PSLE Learner’s Guide · Volume 0936
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Two quantities are directly proportional only when their ratio stays constant; merely rising together shows a trend, not direct proportion.
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This guide uses original Primary 6 practice and does not predict a live question. Consult the SEAB PSLE formats examined in 2026 page for official information.
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CHAPTER 1 OF 12 · Back to contents
1. Translate the claim
If y is directly proportional to x, then y=kx for a constant k. State what x, y and k mean and include units when k is a rate.
Build the explanation by naming the two named quantities units and ordered pairs and a constant output-to-input ratio under the stated conditions. A remembered keyword is not enough: connect the observation to the mechanism and identify what would have to change for the conclusion to change.
Repair the nearest misconception by checking both increasing versus multiplying by the same factor and returning to zero case graph origin measurement uncertainty controls and claim strength. State why the tempting alternative is too strong, incomplete or about a different stage.
- Check the two named quantities units and ordered pairs.
- Check a constant output-to-input ratio under the stated conditions.
- Check both increasing versus multiplying by the same factor.
- Check zero case graph origin measurement uncertainty controls and claim strength.
CHAPTER 2 OF 12 · Back to contents
2. Test the ratio
Calculate y÷x for several non-zero pairs. Equal ratios support direct proportion under the observed conditions; changing ratios reject the simple model.
Build the explanation by naming the two named quantities units and ordered pairs and a constant output-to-input ratio under the stated conditions. A remembered keyword is not enough: connect the observation to the mechanism and identify what would have to change for the conclusion to change.
Repair the nearest misconception by checking both increasing versus multiplying by the same factor and returning to zero case graph origin measurement uncertainty controls and claim strength. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 3 OF 12 · Back to contents
3. Use a factor test
When x doubles, y must double; when x triples, y must triple. Equal additive increases are not the defining test.
Build the explanation by naming the two named quantities units and ordered pairs and a constant output-to-input ratio under the stated conditions. A remembered keyword is not enough: connect the observation to the mechanism and identify what would have to change for the conclusion to change.
Repair the nearest misconception by checking both increasing versus multiplying by the same factor and returning to zero case graph origin measurement uncertainty controls and claim strength. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 4 OF 12 · Back to contents
4. Read the graph
A direct-proportion graph is a straight line through the origin when axes use ordinary linear scales. A straight line with a non-zero intercept is linear but not directly proportional.
Build the explanation by naming the two named quantities units and ordered pairs and a constant output-to-input ratio under the stated conditions. A remembered keyword is not enough: connect the observation to the mechanism and identify what would have to change for the conclusion to change.
Repair the nearest misconception by checking both increasing versus multiplying by the same factor and returning to zero case graph origin measurement uncertainty controls and claim strength. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 5 OF 12 · Back to contents
5. Separate trend from proportion
Height and age can both increase during part of childhood without maintaining a constant height-to-age ratio. Direction alone is insufficient.
Build the explanation by naming the two named quantities units and ordered pairs and a constant output-to-input ratio under the stated conditions. A remembered keyword is not enough: connect the observation to the mechanism and identify what would have to change for the conclusion to change.
Repair the nearest misconception by checking both increasing versus multiplying by the same factor and returning to zero case graph origin measurement uncertainty controls and claim strength. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 6 OF 12 · Back to contents
6. Use language precisely
Write increases as x increases for an observed positive association. Reserve directly proportional for evidence satisfying the constant-ratio model.
Build the explanation by naming the two named quantities units and ordered pairs and a constant output-to-input ratio under the stated conditions. A remembered keyword is not enough: connect the observation to the mechanism and identify what would have to change for the conclusion to change.
Repair the nearest misconception by checking both increasing versus multiplying by the same factor and returning to zero case graph origin measurement uncertainty controls and claim strength. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 7 OF 12 · Back to contents
7. Control scientific conditions
A proportional pattern may hold only within a range and with other variables controlled. Measurement uncertainty can make real data approximate rather than exact.
Build the explanation by naming the two named quantities units and ordered pairs and a constant output-to-input ratio under the stated conditions. A remembered keyword is not enough: connect the observation to the mechanism and identify what would have to change for the conclusion to change.
