“I know the maths, but I don't know where to start.” That is why a child can do routine exercises and still freeze when a PSLE Paper 2 problem sum looks unfamiliar.

Paper 2 asks your child to read a situation, identify relationships, choose a representation, and explain a chain of reasoning. Rote drilling builds calculation fluency, but it does not teach that choice. A child needs a small toolkit of heuristics — reliable ways to begin when the operation is not obvious.

The 12 strategies below are questions your child can ask when a problem feels stuck. Each example is short enough to discuss at home.

Why rote drilling breaks down in Paper 2

Drilling “find 15% of 80” can make that task familiar. A Paper 2 question may hide the same calculation inside a story about a discount or a change in quantity. The hard part is recognising the structure.

Ask, “What do we know, what changes, and what could we draw or organise?” The strategies here give your child sensible starting points without encouraging random guessing.

The 12 PSLE problem-solving strategies

1. Model drawing

When the problem compares quantities or joins parts into a whole, let a picture expose the relationship. For a full introduction to part–whole and comparison bars, see our bar model parent guide.

Worked example: A box has 5 times as many red marbles as blue marbles. There are 72 marbles altogether. Draw 1 unit for blue and 5 for red: 6 units = 72, so 1 unit = 12. Red = 5 × 12 = 60; blue = 12. Check: 60 + 12 = 72.

2. Units and parts method

If a quantity is split into equal parts, find the value of one part before finding the requested number of parts. This is useful for fractions, ratios, and “of the remaining amount” questions.

Worked example: A fruit seller gives away 3/8 of 64 mangoes. One part is 64 ÷ 8 = 8 mangoes. The amount given away is 3 × 8 = 24, so the amount left is 64 − 24 = 40 mangoes.

3. Before–after

Use two snapshots when quantities change. Keep the situation before the change separate from what is true after it.

Worked example: Ali gives Siti 12 stickers, and they then have equal numbers. Together they have 96. After the transfer, each has 96 ÷ 2 = 48. Before the transfer, Ali had 48 + 12 = 60 and Siti had 48 − 12 = 36. Check: 60 − 12 = 48 and 36 + 12 = 48.

4. Working backwards

Start with the final information and undo the operations in reverse order. Addition is undone by subtraction; multiplication is undone by division.

Worked example: After spending $18 and then receiving $7, Mei has $35. Before receiving $7, she had $35 − $7 = $28. Before spending $18, she had $28 + $18 = $46. Check: $46 − $18 + $7 = $35.

5. Guess and check

Make a sensible trial, substitute it into every condition, and use the result to adjust.

Worked example: A smaller number and twice that number plus 6 total 42. Try 10: 10 + (2 × 10) + 6 = 36, too small. Try 12: 12 + (2 × 12) + 6 = 42. The numbers are 12 and 30, and 12 + 30 = 42.

6. Make a list or table

Organise possibilities so that you do not count the same case twice or miss one.

Worked example: A café has 3 drinks and 2 snacks. Listing each drink with each snack gives 3 × 2 = 6 possible sets: drink 1 with snacks 1 and 2, drink 2 with snacks 1 and 2, and drink 3 with snacks 1 and 2.

7. Look for a pattern

Calculate the first few cases and ask what changes each time.

Worked example: A row of joined squares uses 4 sticks for 1 square, 7 for 2 squares, and 10 for 3 squares. Each new square adds 3 sticks. Ten squares use 4 + (9 × 3) = 31 sticks.

8. Remainder concept

When a quantity does not divide evenly, ask what the remainder means in the story: leftover items, incomplete groups, or one extra group needed.

Worked example: Ninety-five pupils are put into groups of 6. 95 ÷ 6 = 15 remainder 5, because 15 × 6 = 90 and 95 − 90 = 5. There are 15 full groups and 5 pupils left; if every pupil must join a group, 16 groups are needed.

9. Assumption method

Assume every item has one convenient value, then measure the difference between that assumption and the actual total. This turns a mixed group into one clear adjustment.

Worked example: Seven tickets cost $72. Adult tickets cost $12 and child tickets cost $8. Assume all 7 are adult tickets: 7 × $12 = $84. Each child ticket reduces the total by $4. The difference is $84 − $72 = $12, so there are $12 ÷ $4 = 3 child tickets and 4 adult tickets. Check: 3 × $8 + 4 × $12 = $72.

10. Equal fractions

If two fractions describe the same amount, make that shared amount your starting point. This can reveal a simple ratio without jumping straight to algebra.

Worked example: One-third of A equals one-quarter of B, and A + B = 56. If the shared amount is one unit, A is 3 units and B is 4 units. Seven units = 56, so one unit = 8. Therefore A = 24 and B = 32; 24 ÷ 3 = 8 and 32 ÷ 4 = 8.

