Primary 5 Mathematics word problems require pupils to read a situation, identify the relationship between quantities and state the final answer accurately. This guide contains 30 original worked backwards questions, a concept-by-concept explanation and a revision method that parents can use without a specialist workbook.
Working backwards is a problem-solving heuristic: start from the final known quantity and undo the changes in reverse order. If a number is increased and then multiplied, divide first and subtract second. This guide teaches a reliable reverse check without introducing formal P6 algebra as compulsory P5 content. These examples are independent educational practice aligned with the current MOE Primary Mathematics syllabus. They are not a leaked, official or predicted 2027 school paper. P5 school assessments differ in topic scope, paper arrangements and calculator instructions.
- Thirty worked examples: attempt each before revealing the solution.
- Choose the relationship: identify what is known and what must be found.
- Write useful working: name the intermediate quantities and units.
- Check independently: use a reverse operation, estimate or diagram.
- Separate subject levels: Standard and Foundation P5 have distinct learning outcomes.
- Use school instructions: the current assessment notice decides the actual tested scope.
- Correct the first wrong step: do not label every misunderstanding a careless mistake.
Why this skill matters in P5 Mathematics
Working backwards is a problem-solving heuristic: start from the final known quantity and undo the changes in reverse order. If a number is increased and then multiplied, divide first and subtract second. This guide teaches a reliable reverse check without introducing formal P6 algebra as compulsory P5 content. The updated MOE syllabus emphasises mathematical problem solving, representation and communication. A child should understand why an operation fits a story instead of merely remembering a numerical answer.
The MOE syllabus updated October 2025 distinguishes P5 Standard and P5 Foundation outcomes. Use the relevant section and the school’s latest circular. A home practice pack cannot establish a national P5 exam format because no separate national SEAB P5 paper exists.
Concept 1: a rule to understand
Working backwards reverses the last forward step first. The order is as important as the choice of operation.
How to explain this to a child: Ask what each number represents, which quantity is the starting point and which quantity is the final target. Use a simple diagram or a short sentence. Then change the numbers so the child must apply the idea again.
A common examination trap: A pupil may use a correct calculation on the wrong quantity or stop at an intermediate answer. Check the wording and the units before treating the arithmetic as the problem.
How to test real understanding: Give a similar problem without naming the chapter. Ask the learner to select the operation and explain the result. Independent selection is a stronger signal than copying a model answer.
Concept 2: a rule to understand
Addition is undone by subtraction. Subtraction is undone by addition, when the same amount is involved.
How to explain this to a child: Ask what each number represents, which quantity is the starting point and which quantity is the final target. Use a simple diagram or a short sentence. Then change the numbers so the child must apply the idea again.
A common examination trap: A pupil may use a correct calculation on the wrong quantity or stop at an intermediate answer. Check the wording and the units before treating the arithmetic as the problem.
How to test real understanding: Give a similar problem without naming the chapter. Ask the learner to select the operation and explain the result. Independent selection is a stronger signal than copying a model answer.
Concept 3: a rule to understand
Multiplication is undone by division. Division is undone by multiplication, provided the quantities and conditions are clear.
How to explain this to a child: Ask what each number represents, which quantity is the starting point and which quantity is the final target. Use a simple diagram or a short sentence. Then change the numbers so the child must apply the idea again.
A common examination trap: A pupil may use a correct calculation on the wrong quantity or stop at an intermediate answer. Check the wording and the units before treating the arithmetic as the problem.
How to test real understanding: Give a similar problem without naming the chapter. Ask the learner to select the operation and explain the result. Independent selection is a stronger signal than copying a model answer.
Concept 4: a rule to understand
A stage table helps a student avoid undoing operations in the wrong order. Write the final result at the bottom and move upwards.
How to explain this to a child: Ask what each number represents, which quantity is the starting point and which quantity is the final target. Use a simple diagram or a short sentence. Then change the numbers so the child must apply the idea again.
A common examination trap: A pupil may use a correct calculation on the wrong quantity or stop at an intermediate answer. Check the wording and the units before treating the arithmetic as the problem.
How to test real understanding: Give a similar problem without naming the chapter. Ask the learner to select the operation and explain the result. Independent selection is a stronger signal than copying a model answer.
