PSLE English, Maths & Science: Is There Enough Information?

PSLE Learner’s Guide · Vol 0103 · English, Mathematics and Science · Primary 6

The question may look complete before the evidence is complete

A school notice says a trip will start at 9 a.m. It gives the departure time but not the meeting place. If a friend asks, ‘Where should we gather?’, can you answer with ‘outside the library’ simply because school trips often gather there? No. The time is known; the location is not stated. One plausible location is not the same as one supported location.

Now consider a Mathematics question: twenty pupils play basketball and eighteen play badminton in a class of thirty. How many pupils play both sports? You can see that at least eight must be in both groups, because 20 + 18 exceeds the class total by eight. But there might be more than eight in both if some pupils play neither. Without information about how many play at least one sport, an exact overlap is not determined. An answer of eight looks attractive because the arithmetic is neat, yet it silently assumes that every pupil plays at least one.

In Science, two plants end at different heights. Does that prove the taller plant received more sunlight? Not from final height alone. The plants may have started at different heights, received different amounts of water or differed in other relevant ways. You can report the height difference accurately, but explaining its cause needs further controlled evidence. The same core problem crosses three subjects: do the supplied facts justify exactly the conclusion the question appears to ask for?

This guide develops the examination habit of distinguishing a uniquely supported answer from a plausible guess, a conditional answer or a range of possibilities. The goal is not to write ‘not enough information’ whenever a problem looks difficult. Real PSLE questions are designed to be answerable from their full stimuli and instructions. Often the missing piece is present somewhere else, in a caption, passage line, key or earlier part. First search carefully; only then assess what the stated evidence really allows.

The official SEAB 2026 PSLE formats identify the English, revised Mathematics and revised Science papers for this examination year. The exercises below are original diagnostic examples, some deliberately lacking information to teach you what insufficiency looks like. They are not presented as actual unanswerable PSLE questions. In a real paper, answer the complete question and use the whole source before deciding that a particular interpretation is unsupported.

1. Four levels of information sufficiency

Level 1 — directly stated: A notice gives the event date and time. A table gives the number of pupils. A Science observation says the temperature rose by 5 °C over five minutes. You can report those facts without guessing. But the stated fact may not answer a different question about place, cause or starting temperature.

Level 2 — uniquely derived: The full set of facts determines one result through a justified method. A class has 30 pupils, 20 like A, 18 like B and every pupil likes at least one. The overlap must be 20 + 18 − 30 = 8. The ‘every pupil’ condition removes the ambiguity in our opening example. A maths answer need not be written directly in a chart for it to be fully determined.

Level 3 — limited conclusion: The evidence supports a bound or a comparison but not one exact value. In the class of 30 with 20 liking A and 18 liking B, at least eight are in both. The overlap cannot exceed the smaller reported group of eighteen. Thus eight through eighteen are numerically possible when other constraints permit. You have learned something meaningful without being able to identify the exact overlap.

Level 4 — competing explanations: An observation has several plausible causes, and the information supplied does not distinguish them. The Science task may ask which variable to control next, what can be concluded, or why one interpretation is premature. Identifying this is stronger than confidently inventing a cause. In English, a pronoun in a tiny excerpt may refer to more than one person; the full passage may remove that ambiguity. Always distinguish the limits of a snippet from the limits of a complete text.

Sufficiency is relative to the precise question. A chart might be enough to tell you that 24 visitors arrived on Tuesday but not enough to explain why Tuesday was busier than Monday. A notice may establish where pupils gather but not why a trip was rescheduled. A simple experiment can show that a variable changed without identifying every possible physical cause. Ask what job the question assigns before deciding how much evidence is necessary.

2. A five-move sufficiency test

Move 1: Name the exact output

Is the task asking for a number, person’s identity, location, reason, trend, explanation, procedure or possibility? ‘What happened?’ and ‘Why did it happen?’ require different kinds of evidence. Write the output in plain words before searching the stimulus.

A useful check is to reverse the question slightly: what observation or condition, if changed, would make the proposed answer false? If you cannot identify the warrant connecting your claim to the source, revisit the actual data rather than the fluency of your final sentence.

Move 2: Inventory the given facts

Read every relevant line, table label, key, unit and earlier result. Separate explicit data from details you supplied from general expectations. A familiar setting does not authorise a missing number or location.