Repair the nearest misconception by checking both increasing versus multiplying by the same factor and returning to zero case graph origin measurement uncertainty controls and claim strength. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 8 OF 12 · Back to contents
8. Control the examination response
Name the variables, compare at least two ratios or scale factors, inspect the origin and units, then state proportional, not proportional or approximately proportional within the tested range.
Build the explanation by naming the two named quantities units and ordered pairs and a constant output-to-input ratio under the stated conditions. A remembered keyword is not enough: connect the observation to the mechanism and identify what would have to change for the conclusion to change.
Repair the nearest misconception by checking both increasing versus multiplying by the same factor and returning to zero case graph origin measurement uncertainty controls and claim strength. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 9 OF 12 · Back to contents
9. Worked examples
Worked case 1: Pairs are (2,6), (4,12), (5,15). Directly proportional?
Controlled answer. Yes. Each y÷x ratio is 3.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. State y=3x. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Yes” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 2: Pairs are (2,6), (4,10), (6,14). Directly proportional?
Controlled answer. No. The ratios 3, 2.5 and about 2.33 change.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Notice the fixed additive pattern instead. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “No” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 3: x doubles from 3 to 6 while y rises from 8 to 11. Direct proportion?
Controlled answer. No. y did not double.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Both quantities still increased. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “No” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 4: A line follows y=4x. What is k?
Controlled answer. 4. The output-to-input ratio is constant.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Attach units if quantities have units. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “4” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 5: A line follows y=4x+2. Direct proportion?
Controlled answer. No. The non-zero intercept prevents passage through the origin.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. It is still linear. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “No” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 6: At constant speed, distance and time directly proportional?
Controlled answer. Yes within the constant-speed interval. Distance divided by time is the fixed speed.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. State the control condition. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Yes within the constant-speed interval” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 7: Are taxi fare and distance always directly proportional?
Controlled answer. Not if there is a fixed starting charge or tiered rate. A non-zero base fare or changing rate alters the ratio.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Inspect the tariff. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Not if there is a fixed starting charge or tiered rate” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 8: Mass and volume for one uniform material directly proportional?
Controlled answer. Approximately yes under fixed material conditions. Density mass÷volume stays constant.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Do not combine different materials. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Approximately yes under fixed material conditions” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 9: Plant height and time both rise. Is that enough?
Controlled answer. No. The height-to-time ratio may change as growth rate changes.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Calculate ratios or examine a model. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “No” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 10: If x triples and y triples for one pair, is that conclusive?
Controlled answer. It supports the model but more valid pairs and conditions strengthen the conclusion. One comparison may miss later changes.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Test another scale factor. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “It supports the model but more valid pairs and conditions strengthen the conclusion” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 11: Repair: both graphs rise, so both show direct proportion.
Controlled answer. A rising graph shows increase; direct proportion also requires a straight line through the origin and constant ratio. Direction is only one clue.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Check ratios. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “A rising graph shows increase; direct proportion also requires a straight line through the origin and constant ratio” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 12: Repair: equal differences prove direct proportion.
Controlled answer. Equal differences show a linear pattern, which may have a non-zero intercept. Direct proportion is multiplicative from zero.
Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.
Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.
Transfer. Test y=2x+5. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Equal differences show a linear pattern, which may have a non-zero intercept” and invent a fresh prompt that would justify it for the same reason. Then change one decisive condition to create a near-nonexample. This reverse task checks whether the learner owns the boundary rather than merely recognising the original sentence.
Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.
Audit. Recheck the two named quantities units and ordered pairs, a constant output-to-input ratio under the stated conditions, both increasing versus multiplying by the same factor, zero case graph origin measurement uncertainty controls and claim strength. Decide whether the evidence proves the conclusion or only supports a limited statement.
CHAPTER 10 OF 12 · Back to contents
10. Independent practice
Practice 1: What numerical test is strongest for a table?
Explained answer. Compare y divided by x for several non-zero rows. The ratio must remain constant.
Delayed transfer. Do not divide by zero. Cover the answer later and rebuild the chain.
