Quick answer: Before-and-after word problems become manageable when pupils track what changes and what stays the same. Write the original amount, the change, the new amount and the unknown, then use a bar model or timeline only where it clarifies the relationship.
This detailed Singapore Primary 4 Mathematics guide focuses on before-and-after word problems: bar models, equal groups and remaining amounts. It includes eighteen original worked examples, error diagnosis, independent practice, revision routines and parent FAQs. P4 school assessments follow the MOE syllabus; the national SEAB examination is the P6 PSLE. There is no universal P4 paper format or reliable advance knowledge of 2027 school questions.
- Original = amount removed + amount remaining
- New amount = original + amount added − amount removed
- When two people exchange items, their combined total stays the same if nothing enters or leaves the pair
- When one quantity is twice another, draw two equal units versus one unit
- A fraction of the remaining amount refers to a new whole after the earlier event
MOE syllabus context and the school examination boundary
The MOE Primary Mathematics Syllabus, updated October 2025 sets out the P4 number, measurement, geometry and data strands, as well as mathematical reasoning and problem-solving processes. Before-and-after word problems become manageable when pupils track what changes and what stays the same. Write the original amount, the change, the new amount and the unknown, then use a bar model or timeline only where it clarifies the relationship. Schools decide the particular term’s tested scope, question formats and assessment instructions. A useful guide should build understanding without pretending to predict the paper.
Pupils benefit from moving from a simple representation to a clear explanation, then to a new problem attempted independently. If a child can repeat a model solution but cannot identify the relationship when the numbers change, the topic is not yet secure. The most useful next step is a precise correction and a delayed retest, not necessarily a harder question.
Eighteen worked questions: what to do, why it works and how to check
Worked question 1: A child has 83 stamps after giving away 27. How many originally?
Correct answer: 110 stamps. Working: 83 + 27 = 110.
First identify the quantity the question requests, then use the relationship shown in the working: 83 + 27 = 110. The result 110 stamps should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 2: A shop starts with 245 pens and sells 78. How many remain?
Correct answer: 167 pens. Working: 245 − 78 = 167.
First identify the quantity the question requests, then use the relationship shown in the working: 245 − 78 = 167. The result 167 pens should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 3: There are 72 cards. One quarter are removed, then 12 are added. Final?
Correct answer: 66 cards. Working: 72−18+12=66.
First identify the quantity the question requests, then use the relationship shown in the working: 72−18+12=66. The result 66 cards should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 4: A child has 80 sweets, uses half and then one quarter of the remainder. Final?
Correct answer: 30 sweets. Working: 80−40−10=30.
First identify the quantity the question requests, then use the relationship shown in the working: 80−40−10=30. The result 30 sweets should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 5: A child has 80 sweets, uses half and then one quarter of the original. Final?
Correct answer: 20 sweets. Working: 80−40−20=20.
First identify the quantity the question requests, then use the relationship shown in the working: 80−40−20=20. The result 20 sweets should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 6: A has 25 more cards than B, and they have 95 together. How many each?
Correct answer: A 60, B 35. Working: (95−25)÷2=35; 35+25=60.
First identify the quantity the question requests, then use the relationship shown in the working: (95−25)÷2=35; 35+25=60. The result A 60, B 35 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 7: One group has twice another, total 96. Find groups.
Correct answer: 32 and 64. Working: Three equal units; 96÷3=32.
First identify the quantity the question requests, then use the relationship shown in the working: Three equal units; 96÷3=32. The result 32 and 64 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 8: Maya has 48 stickers and gives 12 to Kai. How much does their combined total change?
Correct answer: No change. Working: Transfer between the two preserves the combined total.
First identify the quantity the question requests, then use the relationship shown in the working: Transfer between the two preserves the combined total. The result No change should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 9: There were 300 books. 85 were donated and 43 borrowed. Remaining?
Correct answer: 172 books. Working: 300−85−43=172.
First identify the quantity the question requests, then use the relationship shown in the working: 300−85−43=172. The result 172 books should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 10: A set has 60 counters. One third are used, then one fourth of the remaining used. Final?
Correct answer: 30 counters. Working: 60−20=40; 40−10=30.
First identify the quantity the question requests, then use the relationship shown in the working: 60−20=40; 40−10=30. The result 30 counters should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 11: Three equal packs plus 14 loose items total 92. Items per pack?
Correct answer: 26 items. Working: (92−14)÷3=26.
First identify the quantity the question requests, then use the relationship shown in the working: (92−14)÷3=26. The result 26 items should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 12: Four equal rows plus six spare chairs total 90. Chairs per row?