Move 3: Identify the required link

For a calculation, name the equation or relationship. For comprehension, locate evidence for the precise referent or inference. For Science, connect the measured variable and conditions to the proposed mechanism. If the bridge is missing, the answer may be underdetermined.

Move 4: Try a second situation that also fits

For a genuinely ambiguous task, see whether two different answers can satisfy all stated facts. If both do, the facts do not determine one result. If an additional constraint rules one out, the answer may become unique. This is a powerful diagnostic during revision, not a requirement to invent alternatives during every timed question.

Move 5: State only what follows and what would resolve the gap

When the problem determines one answer, give it clearly. When the information only sets limits, state those limits. When the issue is a missing piece, identify the specific fact or control that would make the conclusion defensible. Do not use vague uncertainty to avoid work that the question actually supports.

3. English: distinguish a supported answer from an imagined story

English case 1: The notice without a venue

Stimulus: A message says: ‘The reading competition begins at 2 p.m. on Thursday. Please bring your prepared passage.’ A student asks where to report. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The time, day and required item are known. The meeting place is not stated in this excerpt. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: The library, hall and classroom are all plausible venues, but choosing one from habit would invent an event detail. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Add ‘Participants must report to the hall’ and show how this new line determines the answer. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 2: A pronoun before its referent is clear

Stimulus: The excerpt says: ‘Asha spoke to Mei after she had finished rehearsing.’ No other lines clarify who rehearsed. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The pronoun ‘she’ is ambiguous in this isolated sentence; it may refer to either girl. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: A pupil choosing the nearest name may occasionally be right, but the grammar and context provided here do not establish one actor. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Add a following sentence explicitly identifying the rehearsing pupil; then reverse that clue. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 3: A reason versus a coincidence

Stimulus: A passage says: ‘The school concert was postponed. Rain began in the afternoon.’ There is no explicit explanation of postponement. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The concert was postponed, and it rained that afternoon. The text does not establish rain as the cause. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: The two events occurring together is insufficient to prove one caused the other. This is a reading-evidence problem, not a grammar problem. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Add the line ‘The outdoor stage had become unsafe because of the rain’ and rewrite the answer to ‘why’. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 4: The two possible owners

Stimulus: A sentence reads: ‘Daniel placed his folder beside Aaron’s bag.’ A question asks whose folder was moved. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: Daniel’s folder was moved. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: ‘His’ refers to Daniel in this clear construction. The mere presence of Aaron’s bag does not create a need to call the answer uncertain. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Change the wording to ‘Daniel placed a folder beside Aaron’s bag’ and explain what ownership is no longer established. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 5: The wrong part of a notice

Stimulus: A notice gives the bus departure time and asks pupils to arrive ten minutes beforehand. It does not state the time school ends. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The required arrival time can be calculated from the departure time, but the school dismissal time cannot be inferred. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: A problem can contain enough information for one requested detail and not another. Do not declare the whole notice useless because one field is absent. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Give a bus departure time of 9:20 and calculate the required reporting time; then ask for dismissal time. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 6: A character’s feeling from weak evidence

Stimulus: A character pauses before opening a letter, but the excerpt offers no further thoughts, actions or descriptive clues. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The pause is observable; a precise emotion such as anger, fear or excitement is not uniquely established by that act alone. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: Several feelings could produce a pause. A cautious inference may be possible in wider context, but a specific emotional label needs stronger support. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Add details showing the character’s reaction to a long-awaited acceptance letter and discuss what emotions are now supported. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 7: A stated promise with a condition

Stimulus: An email says, ‘I will help with the display if I finish my project by Wednesday.’ A pupil reports, ‘The writer has promised to help, no matter what.’ Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The commitment is conditional on finishing the project by Wednesday. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: The exact condition is in the source. The unconditional claim is not merely too confident; it changes the meaning. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Replace ‘if’ with ‘when’ and discuss how the certainty of the condition changes. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 8: A paragraph that answers a different question

Stimulus: A passage states that a team left early and later reached the hall before other teams. The question asks for the reason the team left early. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The arrival order is stated, but the cause of the early departure may be unknown unless another line gives it. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: A learner who writes ‘to arrive before the others’ is adding a purpose. This may be a reasonable story but is not necessarily the author’s stated motive. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Insert an explicit line ‘They left early because they needed to collect equipment’ and answer again. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 9: An instruction about an item, not its purpose