Control question. Which exact condition does the nearest wrong answer miss? State it before checking.
Extension. Change one decisive feature while keeping the story similar. Explain why the conclusion now stays or changes.
Independent proof. Restate the answer without copying its wording. Your version must identify the evidence, the governing relationship and the boundary of the claim. Then write one fact that would be relevant but still insufficient on its own. This separates explanation from repetition.
Delayed comparison. Save this item beside the near-nonexample you created. On the next attempt, compare them before answering and point to the single feature that controls the difference. If more than one feature changed, revise the pair so the comparison stays fair.
Practice 2: What happens at x=0 in an exact direct proportion?
Explained answer. y=0. The graph passes through the origin.
Delayed transfer. Separate from undefined ratio 0÷0. Cover the answer later and rebuild the chain.
Control question. Which exact condition does the nearest wrong answer miss? State it before checking.
Extension. Change one decisive feature while keeping the story similar. Explain why the conclusion now stays or changes.
Independent proof. Restate the answer without copying its wording. Your version must identify the evidence, the governing relationship and the boundary of the claim. Then write one fact that would be relevant but still insufficient on its own. This separates explanation from repetition.
Delayed comparison. Save this item beside the near-nonexample you created. On the next attempt, compare them before answering and point to the single feature that controls the difference. If more than one feature changed, revise the pair so the comparison stays fair.
Practice 3: Can k have units?
Explained answer. Yes. For distance versus time, k has speed units.
Delayed transfer. Interpret k rather than treating it as a bare number. Cover the answer later and rebuild the chain.
Control question. Which exact condition does the nearest wrong answer miss? State it before checking.
Extension. Change one decisive feature while keeping the story similar. Explain why the conclusion now stays or changes.
Independent proof. Restate the answer without copying its wording. Your version must identify the evidence, the governing relationship and the boundary of the claim. Then write one fact that would be relevant but still insufficient on its own. This separates explanation from repetition.
Delayed comparison. Save this item beside the near-nonexample you created. On the next attempt, compare them before answering and point to the single feature that controls the difference. If more than one feature changed, revise the pair so the comparison stays fair.
Practice 4: What wording is safer when only direction is known?
Explained answer. Y tends to increase as x increases. This reports the trend without claiming proportionality.
Delayed transfer. Add the tested range. Cover the answer later and rebuild the chain.
Control question. Which exact condition does the nearest wrong answer miss? State it before checking.
Extension. Change one decisive feature while keeping the story similar. Explain why the conclusion now stays or changes.
Independent proof. Restate the answer without copying its wording. Your version must identify the evidence, the governing relationship and the boundary of the claim. Then write one fact that would be relevant but still insufficient on its own. This separates explanation from repetition.
Delayed comparison. Save this item beside the near-nonexample you created. On the next attempt, compare them before answering and point to the single feature that controls the difference. If more than one feature changed, revise the pair so the comparison stays fair.
Practice 5: Can experimental data be approximately proportional?
Explained answer. Yes. Measurement uncertainty may cause small ratio variation around a stable value.
Delayed transfer. State tolerance and controls. Cover the answer later and rebuild the chain.
Control question. Which exact condition does the nearest wrong answer miss? State it before checking.
Extension. Change one decisive feature while keeping the story similar. Explain why the conclusion now stays or changes.
Independent proof. Restate the answer without copying its wording. Your version must identify the evidence, the governing relationship and the boundary of the claim. Then write one fact that would be relevant but still insufficient on its own. This separates explanation from repetition.
Delayed comparison. Save this item beside the near-nonexample you created. On the next attempt, compare them before answering and point to the single feature that controls the difference. If more than one feature changed, revise the pair so the comparison stays fair.
Practice 6: What is the nearest wrong shortcut?
Explained answer. Equating positive association with direct proportion. A constant multiplicative relationship is stricter.
Delayed transfer. Use a counterexample with non-zero intercept. Cover the answer later and rebuild the chain.
Control question. Which exact condition does the nearest wrong answer miss? State it before checking.
Extension. Change one decisive feature while keeping the story similar. Explain why the conclusion now stays or changes.