Concept 5: a rule to understand
Always check the reconstructed starting number by applying the original forward steps.
How to explain this to a child: Ask what each number represents, which quantity is the starting point and which quantity is the final target. Use a simple diagram or a short sentence. Then change the numbers so the child must apply the idea again.
A common examination trap: A pupil may use a correct calculation on the wrong quantity or stop at an intermediate answer. Check the wording and the units before treating the arithmetic as the problem.
How to test real understanding: Give a similar problem without naming the chapter. Ask the learner to select the operation and explain the result. Independent selection is a stronger signal than copying a model answer.
Concept 6: a rule to understand
A working-backwards method is a heuristic. P5 pupils do not need to learn formal P6 algebra to use it successfully.
How to explain this to a child: Ask what each number represents, which quantity is the starting point and which quantity is the final target. Use a simple diagram or a short sentence. Then change the numbers so the child must apply the idea again.
A common examination trap: A pupil may use a correct calculation on the wrong quantity or stop at an intermediate answer. Check the wording and the units before treating the arithmetic as the problem.
How to test real understanding: Give a similar problem without naming the chapter. Ask the learner to select the operation and explain the result. Independent selection is a stronger signal than copying a model answer.
Thirty original questions and worked answers
These questions practise a consistent mathematical relationship with changing numbers and contexts. The repeated structure builds fluency; later, mix them with other topics so that the chapter heading does not give away the method.
Question 1
Problem: A number is increased by 5, then multiplied by 2. The final value is 90. What was the starting number?
Complete worked solution: Reverse multiplication: 90 ÷ 2 = 45. Reverse addition: 45 − 5 = 40.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (40 + 5) × 2 = 90.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 2
Problem: A number is increased by 6, then multiplied by 3. The final value is 150. What was the starting number?
Complete worked solution: Reverse multiplication: 150 ÷ 3 = 50. Reverse addition: 50 − 6 = 44.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (44 + 6) × 3 = 150.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 3
Problem: A number is increased by 7, then multiplied by 4. The final value is 220. What was the starting number?
Complete worked solution: Reverse multiplication: 220 ÷ 4 = 55. Reverse addition: 55 − 7 = 48.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (48 + 7) × 4 = 220.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 4
Problem: A number is increased by 8, then multiplied by 2. The final value is 120. What was the starting number?
Complete worked solution: Reverse multiplication: 120 ÷ 2 = 60. Reverse addition: 60 − 8 = 52.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (52 + 8) × 2 = 120.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 5
Problem: A number is increased by 9, then multiplied by 3. The final value is 195. What was the starting number?
Complete worked solution: Reverse multiplication: 195 ÷ 3 = 65. Reverse addition: 65 − 9 = 56.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (56 + 9) × 3 = 195.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 6
Problem: A number is increased by 10, then multiplied by 4. The final value is 280. What was the starting number?
Complete worked solution: Reverse multiplication: 280 ÷ 4 = 70. Reverse addition: 70 − 10 = 60.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (60 + 10) × 4 = 280.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 7
Problem: A number is increased by 11, then multiplied by 2. The final value is 150. What was the starting number?
Complete worked solution: Reverse multiplication: 150 ÷ 2 = 75. Reverse addition: 75 − 11 = 64.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (64 + 11) × 2 = 150.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 8
Problem: A number is increased by 12, then multiplied by 3. The final value is 240. What was the starting number?
Complete worked solution: Reverse multiplication: 240 ÷ 3 = 80. Reverse addition: 80 − 12 = 68.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (68 + 12) × 3 = 240.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 9
Problem: A number is increased by 13, then multiplied by 4. The final value is 340. What was the starting number?
Complete worked solution: Reverse multiplication: 340 ÷ 4 = 85. Reverse addition: 85 − 13 = 72.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (72 + 13) × 4 = 340.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 10
Problem: A number is increased by 5, then multiplied by 2. The final value is 162. What was the starting number?
Complete worked solution: Reverse multiplication: 162 ÷ 2 = 81. Reverse addition: 81 − 5 = 76.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (76 + 5) × 2 = 162.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 11
Problem: A number is increased by 6, then multiplied by 3. The final value is 258. What was the starting number?