Stimulus: A teacher says, ‘Bring one clear bottle to class tomorrow.’ The passage does not say what the bottle will be used for. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The pupils must bring one clear bottle; the intended experiment or activity is not specified. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: Calling it a ‘science experiment’ from the object alone would be an unverified assumption about the teacher’s plan. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Add a line that the bottle will be used to observe seed roots and describe how this determines the purpose. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

English case 10: An unhelpful answer of ‘not enough information’

Stimulus: A visual notice has a large header ‘Meet at the foyer’ and a smaller footer giving the event time. A student looks only at the footer. Begin by identifying the exact question and the words available, rather than relying on what usually happens in a similar situation.

What the evidence supports: The location is given in the full notice: the foyer. This distinction protects an answer from becoming either more certain or less certain than the passage warrants.

Why a plausible shortcut fails: The problem is insufficient reading, not insufficient information. Always search captions, labels and headings before diagnosing a genuine absence. Comprehension is not a competition to invent a convincing backstory; it is a disciplined reading of the source and its implications.

Changed-source test: Put the location inside a side panel instead and practise scanning the whole document. When new information arrives, ask whether it narrows the possibilities to a single supported reading. A good method updates with the evidence.

In a real English paper, the question designer will normally provide the relevant passage or stimulus, and an apparently ambiguous excerpt may be resolved in surrounding lines. So the examination habit is search first, infer second, claim only what the source carries. Do not use ‘not enough information’ as an escape from rereading. For broader comprehension and writing support, the English Learning Hub owns deeper topic teaching; this volume owns the sufficiency decision.

4. Mathematics: prove whether one numerical value follows

Mathematics case 1: Two sport preferences with unknown overlap

Given data: Of 30 pupils, 20 enjoy football and 18 enjoy badminton, but nobody reports how many enjoy both or neither. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: At least 8 and at most 18 can be in both. One exact overlap is not determined. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: If all 30 enjoy at least one, the overlap is 8. If 5 enjoy neither, the union is 25 and overlap is 13. Both scenarios fit the original group counts. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Add ‘every pupil enjoys at least one sport’ and calculate exactly 8. For deeper set-count arithmetic use the existing Vol 0094 overlap guide. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 2: A ratio without a total

Given data: Red and blue marbles are in the ratio 2:3. The question asks for the number of red marbles but gives no total or number of parts. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: The red share is 2/5 of the combined red-and-blue group, but the exact red count is unknown. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: There could be 2 red and 3 blue, or 4 red and 6 blue, or another integer multiple. The ratio fixes proportion, not scale. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Add ‘there are 25 marbles in all’, then find 10 red. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 3: Perimeter without area

Given data: A rectangle has perimeter 30 cm, but no side length is given. Find its exact area. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: There is no unique area from the perimeter alone. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: A 10 cm by 5 cm rectangle has area 50 cm²; a 9 cm by 6 cm rectangle has area 54 cm². Both have perimeter 30 cm. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Add ‘one side is 5 cm’ and compute the area. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 4: An average without a count

Given data: The average score is 18 points, but the number of pupils is absent. Find the total score. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: The total is 18 × number of scores and cannot be one exact value without the count. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: Three pupils would total 54 points; five pupils would total 90 points. Both fit the average. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Supply ‘four pupils’ and compute the total of 72 points. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 5: A distance without time

Given data: A cyclist travels 24 km. The average speed is requested, but no travel time is reported. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: Distance alone does not determine average speed. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: The same distance can be travelled in one hour at 24 km/h or two hours at 12 km/h. The missing time changes the result. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Add an elapsed time of 1.5 hours and find 16 km/h. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 6: Temperature change without a start

Given data: A thermometer reading increases by 7 °C. The question asks for the final temperature, but the starting reading is not supplied. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: The increase is known, but the final reading is not unique. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: A start of 20 °C gives 27 °C; a start of 25 °C gives 32 °C. Both represent the same increase. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Supply an initial reading of 18 °C and compute the new value. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 7: A graph with an unlabelled axis

