” Reverse it: $9 + $6 = $15, which was half, so she started with $30.
This is the classroom version of a broader thinking habit, explained in our piece on inversion thinking and solving problems by working backwards. Remind your child that each operation is reversed too: subtraction becomes addition, halving becomes doubling.
Before and After
Common in ratio and fraction questions, this heuristic sets out the situation before a change and after it, usually in a table or two sets of models. The trick is spotting what stays the same. If only one person gives money away, the other person’s amount is unchanged, so their units can be matched across the before and after lines.
Look for a Pattern
Number sequences, figure patterns and “the 50th term” questions reward children who list the first few cases, spot what is changing and then generalise. Encourage them to write the pattern as a rule in words before jumping to the answer.
Make a Systematic List
For questions asking “how many ways”, a careful list in a fixed order stops children from missing or repeating combinations. This links naturally with guess and check, since both rely on organised recording.
Simplify the Problem or Solve Part of It
If the numbers are large, try the same question with small numbers to understand the structure, then scale up. For long multi-part questions, solving one smaller part first often reveals the next step.
Which Heuristic Fits Which Question
Children improve fastest when they learn to recognise question types. This table is a starting guide, not a rule, since many questions can be solved more than one way.
| Question clue | Heuristic to try first | Why it helps |
|---|---|---|
| Two kinds of items with a total count and total value (legs, wheels, coins) | Supposition, or guess and check | Turns a two-unknown problem into one adjustment |
| A series of spending or giving steps, final amount known | Working backwards | Undoes each step to reach the start |
| Ratio or fraction changes after a transfer | Before and after, with models | Shows which quantity stayed constant |
| Sequences, shapes growing, “the nth figure” | Look for a pattern | Builds a rule from the first few cases |
| “How many different ways” or combinations | Make a systematic list | Prevents missed or repeated cases |
| Comparing quantities, more than or less than | Draw a model | Makes the relationships visible |
How Parents Can Help at Home
You do not need to be a maths expert. The most useful support is about habits, not answers.
- Ask before telling. When your child is stuck, ask “What is the question really asking?” and “Which strategy have you tried?” before showing anything.
- Insist on neat working. Most heuristics fail when the recording is messy. A tidy table or labelled model is half the solution.
- Accept different methods. If your child solves something correctly using a method you did not expect, praise the reasoning. Marking schemes generally give credit for valid working, but check with the teacher if you are unsure how a particular method is assessed.
- Do not rush into algebra. It may be quicker for you, but primary pupils are expected to reason with models and heuristics. Introducing algebra too early can confuse them about what the school expects.
- Review mistakes, not just scores. After practice papers, sort errors into “careless”, “did not understand the question” and “did not know which strategy”. Each needs a different fix.
- Keep sessions short. Two or three well-chosen problems discussed properly beat a whole paper done in frustration.
Building Confidence Before the PSLE
Heuristics take time to feel natural. A child who can name the strategies but freezes in an exam usually needs more practice choosing between them, not more new techniques. Mixed practice, where question types are shuffled rather than grouped by topic, helps build that judgement.
Time management matters too. Encourage your child to attempt every question, show partial working on the long ones, and come back to the hardest at the end. If exam stress starts to affect sleep, appetite or mood, speak with the form teacher or school counsellor early.
Finally, remember that heuristics are thinking skills that outlast the PSLE. Learning to break a problem down, try something, check it and adjust is useful well into secondary school and beyond, and the same mindset shows up in tools like the 5 Whys technique for problem solving. Treat each tricky problem sum as practice in staying calm and methodical, and the marks tend to follow.
Further reading: PSLE Maths Paper 1 and Paper 2: Format, Timing and When Calculators Are Allowed · Maths Olympiad and Competitions for Singapore Students: A Parent’s Guide · How Singapore Maths Differs From the China Curriculum