Correct answer: 21. Working: (90−6)÷4=21.
First identify the quantity the question requests, then use the relationship shown in the working: (90−6)÷4=21. The result 21 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 13: A box has 64 items after receiving 18. Before?
Correct answer: 46. Working: 64−18=46.
First identify the quantity the question requests, then use the relationship shown in the working: 64−18=46. The result 46 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 14: A pupil has $20, spends $7.65, receives $2.40. Final?
Correct answer: $14.75. Working: 20−7.65+2.40=14.75.
First identify the quantity the question requests, then use the relationship shown in the working: 20−7.65+2.40=14.75. The result $14.75 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 15: A has 20 cards, B 34. B gives A seven. New difference?
Correct answer: 0. Working: A=27 and B=27.
First identify the quantity the question requests, then use the relationship shown in the working: A=27 and B=27. The result 0 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 16: Two collections total 150. One has 30 more. Find both.
Correct answer: 90 and 60. Working: (150−30)÷2=60.
First identify the quantity the question requests, then use the relationship shown in the working: (150−30)÷2=60. The result 90 and 60 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 17: A child has 48 after losing one quarter of original. Original?
Correct answer: 64. Working: Three quarters=48, one quarter=16, whole=64.
First identify the quantity the question requests, then use the relationship shown in the working: Three quarters=48, one quarter=16, whole=64. The result 64 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Worked question 18: Five groups of 18 items each lose 13 items. Remaining?
Correct answer: 77. Working: 5×18−13=77.
First identify the quantity the question requests, then use the relationship shown in the working: 5×18−13=77. The result 77 should be checked against the original numbers and any units or restrictions. This prevents a correct intermediate calculation from being mistaken for the final answer. A clear short explanation is preferable to a long list of unlabelled numbers.
For independent transfer, change the story’s context or one number while preserving its mathematical structure. Ask the pupil to solve without looking at this model and to explain which part of the original method still applies. If a different target is requested, discuss why the operation may need to change. A later retest reveals whether the idea has been retained.
Four recurring error patterns and specific repairs
Error 1: Treating ‘originally’ as an instruction to subtract in every problem
This is not adequately explained by the word ‘careless’. Find the first step where the pupil’s interpretation, representation or arithmetic ceased to match the question. Use a contrasting example to make the mistaken assumption visible. Ask for a short verbal explanation, then a new independent calculation. A specific error description gives the child a practical way to improve.
Record the mistake, the corrected principle and a changed retest question. Do not assume copying the correct answer is the same as mastering it. If the error recurs, return to a simpler prerequisite and rebuild the relationship before increasing the difficulty.
Error 2: Applying a later fraction to the original total instead of the remainder
This is not adequately explained by the word ‘careless’. Find the first step where the pupil’s interpretation, representation or arithmetic ceased to match the question. Use a contrasting example to make the mistaken assumption visible. Ask for a short verbal explanation, then a new independent calculation. A specific error description gives the child a practical way to improve.
Record the mistake, the corrected principle and a changed retest question. Do not assume copying the correct answer is the same as mastering it. If the error recurs, return to a simpler prerequisite and rebuild the relationship before increasing the difficulty.
Error 3: Forgetting that a transfer between two people preserves their combined total
This is not adequately explained by the word ‘careless’. Find the first step where the pupil’s interpretation, representation or arithmetic ceased to match the question. Use a contrasting example to make the mistaken assumption visible. Ask for a short verbal explanation, then a new independent calculation. A specific error description gives the child a practical way to improve.
Record the mistake, the corrected principle and a changed retest question. Do not assume copying the correct answer is the same as mastering it. If the error recurs, return to a simpler prerequisite and rebuild the relationship before increasing the difficulty.
Error 4: Confusing ‘how many more’ with ‘how many altogether’
This is not adequately explained by the word ‘careless’. Find the first step where the pupil’s interpretation, representation or arithmetic ceased to match the question. Use a contrasting example to make the mistaken assumption visible. Ask for a short verbal explanation, then a new independent calculation. A specific error description gives the child a practical way to improve.
Record the mistake, the corrected principle and a changed retest question. Do not assume copying the correct answer is the same as mastering it. If the error recurs, return to a simpler prerequisite and rebuild the relationship before increasing the difficulty.
Independent practice and answer-checking routine
Practice 1: A child has 83 stamps after giving away 27. How many originally? Answer: 110 stamps. Verification: 83 + 27 = 110. Cover the answer first and explain the method in your own words.
Practice 2: A shop starts with 245 pens and sells 78. How many remain? Answer: 167 pens. Verification: 245 − 78 = 167. Cover the answer first and explain the method in your own words.