Given data: Two equally high bars appear in a diagram, but the vertical axis has no numerical values or unit. Find the exact counts. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: The bars appear equal in plotted height, but the exact count represented by that height is unavailable. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: The drawing could represent five pupils each or fifty pupils each. The lack of scale stops an exact numerical answer. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Add labels 0, 10, 20 and 30 at equal spacing, then identify the bar values from the stated positions. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 8: A sum and difference determine two numbers

Given data: Two numbers sum to 24, and the larger exceeds the smaller by 6. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: The numbers are uniquely 15 and 9. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: Unlike a single equation with two unknowns, the sum and difference together fix both values: (24+6)/2=15 and (24−6)/2=9. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Remove the difference statement and explain why infinitely many nonnegative pairs now fit the sum. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 9: A number of poles without spacing

Given data: Seven posts stand on a straight path with equal gaps, but the distance of each gap is not stated. Find total distance. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: There are six gaps if both endpoints are posts, but total metres cannot be determined without gap length. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: Six gaps of 2 metres give 12 metres, while six gaps of 3 metres give 18 metres. Count and physical length answer different questions. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Add ‘each gap is 4 m’ and find 24 m; for interval structure use the Vol 0101 guide. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 10: A percentage without a whole

Given data: Twenty percent of a class joined a club. The question asks how many pupils joined, without class size. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: The fraction 1/5 is known, but the count is undetermined. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: A class of 30 would yield 6 members; a class of 40 would yield 8 members. A percentage alone does not fix an absolute amount. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Give a class size of 35 and find 7 club members. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 11: A comparison uniquely determined despite extra wording

Given data: There are 16 red counters and 9 blue counters, with an irrelevant sentence describing the container’s colour. How many more red counters? Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: The answer is exactly 7 counters. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: The colour of the container is not needed. Do not write ‘insufficient’ simply because a problem contains extraneous information or an unused description. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Change the question to the percentage of the total counters that are red and solve from the same counts. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics case 12: Only a lower bound is supported

Given data: A group of 40 pupils includes 29 who play chess and 25 who play drama. Some pupils may play neither. Decide whether the requested number is fully specified or whether one required total, interval, scale or other condition is absent.

Supported result: At least 14 pupils play both, but the exact overlap is unknown. If a range is supported but not one exact value, say what the data do determine. If the result is exact, show the relationship that makes it exact.

Second-solution test: The two memberships total 54. At most 40 distinct pupils can be in the union, so at least 14 memberships are duplicated. More overlap is possible if some belong to neither. Two valid different results satisfying the same stated conditions demonstrate that an exact value is not fixed. Do not confuse that with an arithmetic mistake.

Information repair: Add that six play neither. Then the union is 34 and the overlap is 20. Solve the changed problem after adding the decisive fact. You should now be able to explain why the new information made the answer unique.

Mathematics is not a game of refusing every question with an unknown. Some unknowns can be found from other constraints, and some are unnecessary because a question asks only for a relation. A ratio can determine a fraction without determining the total count. A perimeter plus one side can determine area. The examination job is to test whether the available relationships determine the requested quantity. The Mathematics Learning Hub provides the canonical topic lessons.

5. Science: observations may be certain while causes are not

Science case 1: Two plants with different heights

Observation: Plant A measures 18 cm and Plant B measures 15 cm after one week. Starting heights and growing conditions are not reported. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: The final measured heights differ by 3 cm. No unique cause of the difference is established. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: The plants might have started at different heights or experienced different relevant conditions. Taller at the end does not necessarily mean faster growth. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Give equal starting heights and controlled conditions except sunlight. Explain how the improved comparison changes the strength of a causal claim. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 2: Water disappears from an open dish

Observation: An open dish contains less water after a day, but the question gives no observations of spills or conditions. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: Water amount in the dish decreased. A particular route for all missing water is not established solely by the one reading. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: Evaporation is a plausible process under ordinary conditions, but a spill or removal cannot be excluded if the setup is not controlled. Evidence must address the actual alternative routes. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Add that the dish was protected from spilling and handled carefully in a controlled experiment. Discuss what evidence would support evaporation. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 3: A lamp is off in a circuit