Independent proof. Restate the answer without copying its wording. Your version must identify the evidence, the governing relationship and the boundary of the claim. Then write one fact that would be relevant but still insufficient on its own. This separates explanation from repetition.
Delayed comparison. Save this item beside the near-nonexample you created. On the next attempt, compare them before answering and point to the single feature that controls the difference. If more than one feature changed, revise the pair so the comparison stays fair.
Practice 7: How should a graph be checked?
Explained answer. Inspect straightness, origin, axis scales and the range of data. A cropped or nonlinear axis can mislead.
Delayed transfer. Read labels first. Cover the answer later and rebuild the chain.
Control question. Which exact condition does the nearest wrong answer miss? State it before checking.
Extension. Change one decisive feature while keeping the story similar. Explain why the conclusion now stays or changes.
Independent proof. Restate the answer without copying its wording. Your version must identify the evidence, the governing relationship and the boundary of the claim. Then write one fact that would be relevant but still insufficient on its own. This separates explanation from repetition.
Delayed comparison. Save this item beside the near-nonexample you created. On the next attempt, compare them before answering and point to the single feature that controls the difference. If more than one feature changed, revise the pair so the comparison stays fair.
Practice 8: State the full method.
Explained answer. Name x and y, calculate several output-to-input ratios, test common scale factors, inspect whether a linear graph passes through the origin, preserve units and limit the claim to controlled conditions. Use trend language when evidence is weaker.
Delayed transfer. Apply once in each subject. Cover the answer later and rebuild the chain.
Control question. Which exact condition does the nearest wrong answer miss? State it before checking.
Extension. Change one decisive feature while keeping the story similar. Explain why the conclusion now stays or changes.
Independent proof. Restate the answer without copying its wording. Your version must identify the evidence, the governing relationship and the boundary of the claim. Then write one fact that would be relevant but still insufficient on its own. This separates explanation from repetition.
Delayed comparison. Save this item beside the near-nonexample you created. On the next attempt, compare them before answering and point to the single feature that controls the difference. If more than one feature changed, revise the pair so the comparison stays fair.
CHAPTER 11 OF 12 · Back to contents
11. Delayed transfer
On day one, solve clear examples. On day three, mix examples, near-nonexamples and incomplete evidence. On day seven, solve without headings or a word bank. Delay reveals whether the method can be reconstructed independently.
Keep an error log for the first failed stage: reading, representation, rule, execution or checking. The earliest failure identifies the repair.
Interleave this skill with neighbouring ideas that share vocabulary. Classify each item only after naming the distinguishing condition.
In timed work, mark the relationship, apply the rule, write the conclusion and audit one condition. If checking changes the answer, record the overlooked feature.
Create a teach-back card with a near-nonexample on the front and the repaired mechanism on the back. Explain why the tempting answer fails.
Finish with one basic example, one boundary case and one transfer case. Supply explanations that a classmate can verify.
For a second delayed test, reverse the direction: start from a conclusion and invent evidence that would justify it, then evidence that would be insufficient. This exposes the boundary between relevance and proof.
CHAPTER 12 OF 12 · Back to contents
12. Family guidance and FAQs
Guidance for parents and tutors
Ask for the decisive condition before confirming the answer. Use prompts such as “What exactly happened?”, “Which stage or meaning is this?” and “What would prove it?”
Fade support from labelled examples to mixed questions and delayed open response. Independent retrieval after time and topic change is the target.
Praise precise claim control. Narrowing an answer when evidence is incomplete is scientific and academic strength.
Frequently asked questions
Should I memorise the rule?
Memorise the compact rule, then practise examples and near-nonexamples so the conditions remain visible.
What if two answers seem possible?
Return to the exact relationship and choose the option satisfying every stated condition without adding facts.
Why delay practice?
Immediate repetition may depend on the recent explanation; delay tests reconstruction.
How should an error be corrected?
Name the first failed stage and practise it with a changed example.
When is the skill ready?
When the learner can explain, apply and transfer it after a delay.
What is the final audit?
Check relationship, mechanism, claim strength and whole-question fit.
Next routes
Continue at the English, Mathematics and Science learning hub or return to the series directory.