11. Simplify the problem

Replace a large or complicated case with a smaller version that keeps the same structure. Solve the small case first, then use what it teaches you about the original.

Worked example: In a handshake problem, 3 children make 2 + 1 = 3 handshakes because each new child greets everyone already there. With 5 children, the total is 2 + 3 + 4 + 1 = 10 handshakes. The smaller cases show that each new child adds the number of children already present.

12. Eliminate possibilities

Use every condition to cross out answers that cannot work. It is often faster and safer than trying to solve everything at once.

Worked example: A two-digit number is greater than 50, less than 70, even, and has a digit sum of 10. The tens digit must be 5 or 6; the even and digit-sum conditions leave 64. Check: 64 is between 50 and 70, it is even, and 6 + 4 = 10.

How to practise heuristics without turning them into another worksheet

Do not ask your child to memorise the names in order. Put an unfamiliar problem in front of them and ask, “What could you represent first?” Choosing a method and explaining why is progress, even before the final answer is right.

Use variety — a comparison problem, a before–after problem, a remainder problem — and ask what clue suggested the method. That reflection helps your child recognise the same structure in a new story.

Singapore Math Drills includes heuristics and PSLE-style word problems, with bar models and Concrete–Pictorial–Abstract pedagogy throughout. It gives your child practice choosing a method, not just repeating one operation. See the targeted-drills guide for a focused practice approach.

How Singapore Math Drills helps

The method is most useful when your child can make it visible, receive help without losing the thinking, and practise in a way that matches the goal.

• Built-in scratch pad: The full-screen canvas lets your child draw a bar, table, number line, or quick trial by hand without leaving the app. That keeps the missing thinking visible.
• Progressive hints and worked solutions: If the first attempt goes wrong, the question opens up step by step, with a full worked solution afterwards. Your child sees a useful clue instead of an answer immediately.
• Focus, Sprint, and Worksheet modes: Focus is for unhurried accuracy, Sprint is for rapid recall against a timer, and Worksheet is for a whole paper marked at the end. Start a new heuristic in Focus, then move to mixed questions in Worksheet mode.

Start with one P5 or P6 problem, ask your child which heuristic they would try, and let them show the working before looking at help.

Try it free

Give your child a calm place to practise PSLE-style problem solving with a free interactive sample — no login or download required.

Try a free sample drill

“I know the maths, but I don't know where to start.” That is why a child can do routine exercises and still freeze when a PSLE Paper 2 problem sum looks unfamiliar.

Paper 2 asks your child to read a situation, identify relationships, choose a representation, and explain a chain of reasoning. Rote drilling builds calculation fluency, but it does not teach that choice. A child needs a small toolkit of heuristics — reliable ways to begin when the operation is not obvious.

The 12 strategies below are questions your child can ask when a problem feels stuck. Each example is short enough to discuss at home.

Why rote drilling breaks down in Paper 2

Drilling “find 15% of 80” can make that task familiar. A Paper 2 question may hide the same calculation inside a story about a discount or a change in quantity. The hard part is recognising the structure.

Ask, “What do we know, what changes, and what could we draw or organise?” The strategies here give your child sensible starting points without encouraging random guessing.

The 12 PSLE problem-solving strategies

1. Model drawing

When the problem compares quantities or joins parts into a whole, let a picture expose the relationship. For a full introduction to part–whole and comparison bars, see our bar model parent guide.

Worked example: A box has 5 times as many red marbles as blue marbles. There are 72 marbles altogether. Draw 1 unit for blue and 5 for red: 6 units = 72, so 1 unit = 12. Red = 5 × 12 = 60; blue = 12. Check: 60 + 12 = 72.

2. Units and parts method

If a quantity is split into equal parts, find the value of one part before finding the requested number of parts. This is useful for fractions, ratios, and “of the remaining amount” questions.

Worked example: A fruit seller gives away 3/8 of 64 mangoes. One part is 64 ÷ 8 = 8 mangoes. The amount given away is 3 × 8 = 24, so the amount left is 64 − 24 = 40 mangoes.

3. Before–after

Use two snapshots when quantities change. Keep the situation before the change separate from what is true after it.

Worked example: Ali gives Siti 12 stickers, and they then have equal numbers. Together they have 96. After the transfer, each has 96 ÷ 2 = 48. Before the transfer, Ali had 48 + 12 = 60 and Siti had 48 − 12 = 36. Check: 60 − 12 = 48 and 36 + 12 = 48.

4. Working backwards

Start with the final information and undo the operations in reverse order. Addition is undone by subtraction; multiplication is undone by division.