Observation: A lamp in an unspecified circuit does not light; no diagram or test of components is supplied. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: The lamp is not lit. The exact fault is not determined. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: An open connection, exhausted cell or faulty lamp can each prevent lighting. Naming one without additional evidence is guessing. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Add a clear diagram showing an open switch and otherwise functioning components; explain the direct effect of the break. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 4: A shadow becomes larger

Observation: A shadow’s width increases between two trials, but the description does not say which source, object or screen positions changed. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: The second measured shadow is larger. Which movement caused it remains unknown. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: Source distance, object position, object size and screen placement can influence projection. A size measurement alone does not identify the changed factor. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Add that the toy and wall stayed fixed while a small torch moved closer to the toy; derive a specific prediction. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 5: A book slows after a push

Observation: A book glides over a tabletop and slows when the hand releases it. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: The book slowed after the push. Friction at the book–desk contact is a plausible contributor. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: A complete force explanation depends on the described contact and other relevant influences; the observation alone is not a numerical measurement of frictional force. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: State that the same book slides over the same level surface in a controlled arrangement. Explain the contact mechanism using the Vol 0102 guide. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 6: A seed germinates

Observation: A seed begins growing in a moist container, but the light exposure and other conditions are not specified. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: The seed germinated in the observed conditions. Do not claim from this fact alone that light caused its germination. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: The observation is consistent with several environmental conditions. Explaining one cause requires identifying which variable was tested and what was held constant. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Design a comparison focused on water availability while holding other relevant factors consistent. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 7: A metal object is attracted to a magnet

Observation: A small metal-looking object moves towards a magnet. Its exact material is not identified. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: A magnetic attraction was observed under the stated conditions. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: The word ‘metal-looking’ does not identify a specific metal. It is not justified to claim every metal behaves the same way or to name one alloy from its appearance. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Provide a reliable material identification and test result, then say what additional claim becomes supported. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 8: Two cups finish at one temperature

Observation: Cup A starts at 80 °C and Cup B starts at 60 °C, and both finish at 50 °C after equal time. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: A falls 30 °C and B falls 10 °C. The measured changes are known. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: The same final reading does not mean the same temperature drop or equal heat energy transferred. Additional quantities would be needed for an energy comparison. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Give equal water masses and cup materials as additional conditions and discuss which conclusions become more defensible. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 9: Water droplets on a cold bottle

Observation: Drops appear on the outside of a chilled bottle taken into humid air, but no direct path of water from inside is observed. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: The exterior became wet. In an ordinary closed-bottle demonstration, condensation of moisture from the surrounding air is the relevant scientific explanation. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: Do not claim water necessarily leaked through a sealed wall; use the physical context. If the bottle has an opening or a spill, those would require inspection. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: State that the cap was closed and the exterior was initially dry, then explain how the conditions support condensation. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 10: One fertilised plot grows better

Observation: A school compares a fertilised plot with an unfertilised plot but also waters the fertilised plot more frequently. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: The plot outcomes may differ, but fertiliser alone has not been isolated as the cause. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: Water and fertiliser vary together, making the two-variable comparison insufficient for a unique causal attribution. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Keep watering consistent and change only the fertiliser condition. Describe what repeated evidence would support. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 11: A flat measurement graph

Observation: A plant’s measured height stays at 22 cm at three recorded times. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: There was no recorded height increase over those times, but the plant’s long-term future or exact biological state is not determined. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: A stable height reading could reflect a temporary period without measurable increase or limitations of the measurements. It is not proof of death. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Supply a later height of 23 cm and revise the conclusion without denying the earlier observations. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

Science case 12: Bird numbers decrease

Observation: A class counts fewer birds in a park on Wednesday than on Monday, but no other conditions are described. First report the measured or directly described fact. Do not turn a familiar Science keyword into a conclusion about an unobserved mechanism.

Safe claim: The counts at the observed times differ. A unique reason for the difference is not established. This response is neither artificially vague nor more precise than the source. It distinguishes a supported outcome from a stronger causal story.

Why one explanation may be premature: Weather, observation conditions, timing and bird movement are possible influences. Selecting one is not a measured causal result. Ask which conditions would have to be controlled or which further measurement would discriminate among plausible explanations.

Follow-up test: Repeat observations at controlled times using the same counting area and method; state what improves and what remains uncertain. After the conditions change, reconsider which conclusion the new evidence warrants instead of repeating the original uncertainty or answer.