Complete worked solution: Reverse multiplication: 258 ÷ 3 = 86. Reverse addition: 86 − 6 = 80.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (80 + 6) × 3 = 258.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 12
Problem: A number is increased by 7, then multiplied by 4. The final value is 364. What was the starting number?
Complete worked solution: Reverse multiplication: 364 ÷ 4 = 91. Reverse addition: 91 − 7 = 84.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (84 + 7) × 4 = 364.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 13
Problem: A number is increased by 8, then multiplied by 2. The final value is 192. What was the starting number?
Complete worked solution: Reverse multiplication: 192 ÷ 2 = 96. Reverse addition: 96 − 8 = 88.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (88 + 8) × 2 = 192.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 14
Problem: A number is increased by 9, then multiplied by 3. The final value is 303. What was the starting number?
Complete worked solution: Reverse multiplication: 303 ÷ 3 = 101. Reverse addition: 101 − 9 = 92.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (92 + 9) × 3 = 303.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 15
Problem: A number is increased by 10, then multiplied by 4. The final value is 424. What was the starting number?
Complete worked solution: Reverse multiplication: 424 ÷ 4 = 106. Reverse addition: 106 − 10 = 96.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (96 + 10) × 4 = 424.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 16
Problem: A number is increased by 11, then multiplied by 2. The final value is 222. What was the starting number?
Complete worked solution: Reverse multiplication: 222 ÷ 2 = 111. Reverse addition: 111 − 11 = 100.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (100 + 11) × 2 = 222.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 17
Problem: A number is increased by 12, then multiplied by 3. The final value is 348. What was the starting number?
Complete worked solution: Reverse multiplication: 348 ÷ 3 = 116. Reverse addition: 116 − 12 = 104.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (104 + 12) × 3 = 348.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 18
Problem: A number is increased by 13, then multiplied by 4. The final value is 484. What was the starting number?
Complete worked solution: Reverse multiplication: 484 ÷ 4 = 121. Reverse addition: 121 − 13 = 108.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (108 + 13) × 4 = 484.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 19
Problem: A number is increased by 5, then multiplied by 2. The final value is 234. What was the starting number?
Complete worked solution: Reverse multiplication: 234 ÷ 2 = 117. Reverse addition: 117 − 5 = 112.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (112 + 5) × 2 = 234.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 20
Problem: A number is increased by 6, then multiplied by 3. The final value is 366. What was the starting number?
Complete worked solution: Reverse multiplication: 366 ÷ 3 = 122. Reverse addition: 122 − 6 = 116.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (116 + 6) × 3 = 366.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 21
Problem: A number is increased by 7, then multiplied by 4. The final value is 508. What was the starting number?
Complete worked solution: Reverse multiplication: 508 ÷ 4 = 127. Reverse addition: 127 − 7 = 120.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (120 + 7) × 4 = 508.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 22
Problem: A number is increased by 8, then multiplied by 2. The final value is 264. What was the starting number?
Complete worked solution: Reverse multiplication: 264 ÷ 2 = 132. Reverse addition: 132 − 8 = 124.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (124 + 8) × 2 = 264.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 23
Problem: A number is increased by 9, then multiplied by 3. The final value is 411. What was the starting number?
Complete worked solution: Reverse multiplication: 411 ÷ 3 = 137. Reverse addition: 137 − 9 = 128.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (128 + 9) × 3 = 411.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 24
Problem: A number is increased by 10, then multiplied by 4. The final value is 568. What was the starting number?
Complete worked solution: Reverse multiplication: 568 ÷ 4 = 142. Reverse addition: 142 − 10 = 132.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (132 + 10) × 4 = 568.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 25
Problem: A number is increased by 11, then multiplied by 2. The final value is 294. What was the starting number?
Complete worked solution: Reverse multiplication: 294 ÷ 2 = 147. Reverse addition: 147 − 11 = 136.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (136 + 11) × 2 = 294.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 26
Problem: A number is increased by 12, then multiplied by 3. The final value is 456. What was the starting number?
Complete worked solution: Reverse multiplication: 456 ÷ 3 = 152. Reverse addition: 152 − 12 = 140.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (140 + 12) × 3 = 456.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 27
Problem: A number is increased by 13, then multiplied by 4. The final value is 628. What was the starting number?