Practice 3: There are 72 cards. One quarter are removed, then 12 are added. Final? Answer: 66 cards. Verification: 72−18+12=66. Cover the answer first and explain the method in your own words.
Practice 4: A child has 80 sweets, uses half and then one quarter of the remainder. Final? Answer: 30 sweets. Verification: 80−40−10=30. Cover the answer first and explain the method in your own words.
Practice 5: A child has 80 sweets, uses half and then one quarter of the original. Final? Answer: 20 sweets. Verification: 80−40−20=20. Cover the answer first and explain the method in your own words.
Practice 6: A has 25 more cards than B, and they have 95 together. How many each? Answer: A 60, B 35. Verification: (95−25)÷2=35; 35+25=60. Cover the answer first and explain the method in your own words.
Practice 7: One group has twice another, total 96. Find groups. Answer: 32 and 64. Verification: Three equal units; 96÷3=32. Cover the answer first and explain the method in your own words.
Practice 8: Maya has 48 stickers and gives 12 to Kai. How much does their combined total change? Answer: No change. Verification: Transfer between the two preserves the combined total. Cover the answer first and explain the method in your own words.
Practice 9: There were 300 books. 85 were donated and 43 borrowed. Remaining? Answer: 172 books. Verification: 300−85−43=172. Cover the answer first and explain the method in your own words.
Practice 10: A set has 60 counters. One third are used, then one fourth of the remaining used. Final? Answer: 30 counters. Verification: 60−20=40; 40−10=30. Cover the answer first and explain the method in your own words.
Practice 11: Three equal packs plus 14 loose items total 92. Items per pack? Answer: 26 items. Verification: (92−14)÷3=26. Cover the answer first and explain the method in your own words.
Practice 12: Four equal rows plus six spare chairs total 90. Chairs per row? Answer: 21. Verification: (90−6)÷4=21. Cover the answer first and explain the method in your own words.
Practice 13: A box has 64 items after receiving 18. Before? Answer: 46. Verification: 64−18=46. Cover the answer first and explain the method in your own words.
Practice 14: A pupil has $20, spends $7.65, receives $2.40. Final? Answer: $14.75. Verification: 20−7.65+2.40=14.75. Cover the answer first and explain the method in your own words.
Practice 15: A has 20 cards, B 34. B gives A seven. New difference? Answer: 0. Verification: A=27 and B=27. Cover the answer first and explain the method in your own words.
Practice 16: Two collections total 150. One has 30 more. Find both. Answer: 90 and 60. Verification: (150−30)÷2=60. Cover the answer first and explain the method in your own words.
Practice 17: A child has 48 after losing one quarter of original. Original? Answer: 64. Verification: Three quarters=48, one quarter=16, whole=64. Cover the answer first and explain the method in your own words.
Practice 18: Five groups of 18 items each lose 13 items. Remaining? Answer: 77. Verification: 5×18−13=77. Cover the answer first and explain the method in your own words.
A two-week targeted revision plan
- Day 1: review the school’s actual tested scope and collect marked work.
- Day 2: attempt a short baseline without hints.
- Day 3: classify the first incorrect step in each error.
- Day 4: repair the most common misconception using a simple representation.
- Day 5: solve two changed examples independently.
- Day 6: practise a second weakness with clear working.
- Day 7: rest and briefly recall one corrected method.
- Day 8: mix this topic with an already-mastered P4 skill.
- Day 9: use an inverse operation or alternative check.
- Day 10: practise interpreting the final target and unit.
- Day 11: attempt a short independent mixed set.
- Day 12: introduce gentle timing only if accuracy is stable.
- Day 13: retest the original weakness with different numbers.
- Day 14: record progress and decide whether to consolidate or extend.
This plan is flexible, not a universal P4 school timetable. Families can spread the sessions across more than two weeks, and pupils who need a prerequisite can repeat that lesson. Good progress means the child can explain and solve an unfamiliar example independently. Do not replace sleep, play and ordinary family routines with unnecessary mock examinations.
Frequently asked parent questions
Is this an official national P4 SEAB Maths paper?
No. P4 assessment is school-based, while SEAB administers the national PSLE at P6.
Will these questions definitely appear in 2027?
No. They are original examples that teach syllabus-related mathematical reasoning.
How should parents choose the next revision topic?
Use the earliest recurring error in marked schoolwork and the school’s taught scope.
Should children memorise the worked solutions?
They should understand the relationship and apply it to new numbers and contexts.
What if a child is slow but accurate?
Build confidence and independent method selection before adding time pressure.
Do all schools use the same paper duration?
