PSLE Learner’s Guide · Volume 0782
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A whole number is divisible by 144 exactly when it is divisible by both 9 and 16, because 9 and 16 are coprime and their product is 144.
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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. Factor the target
Since 144 = 9 × 16 and the factors are coprime, passing both factor tests is equivalent to divisibility by 144.
Build the explanation by naming factorisation 144 equals 9 times 16 and digit-sum test for 9. 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 final-four-digit test for 16 and returning to complete candidate verification. State why the tempting alternative is too strong, incomplete or about a different stage.
- Check factorisation 144 equals 9 times 16.
- Check digit-sum test for 9.
- Check final-four-digit test for 16.
- Check complete candidate verification.
CHAPTER 2 OF 12 · Back to contents
2. Test divisibility by 9
Add every digit. The number passes when the digit sum is a multiple of 9.
Build the explanation by naming factorisation 144 equals 9 times 16 and digit-sum test for 9. 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 final-four-digit test for 16 and returning to complete candidate verification. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 3 OF 12 · Back to contents
3. Test divisibility by 16
Inspect the final four digits as a number. Earlier place values contribute multiples of 10,000, which is divisible by 16.
Build the explanation by naming factorisation 144 equals 9 times 16 and digit-sum test for 9. 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 final-four-digit test for 16 and returning to complete candidate verification. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 4 OF 12 · Back to contents
4. Require both tests
A valid digit sum without a multiple-of-16 ending, or a multiple-of-16 ending without a valid digit sum, is insufficient.
Build the explanation by naming factorisation 144 equals 9 times 16 and digit-sum test for 9. 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 final-four-digit test for 16 and returning to complete candidate verification. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 5 OF 12 · Back to contents
5. Handle short numbers
For a number with four or fewer digits, test the whole number for divisibility by 16 as well as its digit sum for 9.
Build the explanation by naming factorisation 144 equals 9 times 16 and digit-sum test for 9. 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 final-four-digit test for 16 and returning to complete candidate verification. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 6 OF 12 · Back to contents
6. Construct systematically
Filter candidate digits by the final-four-digit condition, then retain only those whose complete digit sum is divisible by 9.
Build the explanation by naming factorisation 144 equals 9 times 16 and digit-sum test for 9. 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 final-four-digit test for 16 and returning to complete candidate verification. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 7 OF 12 · Back to contents
7. Use quotient verification
After a candidate passes both rules, divide by 144 to confirm a whole-number quotient and catch arithmetic slips.
Build the explanation by naming factorisation 144 equals 9 times 16 and digit-sum test for 9. 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 final-four-digit test for 16 and returning to complete candidate verification. 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
Write the digit sum and final-four-digit test explicitly, keep every legal candidate and verify that the list is complete.
Build the explanation by naming factorisation 144 equals 9 times 16 and digit-sum test for 9. 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 final-four-digit test for 16 and returning to complete candidate verification. 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: Is 1,440 divisible by 144?
Controlled answer. Yes. Digit sum 9 passes 9 and 1,440 ÷ 16 = 90; the quotient by 144 is 10.
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. Change one digit and retest. 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 2: Is 2,880 divisible by 144?
Controlled answer. Yes. Digit sum 18 passes 9 and 2,880 ÷ 16 = 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. Find the quotient by 144. 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 3: Is 1,600 divisible by 144?
Controlled answer. No. 1,600 passes 16 but its digit sum 7 fails 9.
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 a nearby multiple. 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 4: Is 999 divisible by 144?
Controlled answer. No. Its digit sum passes 9, but 999 is not divisible by 16.
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 failed factor. 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 5: Repair: Any number with digit sum 18 is divisible by 144.
Controlled answer. It must also be divisible by 16. The digit sum establishes only divisibility by 9.
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. Give a counterexample. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “It must also be divisible by 16” 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 6: Repair: Any multiple of 16 is divisible by 144.
Controlled answer. It must also have a digit sum divisible by 9. The factor 9 is missing.
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. Give a passing example. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “It must also have a digit sum divisible by 9” 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 7: Why are 9 and 16 sufficient?
Controlled answer. Their least common multiple is 144. They are coprime factors whose product is the target.
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. Contrast with 8 and 18. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Their least common multiple is 144” 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 8: Do divisibility by 8 and 18 prove divisibility by 144?
Controlled answer. No. Their least common multiple is 72, so 72 itself is a counterexample.
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. Identify the missing extra factor of 2. 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 9: What pair does prove divisibility by 144?
Controlled answer. 9 and 16. Their least common multiple contains 3 squared and 2 to the fourth power.
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 both tests. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “9 and 16” 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 10: Is 5,184 divisible by 144?
Controlled answer. Yes. Digit sum 18 passes 9, 5,184 ÷ 16 = 324 and 5,184 ÷ 144 = 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. Verify by multiplication. 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 11: Is 4,320 divisible by 144?
Controlled answer. Yes. Digit sum 9 passes 9 and 4,320 ÷ 16 = 270; the quotient by 144 is 30.
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 both conditions. 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 12: What is the fastest rejection for 12,345?
Controlled answer. Its digit sum 15 fails 9. One failed required condition is decisive.
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 the final four digits separately. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Its digit sum 15 fails 9” 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 factorisation 144 equals 9 times 16, digit-sum test for 9, final-four-digit test for 16, complete candidate verification. 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: Can the last four digits be 0000?
Explained answer. Yes. Zero is divisible by 16, but the whole number must still pass 9.
Delayed transfer. Test 18,000. 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: The number 1□40 is divisible by 144. Find the digit.
Explained answer. 4. 1,440 is the only candidate of that form that passes both tests; digit sum 9 and divisibility by 16 hold.
Delayed transfer. Verify the quotient 10. 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: The number 5□84 is divisible by 144. Find the digit.
Explained answer. 1. 5,184 passes both tests; the digit sum is 18.
Delayed transfer. Test all digits systematically. 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: Why test the complete digit sum after the ending?
Explained answer. The missing digit may satisfy divisibility by 16 but fail divisibility by 9. Both conditions must hold on the same candidate.
Delayed transfer. Build a candidate table. 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: Is zero divisible by 144?
Explained answer. Yes. Zero equals 144 × 0.
Delayed transfer. Distinguish division 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 6: A store packs 7,200 cards in bundles of 144. Are any left?
Explained answer. No. Digit sum 9 passes 9, 7,200 ÷ 16 = 450 and 7,200 ÷ 144 = 50.
Delayed transfer. State quotient and remainder. 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 do you prove a candidate list is complete?
Explained answer. Test every allowed digit against both conditions and record each result. Systematic filtering prevents omissions.
Delayed transfer. Make a table for 5□84. 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. Require a digit sum divisible by 9 and final four digits divisible by 16, apply both to every candidate and verify with division by 144. The joint conditions are exactly equivalent to divisibility by 144.
Delayed transfer. Create a missing-digit question. 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.