An explanation question may supply a complete fair-test design elsewhere in the question, so do not stop reading after the first graph or observation. The correct Science answer often emerges from combining the diagram, the variable table and the requested conclusion. The general experimental-variable skill has its own Vol 0095 guide; this article concentrates on whether the available evidence determines the claim. The Science Learning Hub covers the underlying topics in greater depth.

6. Four cross-subject investigations: change one fact and watch the answer change

Integrated investigation 1: A missing time in a school-fair report

Combined scenario: An English notice tells pupils what to bring but omits the reporting time. A Maths table gives 12 and 18 visitors in two categories but does not say whether the categories overlap. A Science observation compares materials without controlled testing times.

Reasoning task: In every case, name the omitted relationship before calculating or explaining. A time, an overlap and a measurement window are different missing facts, even if each makes a final answer unreliable. Notice that the grammar, operation and physical mechanism differ, but the discipline of not inventing an unavailable fact is shared.

Transfer: Add one precisely chosen fact to each: reporting time, number in both, and equal test durations. Observe how the appropriate response becomes better determined. A strong learner knows not merely that an answer is uncertain but what specific evidence would make the uncertainty disappear.

Integrated investigation 2: One apparent answer, two possible situations

Combined scenario: A character smiles after reading a note; two ratios share a 2:3 proportion with different totals; two plants end at the same height after different starting heights.

Reasoning task: A smile does not uniquely name one emotion, a ratio does not fix one absolute count, and a final height does not fix one growth amount. Build two compatible scenarios in each subject rather than assuming an unstated detail. Notice that the grammar, operation and physical mechanism differ, but the discipline of not inventing an unavailable fact is shared.

Transfer: Supply a strong textual reaction, an exact total and two starting heights. Determine which new answers become exact and which still need interpretation. A strong learner knows not merely that an answer is uncertain but what specific evidence would make the uncertainty disappear.

Integrated investigation 3: Enough for one question but not the next

Combined scenario: A notice states a departure time but not the reason for delay. A graph shows a bar at 30 on a labelled axis but does not explain why attendance increased. A Science table reports a temperature change without establishing a physical cause.

Reasoning task: Answer the supported question directly: time, count or change. Do not let the absence of causal evidence make you deny a directly stated numerical fact. Sufficiency is a property of the claim being made. Notice that the grammar, operation and physical mechanism differ, but the discipline of not inventing an unavailable fact is shared.

Transfer: Write two questions for each stimulus: one answerable immediately and one requiring additional evidence. Explain the difference. A strong learner knows not merely that an answer is uncertain but what specific evidence would make the uncertainty disappear.

Integrated investigation 4: An apparently helpful adult hint

Combined scenario: A teacher says ‘Think about the library’ before a pupil answers a reading location question; ‘subtract the overlap’ before a Maths survey; and ‘check the water’ before a plant inquiry.

Reasoning task: A hinted answer may become correct without showing that the learner located the evidence or selected the right method independently. During revision, record the hint separately from the outcome. Notice that the grammar, operation and physical mechanism differ, but the discipline of not inventing an unavailable fact is shared.

Transfer: Return later with a new notice, survey and plant experiment without hints. If the learner can choose the necessary data alone, the skill is stronger. A strong learner knows not merely that an answer is uncertain but what specific evidence would make the uncertainty disappear.

Integrated investigation 5: A revised source must revise the claim

Combined scenario: An extra sentence names the narrator; a new equation supplies the missing count; a controlled experiment rules out an earlier alternative explanation.

Reasoning task: A sound learner updates the answer when relevant evidence arrives, even if the initial guess seemed reasonable. A once-underdetermined problem may become exact, while an initially likely explanation may become unlikely. Notice that the grammar, operation and physical mechanism differ, but the discipline of not inventing an unavailable fact is shared.

Transfer: Remove one of the new facts and ask whether the earlier uncertainty returns. Explain exactly which warrant has vanished. A strong learner knows not merely that an answer is uncertain but what specific evidence would make the uncertainty disappear.

7. Common mistakes: inventing certainty or inventing doubt

Misconception 1: Treating a likely explanation as an observed fact

A common event sequence or scientific mechanism can be plausible without having been observed in this case. Mark direct evidence separately from a proposed interpretation.