Complete worked solution: Reverse multiplication: 628 ÷ 4 = 157. Reverse addition: 157 − 13 = 144.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (144 + 13) × 4 = 628.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 28
Problem: A number is increased by 5, then multiplied by 2. The final value is 306. What was the starting number?
Complete worked solution: Reverse multiplication: 306 ÷ 2 = 153. Reverse addition: 153 − 5 = 148.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (148 + 5) × 2 = 306.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 29
Problem: A number is increased by 6, then multiplied by 3. The final value is 474. What was the starting number?
Complete worked solution: Reverse multiplication: 474 ÷ 3 = 158. Reverse addition: 158 − 6 = 152.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (152 + 6) × 3 = 474.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
Question 30
Problem: A number is increased by 7, then multiplied by 4. The final value is 652. What was the starting number?
Complete worked solution: Reverse multiplication: 652 ÷ 4 = 163. Reverse addition: 163 − 7 = 156.
Why this works: Undo the last forward operation first, then the earlier one.
Independent check: Forward check: (156 + 7) × 4 = 652.
Student reflection: Which quantity was given, which was unknown, and what feature of the question told you how to connect them? Explain why the final answer has the correct size and unit.
How to use a practice pack without memorising answers
Complete five questions in one sitting and cover the solutions until the attempt is finished. Ask the child to explain the quantities, the mathematical relationship and the final unit. A correct numerical answer reached by guessing is not yet secure understanding.
When an error occurs, find the first wrong decision. Was the whole incorrect? Was a unit missing? Did the child reverse multiplication and division? Was a diagram’s height chosen incorrectly? Record the actual cause rather than simply writing “careless mistake”.
After a short delay, change the numbers and give a similar question without the chapter label. A pupil who can choose and explain the method independently is showing stronger learning than one who copies a familiar worked solution.
A seven-day targeted revision sequence
On the first day, review the underlying rule using small numbers and one diagram or table. On the second day, solve five straightforward questions. On the third day, practise five more questions with the answer key covered. On the fourth day, explain the rule aloud without notes.
On the fifth day, combine the topic with another syllabus concept. On the sixth day, solve a short mixed set under a gentle time limit. On the seventh day, revisit two mistakes using fresh numbers. The timetable is a suggested learning aid, not an MOE-mandated sequence.
If the child is not yet ready for the multi-step problems, return to the prerequisite. Building a secure relationship between quantities is more important than finishing a large number of worksheets.
How parents can support mathematical reasoning
Ask “What is the question asking for?”, “What is the unit?”, “Which operation fits the relationship?” and “How could you check that result?” These prompts preserve the learner’s chance to make decisions. Avoid giving a rule solely because a keyword appears in the sentence.
A pupil who struggles with reading a long problem may benefit from separating the story into given facts, changes and final request. A pupil who struggles with arithmetic may need a brief fact-retrieval routine. The right support depends on the actual source of difficulty.
Frequently asked questions
Are these official 2027 examination questions?
No. They are independently written practice questions. P5 examinations are set by schools, and no separate national SEAB P5 Mathematics paper is administered.
Are the questions suitable for both Standard and Foundation Mathematics?
Not automatically. Each subject level has its own syllabus. Check the child’s school scope and select exercises that match the course.
How should a child check a word-problem answer?
Use an inverse calculation, a unit check, an estimate or a conservation check depending on the relationship. Repeating the same incorrect operation is not an independent check.
Does a correct practice score predict PSLE AL1 or AL2?
No. Home practice and school P5 papers are not calibrated to future PSLE Achievement Levels.
What if the pupil repeatedly makes the same mistake?
Teach the underlying idea with a simpler representation, then retest independently after a delay. Avoid relying on repeated copying of the same answer.
Official and related references
- MOE Primary Mathematics syllabus updated October 2025
- P5 Maths exam scope and revision plan
- P5 Standard Maths 50-question practice paper
- P5 Foundation Maths practice paper
- P5 Maths word-problem vocabulary
- eduKate Mathematics Learning Hub
Reviewed November 2026. Original educational exercises, not official or predicted school questions.