PSLE Learner’s Guide · Volume 0690
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Test divisibility by 4 from the final two digits, then explain the place-value reason behind the shortcut.
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. State the rule precisely
- 2. Explain why the rule works
- 3. Read endings as numbers
- 4. Separate divisibility from evenness
- 5. Use remainders when the ending is unfamiliar
- 6. Constrain missing digits
- 7. Combine conditions carefully
- 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. State the rule precisely
A whole number is divisible by 4 when the number formed by its last two digits is divisible by 4. The final two digits may be read with a leading zero, so 1,208 ends in 08 and is divisible by 4.
Build the explanation by naming last two digits and multiple of four. 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 place-value decomposition and returning to remainder check. State why the tempting alternative is too strong, incomplete or about a different stage.
- Check last two digits.
- Check multiple of four.
- Check place-value decomposition.
- Check remainder check.
CHAPTER 2 OF 12 · Back to contents
2. Explain why the rule works
Every whole number can be split into hundreds plus a final two-digit number. Because 100 is divisible by 4, every complete group of hundreds contributes no remainder when divided by 4. Only the final two-digit part can determine the remainder.
Build the explanation by naming last two digits and multiple of four. 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 place-value decomposition and returning to remainder check. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 3 OF 12 · Back to contents
3. Read endings as numbers
Endings such as 00, 04, 08, 12 and 16 are multiples of 4. Do not test each digit separately: the ending 12 is one number, not the unrelated digits 1 and 2.
Build the explanation by naming last two digits and multiple of four. 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 place-value decomposition and returning to remainder check. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 4 OF 12 · Back to contents
4. Separate divisibility from evenness
Every multiple of 4 is even, but not every even number is a multiple of 4. An ending of 18 is even yet leaves a remainder of 2 when divided by 4.
Build the explanation by naming last two digits and multiple of four. 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 place-value decomposition and returning to remainder check. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 5 OF 12 · Back to contents
5. Use remainders when the ending is unfamiliar
Find the nearest lower multiple of 4. Since 76 is divisible by 4, an ending of 79 leaves remainder 3. The same remainder belongs to the entire number because the hundreds part is divisible by 4.
Build the explanation by naming last two digits and multiple of four. 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 place-value decomposition and returning to remainder check. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 6 OF 12 · Back to contents
6. Constrain missing digits
For a number ending in 3□, list the two-digit values from 30 to 39 that are multiples of 4: 32 and 36. Therefore the missing unit digit can be 2 or 6. Check every permitted digit rather than stopping at the first.
Build the explanation by naming last two digits and multiple of four. 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 place-value decomposition and returning to remainder check. State why the tempting alternative is too strong, incomplete or about a different stage.
CHAPTER 7 OF 12 · Back to contents
7. Combine conditions carefully
If a number must be divisible by both 3 and 4, first use the final-two-digits test for 4, then apply the digit-sum test for 3. Passing one test does not guarantee the other.
Build the explanation by naming last two digits and multiple of four. 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 place-value decomposition and returning to remainder check. 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
Box the final two digits, name the nearest multiple of 4 and record the conclusion. For proof questions, show the split into a multiple of 100 plus the ending instead of quoting the shortcut without a reason.
Build the explanation by naming last two digits and multiple of four. 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 place-value decomposition and returning to remainder check. 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 3,716 divisible by 4?
Controlled answer. Yes. The final two digits are 16, and 16 is divisible by 4.
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 8,916 without long division. 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 2: Is 5,438 divisible by 4?
Controlled answer. No. The ending 38 leaves remainder 2 when divided by 4.
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 final digit to make the number divisible. 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 3: Test 12,300.
Controlled answer. Divisible by 4. The ending 00 represents zero, which is divisible by 4.
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. Explain why the hundreds do not affect the remainder. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Divisible by 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 4: Test 1,208.
Controlled answer. Divisible by 4. Read the ending as 08, which equals 8 and is divisible by 4.
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 with 1,206. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Divisible by 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 5: Why can the thousands digits be ignored?
Controlled answer. They belong to complete hundreds, and each hundred is divisible by 4. Place value makes the shortcut valid.
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. Write 6,532 as 6,500 plus 32. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “They belong to complete hundreds, and each hundred is divisible by 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 6: Find the remainder when 9,347 is divided by 4.
Controlled answer. 3. The ending 47 is 3 more than 44.
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. Predict the remainder of 2,747. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “3” 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 7: The number 62□ must be divisible by 4. Find all possible unit digits.
Controlled answer. 0, 4 or 8. The possible endings 20, 24 and 28 are multiples of 4.
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. Apply a second condition that the number is also divisible by 3. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “0, 4 or 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 8: The number 7□6 must be divisible by 4. Find possible tens digits.
Controlled answer. 1, 3, 5, 7 or 9. The endings 16, 36, 56, 76 and 96 are multiples of 4.
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. Explain the alternating pattern. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “1, 3, 5, 7 or 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 9: Repair: 2,514 is divisible by 4 because it is even.
Controlled answer. It is not divisible by 4. The ending 14 is even but leaves remainder 2.
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 an even multiple and an even non-multiple. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “It is not divisible by 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 10: Is 4,444 divisible by 4?
Controlled answer. Yes. The ending 44 is 11 groups of 4.
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 divisibility by 3 separately. 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 11: Choose the smallest digit for 83□ to be divisible by 4.
Controlled answer. 2. The first multiple of 4 from 830 to 839 ends in 32.
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 greatest possible digit. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “2” 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 last two digits, multiple of four, place-value decomposition, remainder check. Decide whether the evidence proves the conclusion or only supports a limited statement.
Worked case 12: A learner tests the digit sum of 3,524 for divisibility by 4. What is wrong?
Controlled answer. Digit sum is not the test for 4. The final two digits 24 provide the relevant test.
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 digit sum for a suitable different divisor. Solve the altered case from the mechanism rather than copying the previous wording.
Reverse construction. Begin with the controlled answer “Digit sum is not the test for 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 last two digits, multiple of four, place-value decomposition, remainder check. 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: Explain 15,672 using place value.
Explained answer. 15,600 + 72; both parts are divisible by 4. The decomposition proves the whole number is divisible.
Delayed transfer. Construct a similar proof with a non-multiple ending. 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: Which endings from 40 to 49 are divisible by 4?
Explained answer. 40, 44 and 48. Consecutive multiples differ by 4.
Delayed transfer. Extend the list to the fifties. 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: A packet count is 2,736 and items are grouped in fours. Are there leftovers?
Explained answer. No. The ending 36 is divisible by 4.
Delayed transfer. Change the count so exactly two remain. 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: Can a number ending in 6 be divisible by 4?
Explained answer. Yes. Endings such as 16, 36, 56, 76 and 96 are multiples of 4.
Delayed transfer. Explain why the final digit alone is insufficient. 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 an odd number be divisible by 4?
Explained answer. No. Every multiple of 4 is even.
Delayed transfer. Explain why evenness remains necessary but not sufficient. 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: Find all two-digit endings that give remainder 1 from 20 to 29.
Explained answer. 21, 25 and 29. Each is one more than a multiple of 4.
Delayed transfer. Use the pattern in a four-digit 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 7: A number is divisible by 12. What must be true about divisibility by 4?
Explained answer. It must be divisible by 4. Twelve is a multiple of 4.
Delayed transfer. State an additional divisibility condition for 12. 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: Write a proof of the last-two-digits rule.
Explained answer. Split the number into a multiple of 100 and its final two-digit part. The first part is divisible by 4, so the second part controls the remainder.
Delayed transfer. Generalise why last three digits can test divisibility by 8. 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.