PSLE Math Heuristics: Complete Guide to All 8 Problem-Solving Strategies

Why Heuristics Matter More Than Ever in PSLE 2026

With Speed removed from the PSLE Math syllabus, heuristic-based word problems now account for 40-50% of the total marks. Every year, MOE allocates increasing weightage to non-routine questions that test whether students can select and apply the right problem-solving strategy.

The 8 heuristics are not optional extras — they are core exam skills. Students who cannot identify which heuristic to use will lose marks, even if they understand the underlying math concepts.

This guide covers every heuristic with:

• ▸Clear definitions in plain English
• ▸When to use it (the decision framework)
• ▸Worked examples with PSLE-style questions
• ▸Common mistakes and how to avoid them

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The 8 PSLE Math Heuristics

1. Draw a Diagram / Model Drawing

What it is: Representing the problem visually using bars, circles, or other shapes.

When to use it:

• ▸Comparing quantities (more/less)
• ▸Showing part-whole relationships
• ▸Ratio problems where visual representation helps

Example:

Ali has 3 times as many stickers as Ben. If Ali gives 12 stickers to Ben, they will have the same number. How many stickers does Ali have originally?

Solution using model:

Step 1 — Draw the "Before" model:

Ali has 3 times as many → ratio is 3 : 1

Ali: ■■■ 3 units

Ben: ■ 1 unit

Step 2 — Show the transfer (Ali gives 12 to Ben):

Ali: ■■■ → 3 units − 12

Ben: ■ → 1 unit + 12

Step 3 — After: They are now equal

Ali: ■■■ − 12

Ben: ■ + 12

Since they are equal: 3 units − 12 = 1 unit + 12

Step 4 — Solve:

3 units − 1 unit = 12 + 12

2 units = 24

1 unit = 12

Step 5 — Find the answer:

Ali originally = 3 units = $3 imes 12 = 36$

Answer: Ali had 36 stickers originally.

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2. Guess and Check

What it is: Making educated guesses and refining based on results.

When to use it:

• ▸Problems with limited possible answers
• ▸When you can eliminate wrong answers logically
• ▸Number puzzles with constraints

Example:

The sum of two numbers is 15. Their difference is 3. What are the two numbers?

Solution:

• ▸Guess: 8 and 7, sum 15, difference 1 (too small)
• ▸Guess: 9 and 6, sum 15, difference 3

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3. Systematic List

What it is: Listing all possible combinations in an organized way.

When to use it:

• ▸Arrangement problems
• ▸Finding all possibilities
• ▸Problems with "how many ways" questions

Example:

How many different 3-digit numbers can be formed using 1, 2, and 3 without repetition?

Solution: 123, 132, 213, 231, 312, 321 Total: 6 numbers

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4. Look for Patterns

What it is: Identifying repeating sequences or relationships.

When to use it:

• ▸Figure pattern problems
• ▸Number sequences
• ▸Finding the nth term

Example:

Figure 1 has 4 dots, Figure 2 has 7 dots, Figure 3 has 10 dots. How many dots in Figure 10?

Solution:

• ▸Common difference: $7 - 4 = 3$, $10 - 7 = 3$ → $d = 3$
• ▸Formula: $T(n) = d imes n + c = 4 + 3(n - 1) = 4 + 3n - 3 = 3n + 1$
• ▸Verify: $T(1) = 4$ ✓, $T(2) = 7$ ✓, $T(3) = 10$ ✓
• ▸Figure 10: $T(10) = 3(10) + 1 = 31$ dots

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5. Work Backwards

What it is: Starting from the end result and reversing operations.

When to use it:

• ▸Problems that describe a sequence of events
• ▸When the starting point is unknown
• ▸Multi-step problems

Example:

Mary had some money. She spent half on books, then $5 on lunch, then half of what remained on transport. She had $8 left. How much did she have originally?

Solution:

• ▸Before transport: $8 x 2 = $16
• ▸Before lunch: $16 + $5 = $21
• ▸Originally: $21 x 2 = $42

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6. Act It Out

What it is: Using physical objects or role-playing to understand the problem.

When to use it:

• ▸Spatial problems (rotation, folding)
• ▸Problems involving movement
• ▸Problems that are hard to visualize

Example:

A square is folded in half horizontally, then in half vertically, then a corner is cut. What does the unfolded paper look like?

Solution: Use paper to fold and cut, then unfold to see the pattern.

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7. Simplify the Problem

What it is: Reducing complex numbers or removing details to find a pattern.

When to use it:

• ▸Very large or small numbers
• ▸Complex word problems
• ▸When you need to understand the structure first

Example:

What is 1 + 2 + 3 + ... + 100?

Solution:

• ▸Write the sum twice: $S = 1 + 2 + 3 + cdots + 100$ and $S = 100 + 99 + 98 + cdots + 1$
• ▸Add vertically: each pair sums to $101$. There are $100$ pairs, so $2S = 100 imes 101$
• ▸Therefore $S = dfrac{n(n+1)}{2}$ where $n = 100$
• ▸Answer: $S = dfrac{100 imes 101}{2} = 5050$

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8. Use Equivalent Items / Make Assumptions

What it is: Replacing items with equivalent ones to simplify calculations.

When to use it:

• ▸Average problems
• ▸Total cost problems
• ▸Problems involving exchanges

Example:

5 children share 8 cookies equally. How much does each child get?

Solution:

• ▸Each child gets $dfrac{8}{5}$ cookies $= 1dfrac{3}{5}$ cookies

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How to Choose the Right Heuristic

Use this decision framework:

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Practice Strategy

1. ▸Learn one heuristic at a time — don't try to master all 8 at once
2. ▸Practice 5 questions per heuristic — focus on recognition, not speed
3. ▸Mixed practice — after mastering each, do mixed problems to practice selection
4. ▸Timed drills — simulate exam conditions in the final month

For adaptive practice with AI-powered hints that guide you through the heuristics, try ReLURN's free diagnostic test.