PSLE Learner’s Guide · Volume 0890
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Walk once around a convex polygon and turn in the same direction at every vertex: the complete change in direction is one full turn, or 360°.
Series routes: Use the complete PSLE Learner’s Guide volume directory, the original PSLE Learning Guide and the Mathematics learning hub.
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.
Open the full chapter index
- 1. Interpret an exterior angle as a turn
- 2. Choose one angle at every vertex
- 3. Keep the turning direction consistent
- 4. See why the total is 360 degrees
- 5. Connect interior and exterior angles
- 6. Use the regular-polygon shortcut
- 7. Do not confuse the total with the interior sum
- 8. Control examination work
- 9. Worked examples
- 10. Independent practice
- 11. Delayed transfer
- 12. Family guidance and FAQs
CHAPTER 1 OF 12 · Back to contents
1. Interpret an exterior angle as a turn
Imagine walking along each side of a convex polygon. At a vertex, turn just enough to face along the next side; that change in direction is the exterior turning angle used in this rule.
Build the explanation by naming one exterior turning angle at each vertex and a consistent clockwise or anticlockwise direction. 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 the full-turn total of 360 degrees and returning to interior-exterior pairing and convention checks. State why the tempting alternative is too strong, incomplete or about a different stage.
- Check one exterior turning angle at each vertex.
- Check a consistent clockwise or anticlockwise direction.
- Check the full-turn total of 360 degrees.
- Check interior-exterior pairing and convention checks.
CHAPTER 2 OF 12 · Back to contents
2. Choose one angle at every vertex
A vertex has several angles around it, so mark the small outside turn consistently. Mixing supplementary exterior angles with reflex angles destroys the full-turn model.
Build the explanation by naming one exterior turning angle at each vertex and a consistent clockwise or anticlockwise direction. 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 the full-turn total of 360 degrees and returning to interior-exterior pairing and convention checks. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 3 OF 12 · Back to contents
3. Keep the turning direction consistent
Turn clockwise at every vertex or anticlockwise at every vertex. Reversing direction part-way introduces signed changes and no longer matches the simple positive-angle sum.
Build the explanation by naming one exterior turning angle at each vertex and a consistent clockwise or anticlockwise direction. 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 the full-turn total of 360 degrees and returning to interior-exterior pairing and convention checks. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 4 OF 12 · Back to contents
4. See why the total is 360 degrees
After one complete circuit, the walker faces the starting direction again. The accumulated change in direction is exactly one full turn, so the exterior turning angles sum to 360°.
Build the explanation by naming one exterior turning angle at each vertex and a consistent clockwise or anticlockwise direction. 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 the full-turn total of 360 degrees and returning to interior-exterior pairing and convention checks. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 5 OF 12 · Back to contents
5. Connect interior and exterior angles
For a convex polygon, the interior angle and its adjacent exterior turning angle form a straight line, so they sum to 180°. This gives exterior = 180° − interior.
Build the explanation by naming one exterior turning angle at each vertex and a consistent clockwise or anticlockwise direction. 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 the full-turn total of 360 degrees and returning to interior-exterior pairing and convention checks. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 6 OF 12 · Back to contents
6. Use the regular-polygon shortcut
In a regular n-sided polygon, all exterior turning angles are equal. Each is therefore 360° ÷ n, and n can be found from 360° ÷ one exterior angle when the quotient is a whole number.
Build the explanation by naming one exterior turning angle at each vertex and a consistent clockwise or anticlockwise direction. 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 the full-turn total of 360 degrees and returning to interior-exterior pairing and convention checks. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 7 OF 12 · Back to contents
7. Do not confuse the total with the interior sum
The interior-angle sum is (n − 2) × 180°, while the chosen exterior turns always total 360°. These formulas answer different questions.
Build the explanation by naming one exterior turning angle at each vertex and a consistent clockwise or anticlockwise direction. 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 the full-turn total of 360 degrees and returning to interior-exterior pairing and convention checks. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 8 OF 12 · Back to contents
8. Control examination work
Mark direction arrows, identify exactly one turn per vertex, use 360° for the total, and test whether regularity is stated before assuming equal angles.
