How to Perform in PSLE | Learner’s Guide Vol 1006 | Mathematics: Predict a Terminating Decimal From the Simplified Denominator’s Prime Factors

CHAPTER 1 OF 12 · Back to contents

1. Simplify before classifying

Cancel every common factor first. A denominator may appear to contain another prime factor that disappears in lowest terms, so the original denominator alone can mislead.

Build the explanation by naming the fraction in lowest terms and its simplified denominator and the denominator prime factors and their relationship to powers of ten. 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 whether multiplying by missing 2s or 5s can make a power of ten and returning to equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. State why the tempting alternative is too strong, incomplete or about a different stage.

• Check the fraction in lowest terms and its simplified denominator.
• Check the denominator prime factors and their relationship to powers of ten.
• Check whether multiplying by missing 2s or 5s can make a power of ten.
• Check equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification.

Contents · Next

CHAPTER 2 OF 12 · Back to contents

2. Connect decimals to powers of ten

A terminating decimal can be written over 10, 100, 1000 or another power of ten. Every power of ten has only the prime factors 2 and 5.

Build the explanation by naming the fraction in lowest terms and its simplified denominator and the denominator prime factors and their relationship to powers of ten. 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 whether multiplying by missing 2s or 5s can make a power of ten and returning to equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. State why the tempting alternative is too strong, incomplete or about a different stage.

Contents · Previous · Next

CHAPTER 3 OF 12 · Back to contents

3. Test the simplified denominator

If the lowest-term denominator contains only 2s, only 5s, both 2s and 5s, or is 1, the fraction terminates. Any remaining prime factor such as 3, 7 or 11 prevents an exact power-of-ten denominator.

Build the explanation by naming the fraction in lowest terms and its simplified denominator and the denominator prime factors and their relationship to powers of ten. 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 whether multiplying by missing 2s or 5s can make a power of ten and returning to equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. State why the tempting alternative is too strong, incomplete or about a different stage.

Contents · Previous · Next

CHAPTER 4 OF 12 · Back to contents

4. Build an equivalent fraction

For a denominator such as 8, multiply numerator and denominator by 125 to reach 1000. For 20, multiply by 5 to reach 100. This also constructs the decimal.

Build the explanation by naming the fraction in lowest terms and its simplified denominator and the denominator prime factors and their relationship to powers of ten. 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 whether multiplying by missing 2s or 5s can make a power of ten and returning to equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. State why the tempting alternative is too strong, incomplete or about a different stage.

Contents · Previous · Next

CHAPTER 5 OF 12 · Back to contents

5. Predict the number of places

If the denominator is 2^a × 5^b, supply the missing factors until both exponents match. The larger exponent gives a power of ten that works, although trailing zeros may be omitted.

Build the explanation by naming the fraction in lowest terms and its simplified denominator and the denominator prime factors and their relationship to powers of ten. 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 whether multiplying by missing 2s or 5s can make a power of ten and returning to equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. State why the tempting alternative is too strong, incomplete or about a different stage.

Contents · Previous · Next

CHAPTER 6 OF 12 · Back to contents

6. Handle improper fractions and wholes

The rule applies after simplification even when the fraction exceeds one. A denominator of 1 gives a whole number, which has a terminating decimal representation.

Build the explanation by naming the fraction in lowest terms and its simplified denominator and the denominator prime factors and their relationship to powers of ten. 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 whether multiplying by missing 2s or 5s can make a power of ten and returning to equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. State why the tempting alternative is too strong, incomplete or about a different stage.

Contents · Previous · Next

CHAPTER 7 OF 12 · Back to contents

7. Separate terminating from rounded

A recurring decimal can be rounded to a finite number of places, but the rounded value is not the exact decimal expansion. Check whether the question asks for exact or approximate value.

Build the explanation by naming the fraction in lowest terms and its simplified denominator and the denominator prime factors and their relationship to powers of ten. 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 whether multiplying by missing 2s or 5s can make a power of ten and returning to equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. State why the tempting alternative is too strong, incomplete or about a different stage.

Contents · Previous · Next

CHAPTER 8 OF 12 · Back to contents

8. Audit the conclusion

Simplify, factor the denominator, test for primes other than 2 and 5, construct or divide to verify, and state whether the result terminates exactly or only after rounding.

Build the explanation by naming the fraction in lowest terms and its simplified denominator and the denominator prime factors and their relationship to powers of ten. 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 whether multiplying by missing 2s or 5s can make a power of ten and returning to equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. State why the tempting alternative is too strong, incomplete or about a different stage.

