PSLE Math Heuristics: All 12 Strategies with Worked Examples
13 October 2026 · Tutor Circle
PSLE problem sums are solved with a small set of heuristics. Model drawing is the one parents know. The other eleven are how a child handles a pattern, a list, a story told backwards, or a cage of chickens and rabbits. Each method below has one worked example, and the practice sheet has a fresh question for each.
- Who this is for
- P4 to P6, and any child whose problem sums stall
- The set
- 12 methods schools and tuition worksheets teach
- Official status
- MOE asks for heuristics. It does not publish this as a list of 12 exam methods
- Paper
- PSLE Mathematics, examined in 2026
- Practice
- A 12-question sheet, downloaded on this page
The 12 heuristics
MOE’s primary mathematics syllabus develops problem-solving and names heuristics as part of that skill. [1] SEAB examines Mathematics at PSLE. [2] Neither document prints “these 12 strategies will be tested.” Schools still teach a stable set, because the same sentence shapes keep returning. Learn the set. Then teach the child to pick, not to cycle through all twelve on every question.
| Heuristic | The sentence that wants it |
|---|---|
| Model drawing | Mei has 4 times as many stickers as Ravi. Together they have 60. How many does Ravi have? |
| Look for a pattern | A dot pattern starts 1, 4, 9, 16. How many dots are in the 8th figure? |
| Make a systematic list | Curry puffs cost $1.50 and spring rolls cost $1. How many ways can Aminah spend exactly $6? |
| Guess and check | Two numbers add up to 36. One is 8 more than the other. What are they? |
| Act it out | Five classmates each shake hands once with each of the others. How many handshakes? |
| Work backwards | Siti gave away half her marbles, then 6 more, and had 10 left. How many did she start with? |
| Before-after | Red beans to green beans were 2 : 5. After 9 red beans were added, the numbers were equal. How many green beans were there? |
| Make a supposition | Chickens and rabbits, 8 heads and 22 legs. How many rabbits? |
| Restate the problem | A number becomes 27 when it is doubled and then 5 is added. What is the number? |
| Simplify the problem | A recipe uses 240 g of flour for every 80 g of sugar. How much flour goes with 200 g of sugar? |
| Solve part of the problem | A book and a pen cost $12. The book costs $8 more than the pen. How much is the pen? |
| Use an equation | The same book and pen. Let the pen cost $p. |
One worked example each
These examples were written for this page. They are not past-year PSLE questions.
1. Model drawing
Mei has 4 times as many stickers as Ravi. Together they have 60. How many does Ravi have?
Draw one bar for Ravi and four equal bars for Mei. That is 5 units. 60 ÷ 5 = 12.
Ravi has 12 stickers. Mei has 48.
2. Look for a pattern
A dot pattern starts 1, 4, 9, 16. How many dots are in the 8th figure?
These are square numbers: 1×1, 2×2, 3×3, 4×4. The 8th figure is 8×8.
64 dots.
3. Make a systematic list
Curry puffs cost $1.50 and spring rolls cost $1. How many ways can Aminah spend exactly $6?
List the number of puffs from 0 upward. One or three puffs leave a half-dollar, which no $1 roll can use. Keep only the rows that land on a whole dollar.
3 ways: 0 puffs and 6 rolls; 2 puffs and 3 rolls; 4 puffs and 0 rolls.
4. Guess and check
Two numbers add up to 36. One is 8 more than the other. What are they?
Guess the smaller number. 10 gives 10 and 18, which add to 28, too small. 14 gives 14 and 22.
14 and 22.
5. Act it out
Five classmates each shake hands once with each of the others. How many handshakes?
The fifth person shakes 4 new hands, the fourth shakes 3, then 2, then 1. Adding those is the whole set.
10 handshakes.
6. Work backwards
Siti gave away half her marbles, then 6 more, and had 10 left. How many did she start with?
Undo the last step first. 10 + 6 = 16. That 16 was the half she kept, so the start was 16 × 2.
32 marbles.
7. Before-after
Red beans to green beans were 2 : 5. After 9 red beans were added, the numbers were equal. How many green beans were there?
Green stays at 5 units. Red grows from 2 units to 5 units. Those 3 units are the 9 beans. One unit is 3.
15 green beans.
8. Make a supposition
Chickens and rabbits, 8 heads and 22 legs. How many rabbits?
Suppose all 8 animals are chickens: 16 legs. The extra 6 legs are 3 rabbits, because each rabbit has 2 more legs than a chicken.
3 rabbits and 5 chickens.
9. Restate the problem
A number becomes 27 when it is doubled and then 5 is added. What is the number?
Restate it before calculating: double the number, add 5, get 27. In numbers, 2 × number + 5 = 27.
11.
10. Simplify the problem
A recipe uses 240 g of flour for every 80 g of sugar. How much flour goes with 200 g of sugar?
Divide 240 and 80 by 80 first. The ratio is 3 : 1. Flour is three times the sugar.
600 g of flour.
11. Solve part of the problem
A book and a pen cost $12. The book costs $8 more than the pen. How much is the pen?
Take the $8 difference out first. The remaining $4 is two equal pen-sized amounts.
The pen is $2. The book is $10.
12. Use an equation
The same book and pen. Let the pen cost $p.
p + (p + 8) = 12. Then 2p = 4.
p = 2. Same answer as the model, written the way Sec 1 will ask for it.
Example 12 is example 11 written with a letter. That is the bridge into Sec 1, set out as a holiday plan on the Sec 1 preparation guide. If the models are solid and the marks still fall apart in the last ten minutes, the gap may be exam technique rather than a missing heuristic. That split is on the EOY recovery plan.
Practice sheet
A child who can do the model and still cannot finish Paper 2 in time needs a P5 or P6 specialist, not another printed list. Say the level and the paper section on the request.
Questions parents ask
What are PSLE math heuristics?
Heuristics are the problem-solving methods primary schools teach for non-routine sums: model drawing, looking for a pattern, a systematic list, guess and check, acting it out, working backwards, before-after, supposition, restating the problem, simplifying, solving part of it, and using an equation. MOE’s mathematics syllabus asks pupils to use heuristics. It does not publish this set as a numbered examination list of 12. Tuition and school worksheets group them this way because these are the methods the papers reward.
Is model drawing one of the heuristics?
Yes. Model drawing is the diagram method most P3 to P6 children meet first. A bar stands for an unknown amount. Equal parts, a comparison, or a before-and-after change is drawn before any calculation. The same relationship is what Sec 1 writes as algebra.
Which heuristic should my child use?
The question decides. A “times as many” sentence wants a model. A story that ends with a leftover wants work backwards. Heads and legs wants a supposition. If the child can explain why that method fits, the method mark is safer than a lucky number. The practice sheet has one question of each type.
Do heuristics still matter if my child is going to Sec 1?
Yes. Sec 1 algebra writes the model as a letter. A child who can draw “4 units equal 48” and also write 4x = 48 has made the crossing. The holiday version of that crossing is on the Sec 1 preparation page.
Where is the practice sheet?
On this page, below the twelve examples. Enter an email address and the file downloads in your browser. It has twelve new questions and an answer key. It is not a past-year paper.
Sources
- Ministry of Education, primary school curriculum and syllabuses. Mathematics is a primary subject, and the syllabus develops problem-solving, including the use of heuristics. Accessed 13 October 2026. https://www.moe.gov.sg/primary/curriculum/syllabus
- Singapore Examinations and Assessment Board, “PSLE Formats Examined in 2026.” Mathematics is a PSLE subject. Accessed 13 October 2026. https://www.seab.gov.sg/psle/psle-formats-examined-in-2026/