Build the explanation by naming one exterior turning angle at each vertex and a consistent clockwise or anticlockwise direction. 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 the full-turn total of 360 degrees and returning to interior-exterior pairing and convention checks. 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: What is the sum of the exterior turning angles of a convex pentagon?
Controlled answer. 360°. One complete circuit produces one full turn.
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 use the pentagon interior sum. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “360°” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 2: A regular hexagon has what exterior angle?
Controlled answer. 60°. 360° divided by 6 equals 60°.
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. Find its interior angle. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “60°” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 3: A regular polygon has exterior angle 45°. How many sides does it have?
Controlled answer. 8. 360° divided by 45° equals 8.
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. Name the polygon. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “8” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 4: One exterior angle of a non-regular quadrilateral is 70°. Are all four 70°?
Controlled answer. No. Equal exterior angles require regularity or other evidence.
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. Use the total to find a missing angle when three are known. 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 5: Find the missing exterior angle if the others are 80°, 95° and 105°.
Controlled answer. 80°. The known total is 280°, so 360°−280°=80°.
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 the four-angle sum. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “80°” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 6: An interior angle is 125°. What is its adjacent exterior turning angle?
Controlled answer. 55°. Adjacent interior and exterior angles form 180°.
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. Draw the straight line. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “55°” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 7: Repair: the exterior angles of an n-gon sum to (n−2)×180°.
Controlled answer. The chosen exterior turning angles sum to 360°. The stated formula belongs to interior angles.
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. Compare both for a triangle. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “The chosen exterior turning angles sum to 360°” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 8: Why must the same turning direction be used?
Controlled answer. The rule accumulates one continuous full turn. Changing direction mixes positive and negative 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. Trace a square walk. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “The rule accumulates one continuous full turn” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 9: Can two exterior angles be drawn at one vertex?
Controlled answer. Many outside angles can be named, but the rule selects one consistent turning angle. The convention must be fixed.
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. Mark the small turn. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Many outside angles can be named, but the rule selects one consistent turning angle” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 10: A regular decagon has what exterior angle?
Controlled answer. 36°. 360° divided by 10 equals 36°.
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. Find the interior angle. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “36°” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 11: A regular polygon has interior angle 150°. How many sides?
Controlled answer. 12. Its exterior angle is 30°, and 360°÷30°=12.
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. Verify with the interior-sum formula. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “12” 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 12: Does the 360° sum require the polygon to be regular?
Controlled answer. No. Convexity and consistent one-direction turning are enough; angles need not be equal.
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. Create four unequal angles totaling 360°. 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 one exterior turning angle at each vertex, a consistent clockwise or anticlockwise direction, the full-turn total of 360 degrees, interior-exterior pairing and convention checks. 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: Why is convexity useful here?
Explained answer. Each small exterior turn has the same direction and stays below 180°. The simple positive-turn model is clear.
Delayed transfer. Avoid extending the rule blindly to self-intersecting paths. 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: A regular polygon has exterior angle 50°. Is it possible?
Explained answer. Not as an exact regular polygon with a whole number of sides. 360°÷50°=7.2, not a whole number.
Delayed transfer. Explain the integer check. 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: What does a full circuit change about facing direction?
Explained answer. It returns to the original direction after a net 360° turn. Position and direction should not be confused.
Delayed transfer. State what happens to location. 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: If five exterior angles total 300°, what is the sixth?
Explained answer. 60°. All six turns must total 360°.
Delayed transfer. Do not assume equality. 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: What is the nearest wrong shortcut?
Explained answer. Assuming every exterior angle equals 360° divided by n without checking regularity. Only the average is 360°÷n for an irregular polygon.
Delayed transfer. Compare average and individual values. 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: How should a diagram with extended sides be audited?
Explained answer. Follow the travel direction and mark the turn from one side to the next. A visually large outside angle may not be the turning angle.
Delayed transfer. Redraw with arrows. 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: Can the rule check measured data?
Explained answer. Yes, add one consistent exterior turn at every vertex and compare with 360°. A mismatch may reveal measurement or convention error.
Delayed transfer. Audit a four-angle set. 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. Select one same-direction exterior turn at each vertex, use a 360° total, relate each to its interior by 180°, and assume equal turns only for a regular polygon. Check the number of sides is a whole number in reverse problems.
Delayed transfer. Solve a mixed case. 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 Mathematics learning hub or return to the series directory.