No. Follow the school’s own assessment notice.
Can pupils draw a bar model or table?
Yes, when it helps show the relationship and complies with school instructions.
How can I tell if a correction worked?
Give a changed question after a delay and remove prompts.
Is one wrong answer proof of a weak topic?
No. Look for the first error mechanism and whether it recurs.
Should I move immediately to P5 material?
Secure P4 prerequisites first, then preview higher-level ideas selectively.
Why is checking important?
An estimate, inverse operation or unit check can detect mistakes not caught by repeating the same method.
Where is the authoritative syllabus?
The MOE Primary Mathematics Syllabus linked in this article.
Six practical before-and-after problems clinics with independent checks
Clinic 1: Changing totals
A class starts with 96 cards, gives away 24, then receives 15. The new total is 87, because 96−24+15=87. A timeline should show 96, then 72, then 87, so each event has an unambiguous direction.
After reading the worked explanation, cover it and ask the pupil to name the unknown, identify the relevant relationship, and solve a new version with changed values. The key is not the final number in the example but why the chosen operation matches the question. If a student can reproduce the explanation but cannot begin the changed version, return to a simpler representation. If the changed version is solved independently, record the success and revisit it after a short delay.
Clinic 2: Transfer between people
Two children together have 120 tokens. If one gives the other 15 tokens, the total stays 120. Their individual counts change, but no tokens enter or leave the pair.
After reading the worked explanation, cover it and ask the pupil to name the unknown, identify the relevant relationship, and solve a new version with changed values. The key is not the final number in the example but why the chosen operation matches the question. If a student can reproduce the explanation but cannot begin the changed version, return to a simpler representation. If the changed version is solved independently, record the success and revisit it after a short delay.
Clinic 3: Reverse an unknown start
After selling 37 books, a shop has 88 left. The original stock is 125 because 88+37=125. The word ‘selling’ describes subtraction going forward but requires addition to reconstruct the start.
After reading the worked explanation, cover it and ask the pupil to name the unknown, identify the relevant relationship, and solve a new version with changed values. The key is not the final number in the example but why the chosen operation matches the question. If a student can reproduce the explanation but cannot begin the changed version, return to a simpler representation. If the changed version is solved independently, record the success and revisit it after a short delay.
Clinic 4: A fraction of remaining
There are 72 pencils. One third are used, leaving 48. One quarter of the remaining 48 is 12, so 36 pencils remain. Using one quarter of 72 for the second step would answer a different story.
After reading the worked explanation, cover it and ask the pupil to name the unknown, identify the relevant relationship, and solve a new version with changed values. The key is not the final number in the example but why the chosen operation matches the question. If a student can reproduce the explanation but cannot begin the changed version, return to a simpler representation. If the changed version is solved independently, record the success and revisit it after a short delay.
Clinic 5: Comparison bar
Two pupils together have 90 cards and one has 18 more. Remove the extra 18 to leave 72 in two equal units. Each base unit is 36, so the pupils have 36 and 54 cards.
After reading the worked explanation, cover it and ask the pupil to name the unknown, identify the relevant relationship, and solve a new version with changed values. The key is not the final number in the example but why the chosen operation matches the question. If a student can reproduce the explanation but cannot begin the changed version, return to a simpler representation. If the changed version is solved independently, record the success and revisit it after a short delay.
Clinic 6: Mixed equal groups
Four identical boxes and 13 loose items contain 105 items altogether. Subtract the 13 loose items to get 92, then divide by four to find 23 items in each box.
After reading the worked explanation, cover it and ask the pupil to name the unknown, identify the relevant relationship, and solve a new version with changed values. The key is not the final number in the example but why the chosen operation matches the question. If a student can reproduce the explanation but cannot begin the changed version, return to a simpler representation. If the changed version is solved independently, record the success and revisit it after a short delay.
A family-friendly way to check genuine improvement
Collect one marked school question that was originally incorrect and identify its first wrong step. Write the corrected principle in a sentence, then set a similar problem with different numbers. Ask the child to solve without seeing the model solution. A later retest is important because immediate correction can reflect recognition rather than durable understanding. This approach also makes it easier to decide whether more teaching is needed or whether the student is ready for mixed practice.
Do not interpret a practice score as an official MOE or SEAB grade. P4 assessments are school-based and the school’s own format and scope are the relevant reference. Good revision builds accurate reasoning, clear working, correct units and a checking habit without requiring a child to memorise future paper questions.
Further reading and official source
For related explanations, read the first P4 companion guide and the second P4 companion guide. The official MOE syllabus establishes the curriculum boundary. These examples are original educational material, not official or predicted examination questions.