Worked example: After spending $18 and then receiving $7, Mei has $35. Before receiving $7, she had $35 − $7 = $28. Before spending $18, she had $28 + $18 = $46. Check: $46 − $18 + $7 = $35.

5. Guess and check

Make a sensible trial, substitute it into every condition, and use the result to adjust.

Worked example: A smaller number and twice that number plus 6 total 42. Try 10: 10 + (2 × 10) + 6 = 36, too small. Try 12: 12 + (2 × 12) + 6 = 42. The numbers are 12 and 30, and 12 + 30 = 42.

6. Make a list or table

Organise possibilities so that you do not count the same case twice or miss one.

Worked example: A café has 3 drinks and 2 snacks. Listing each drink with each snack gives 3 × 2 = 6 possible sets: drink 1 with snacks 1 and 2, drink 2 with snacks 1 and 2, and drink 3 with snacks 1 and 2.

7. Look for a pattern

Calculate the first few cases and ask what changes each time.

Worked example: A row of joined squares uses 4 sticks for 1 square, 7 for 2 squares, and 10 for 3 squares. Each new square adds 3 sticks. Ten squares use 4 + (9 × 3) = 31 sticks.

8. Remainder concept

When a quantity does not divide evenly, ask what the remainder means in the story: leftover items, incomplete groups, or one extra group needed.

Worked example: Ninety-five pupils are put into groups of 6. 95 ÷ 6 = 15 remainder 5, because 15 × 6 = 90 and 95 − 90 = 5. There are 15 full groups and 5 pupils left; if every pupil must join a group, 16 groups are needed.

9. Assumption method

Assume every item has one convenient value, then measure the difference between that assumption and the actual total. This turns a mixed group into one clear adjustment.

Worked example: Seven tickets cost $72. Adult tickets cost $12 and child tickets cost $8. Assume all 7 are adult tickets: 7 × $12 = $84. Each child ticket reduces the total by $4. The difference is $84 − $72 = $12, so there are $12 ÷ $4 = 3 child tickets and 4 adult tickets. Check: 3 × $8 + 4 × $12 = $72.

10. Equal fractions

If two fractions describe the same amount, make that shared amount your starting point. This can reveal a simple ratio without jumping straight to algebra.

Worked example: One-third of A equals one-quarter of B, and A + B = 56. If the shared amount is one unit, A is 3 units and B is 4 units. Seven units = 56, so one unit = 8. Therefore A = 24 and B = 32; 24 ÷ 3 = 8 and 32 ÷ 4 = 8.

11. Simplify the problem

Replace a large or complicated case with a smaller version that keeps the same structure. Solve the small case first, then use what it teaches you about the original.

Worked example: In a handshake problem, 3 children make 2 + 1 = 3 handshakes because each new child greets everyone already there. With 5 children, the total is 2 + 3 + 4 + 1 = 10 handshakes. The smaller cases show that each new child adds the number of children already present.

12. Eliminate possibilities

Use every condition to cross out answers that cannot work. It is often faster and safer than trying to solve everything at once.

Worked example: A two-digit number is greater than 50, less than 70, even, and has a digit sum of 10. The tens digit must be 5 or 6; the even and digit-sum conditions leave 64. Check: 64 is between 50 and 70, it is even, and 6 + 4 = 10.

How to practise heuristics without turning them into another worksheet

Do not ask your child to memorise the names in order. Put an unfamiliar problem in front of them and ask, “What could you represent first?” Choosing a method and explaining why is progress, even before the final answer is right.

Use variety — a comparison problem, a before–after problem, a remainder problem — and ask what clue suggested the method. That reflection helps your child recognise the same structure in a new story.

Singapore Math Drills includes heuristics and PSLE-style word problems, with bar models and Concrete–Pictorial–Abstract pedagogy throughout. It gives your child practice choosing a method, not just repeating one operation. See the targeted-drills guide for a focused practice approach.

How Singapore Math Drills helps

The method is most useful when your child can make it visible, receive help without losing the thinking, and practise in a way that matches the goal.

• Built-in scratch pad: The full-screen canvas lets your child draw a bar, table, number line, or quick trial by hand without leaving the app. That keeps the missing thinking visible.
• Progressive hints and worked solutions: If the first attempt goes wrong, the question opens up step by step, with a full worked solution afterwards. Your child sees a useful clue instead of an answer immediately.
• Focus, Sprint, and Worksheet modes: Focus is for unhurried accuracy, Sprint is for rapid recall against a timer, and Worksheet is for a whole paper marked at the end. Start a new heuristic in Focus, then move to mixed questions in Worksheet mode.

Start with one P5 or P6 problem, ask your child which heuristic they would try, and let them show the working before looking at help.

Try it free

Give your child a calm place to practise PSLE-style problem solving with a free interactive sample — no login or download required.

Try a free sample drill