To check the repair, invent two versions of the task: one in which the information is deliberately incomplete and one with the missing condition supplied. Ask the learner to name the new condition and show how it changes the answer.

Misconception 2: Declaring a problem unsolvable before reading the whole source

Headings, keys, footnotes, earlier question parts and surrounding passage lines can contain the missing fact. Search before diagnosing insufficiency.

Misconception 3: Confusing an exact quantity with a range

A minimum or maximum can follow from the data even when an exact total does not. State the bound rather than writing an unsupported exact number.

Misconception 4: Using one equation for two unknown quantities

A single relation may admit multiple pairs. Try two numerical pairs that satisfy the data to test whether one answer is actually determined.

Misconception 5: Treating missing cause as missing observation

You can report that a plant grew by 3 cm even when you cannot establish which factor caused the growth.

Misconception 6: Treating every ambiguity as a reason to guess

When an excerpt genuinely leaves a pronoun unresolved, choosing the nearest name without contextual support is unsafe. Seek additional evidence.

Misconception 7: Assuming a neat integer proves the problem is complete

Arithmetic can generate a tidy number after an unsupported assumption. Record where each input came from and what it means.

Misconception 8: Assuming a classroom general rule overrides stated conditions

A familiar rule about shadows, friction or averages needs the conditions under which it applies. The question’s precise setup decides what follows.

Misconception 9: Adding irrelevant evidence as if it resolves uncertainty

An extra detail that does not constrain the missing quantity does not make the answer unique. A coloured container does not supply a missing total.

Misconception 10: Remaining vague after decisive evidence appears

Uncertainty should shrink when new facts eliminate alternatives. Once a correct result is uniquely derived, state it confidently rather than repeating ‘maybe’ out of habit.

8. Progressive practice and delayed transfer

Stage one — classification: Prepare nine short examples, three per subject. Without solving, classify each as directly stated, uniquely derived, limited to a range, or needing an extra fact. Explain which information would answer the exact question. The purpose is not to reward the pupil for saying ‘insufficient’; it is to select the right kind of claim.

Stage two — two-scenario demonstration: For incomplete Maths problems, find two different numerical cases satisfying all the stated facts. For incomplete English excerpts, name two interpretations and search the wider context for a decisive clue. For Science, name two causal explanations consistent with the observed result and a control that could distinguish them. Use this during revision, not as an instruction to invent elaborate alternatives during every examination question.

Stage three — supply the missing fact: Add a location to a notice, a class total to a ratio, or the controlled condition to a plant experiment. Solve again and underline the newly sufficient relation. This teaches the difference between a task that is hard and one that truly lacks decisive evidence.

Stage four — mix complete and incomplete problems: Most well-constructed school examination questions will be answerable from the full stimulus. Mix complete cases with deliberately incomplete diagnostic exercises so that the learner has to decide which kind of problem has appeared. A child who labels every difficult problem ‘not enough information’ has not mastered the decision.

Stage five — delayed transfer: Put the cases away for two days. Return with a new reading notice, a different data table and a distinct Science experiment. After another gap, combine them in a small timed practice. Ask the learner to identify what is known, what is derived and what remains open, without naming the error type beforehand.

Stage six — independent examination control: Use the actual command word and source first. When the data determine the result, answer without unnecessary disclaimers. When a question deliberately asks what additional information is needed, name the exact measurement or condition. If you suspect an unanswerable problem in a complete paper, reread all labels and earlier information before moving on.

9. How this becomes a five-second exam check

In English, ask: ‘Which words in the passage tell me this?’ If you can point to a decisive statement or valid inference, give the answer. If you only know what often happens in similar stories, inspect the surrounding text. A clear response is not automatically a supported one.

In Mathematics, ask: ‘Do I have enough independent quantities to solve for what is requested?’ A ratio and total may fix one part; a ratio without the total may not. Do not assume that a diagram is to scale or that every pupil selected one of two clubs unless the question says so. Use a quick substitution or alternative case to challenge an unearned exact answer.

In Science, ask: ‘Does the setup identify the variable and justify the explanation?’ Measurements establish what occurred. A fair controlled comparison helps connect a condition to the observed difference. A keyword such as friction, light or evaporation is not by itself a verified causal chain. Read the trial descriptions before naming a mechanism.

When the evidence is sufficient, avoid spending the final minutes imagining remote alternative worlds unrelated to the question. The goal is proportionate checking. Confirm the required link and move on. The Vol 0092 guide covers how to select the most useful final check; this guide is narrower about whether the facts determine the answer.

10. Parent and tutor guidance: make the missing warrant visible

A useful adult question is ‘What information would let you decide?’ rather than ‘Why don’t you know?’ In a comprehension task, the child may need a line connecting a pronoun to a character. In a ratio problem, the child may need the size of the whole. In a Science investigation, the child may need control of a second variable. Giving the correct answer does not teach the learner how to recognise that missing bridge.

Separate unsupported guessing from a reasonable provisional interpretation. An English inference may be strong but not mathematically certain; language tasks often ask for the best supported interpretation rather than a logically unique one in every imaginable world. Help the pupil distinguish strong textual evidence from arbitrary invention without treating every inference as impossible.

Similarly, a Science comparison can support a well-justified explanation in a standard controlled setup without measuring every microscopic factor. The point is not extreme scepticism. The point is recognising the evidence the question considers relevant and the conditions under which its reasoning is valid. A tutor should mark what evidence was used and what assumption was added.

Track assisted and independent attempts separately. An answer produced after an adult points to the missing table caption is useful learning, but it does not prove the child will find the caption alone in an unseen paper. A fresh independent retest two days later is more informative. Ask for the specific missing fact on the first attempt; later remove the hint.

11. Frequently asked questions

Should I answer ‘not enough information’ whenever I am unsure?

No. First read the full stimulus and identify what the question asks. Your own uncertainty may be a knowledge gap, not a gap in the data. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

What makes an exact Maths answer justified?

The supplied relationships must determine the requested value. If two different values satisfy every stated condition, one exact answer does not yet follow. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

Can a limited answer still be useful?

Yes. A minimum, maximum, comparison or direct observation can be supported even when a precise total or unique cause is not. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

Do English questions always have mathematically unique interpretations?

Not always in that strict sense. They ask for answers warranted by the passage and wording. Use the best textual evidence rather than arbitrary stories. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

Can a Science fact be true but irrelevant?

Yes. A general fact may not explain the particular experiment when the relevant variable was not controlled or the fact was not connected to the observation. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

How do I show that data are insufficient?

During revision, construct two different scenarios that satisfy all the facts but give different requested answers. In a real paper, follow the question’s intended response format. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

What extra information do I need for a ratio count?

Often you need the whole or the value of one part. A ratio alone specifies relative proportions, not necessarily an exact number of items. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

What if the chart has a hidden clue?

Check the title, units, legend, table headings, footnotes and related question parts. An apparently missing quantity may be explicitly provided elsewhere. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

Should I list every possible cause in a Science response?

Usually no. Answer the requested explanation using the supplied controlled conditions and relevant scientific mechanism. Mention alternatives when the task asks about limitations. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

How can a parent help without revealing the answer?

Ask the child to identify the needed evidence or relation, then provide a parallel example. Retest with a new situation without pointing to the critical clue. Work one new example to test the idea, then ask which single extra piece of information would move the task from uncertain to answerable—or whether it is already answerable as written.

12. Exit test and your next learning route

Write three pairs of questions. In the English pair, the first notice omits a meeting place while the second includes it. In the Mathematics pair, the first survey gives group totals with no overlap or union condition, while the second states that everyone chose at least one. In the Science pair, the first experiment varies water and light together, while the second changes one factor and controls the other. For every pair, state what can be concluded from the first, what becomes justified in the second, and why.

If you can do this without prompts, you are learning to distinguish information gaps from hard thinking. Continue to the English Learning Hub, Mathematics Learning Hub or Science Learning Hub for the particular missing subject knowledge. The Vol 0100 English guide, Vol 0101 Mathematics guide and Vol 0102 Science guide provide distinct cases where a missing relationship undermines an answer. Return to the PSLE Learning Guide to choose another focused task. Your strongest next question is: ‘What exactly makes this conclusion follow?’

How to Perform in PSLE | Learner’s Guide Vol 0103 | English, Mathematics and Science: Check Whether the Evidence Determines One Answer