Contents · Previous · Next

CHAPTER 9 OF 12 · Back to contents

9. Worked examples

Worked case 1: Will 3/8 terminate?

Controlled answer. Yes. The denominator 8 is 2^3, so it can be changed to 1000.

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. Construct 375/1000. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 2: Will 7/20 terminate?

Controlled answer. Yes. The denominator 20 is 2^2 × 5 and contains only 2 and 5.

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. Multiply numerator and denominator by 5. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 3: Will 5/12 terminate?

Controlled answer. No. The simplified denominator 12 contains the prime factor 3.

Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.

Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.

Transfer. Divide to observe the recurring part. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 4: Will 6/15 terminate?

Controlled answer. Yes. First simplify 6/15 to 2/5; the denominator is then only 5.

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 inspecting 15 before cancelling gives the wrong prediction. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 5: Will 9/30 terminate?

Controlled answer. Yes. The fraction simplifies to 3/10.

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. Write its exact decimal. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 6: Will 14/21 terminate?

Controlled answer. No. It simplifies to 2/3, whose denominator retains the prime factor 3.

Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.

Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.

Transfer. Distinguish exact decimal from a rounded answer. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 7: Write 11/16 as a terminating decimal.

Controlled answer. 0.6875. Since 16 is 2^4, multiply by enough 5s to make 10000.

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.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 8: Write 13/25 as a terminating decimal.

Controlled answer. 0.52. Multiply numerator and denominator by 4 to obtain 52/100.

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 the percentage form. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 9: Will 21/70 terminate?

Controlled answer. Yes. It simplifies to 3/10 despite the original denominator containing 7.

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 cancelled factor. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 10: Will 4/18 terminate?

Controlled answer. No. It simplifies to 2/9, and 9 contains the prime factor 3.

Mechanism. Identify the exact relationship, apply the relevant rule and preserve every stated condition. A surface clue may be compatible with several explanations, so the answer must show what makes this case decisive.

Misconception repair. Do not turn partial evidence into complete proof. Name the closest wrong answer, identify its missing condition and explain why the observed evidence supports the narrower conclusion.

Transfer. Show a recurring decimal pattern. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 11: Will 17/40 terminate?

Controlled answer. Yes. Forty is 2^3 × 5, so no other prime factor remains.

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 suitable power of ten denominator. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Worked case 12: Will 22/55 terminate?

Controlled answer. Yes. The fraction simplifies to 2/5.

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 cancellation before long division. Solve the altered case from the mechanism rather than copying the previous wording.

Explanation standard. A complete explanation names the observation, connects it to the rule and limits the conclusion to what follows. It should remain valid if decorative details are removed. If the explanation depends on the story topic instead of the decisive relation, rebuild it.

Audit. Recheck the fraction in lowest terms and its simplified denominator, the denominator prime factors and their relationship to powers of ten, whether multiplying by missing 2s or 5s can make a power of ten, equivalent fraction cancellation denominator one recurring decimal place value base ten exponent conversion and verification. Decide whether the evidence proves the conclusion or only supports a limited statement.

Contents · Previous · Next

CHAPTER 10 OF 12 · Back to contents

10. Independent practice

Practice 1: Will 7/125 terminate?

Explained answer. Yes. One hundred twenty-five is 5^3 and can be multiplied by 8 to make 1000.

Delayed transfer. Write the decimal exactly. 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: Will 5/14 terminate?

Explained answer. No. The simplified denominator contains the prime factor 7.

Delayed transfer. Explain why adding zeros in long division never reaches remainder 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 3: Does 12/4 have a terminating decimal?

Explained answer. Yes. It simplifies to the whole number 3 with denominator 1.

Delayed transfer. Write 3.0 and explain why it is terminating. 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: Will 27/45 terminate?

Explained answer. Yes. It simplifies to 3/5.

Delayed transfer. Identify all common factors used. 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: Which terminates, 1/6 or 1/8?

Explained answer. 1/8. Six retains factor 3, while eight contains only factor 2.

Delayed transfer. Compare their long-division remainders. 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 decimal was rounded to 0.33. Does that prove the fraction terminates?

Explained answer. No. A recurring decimal such as 1/3 can be rounded to 0.33.

Delayed transfer. Ask for the exact fraction or further digits. 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: What is the fastest classification check?

Explained answer. Reduce the fraction and factor only the denominator. Any prime other than 2 or 5 means non-terminating recurring; otherwise it terminates.

Delayed transfer. Then construct a power of ten if needed. 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. Simplify the fraction completely, factor the remaining denominator, check that every prime factor is 2 or 5 or that the denominator is 1, construct an equivalent power-of-ten fraction when useful, and verify whether the decimal is exact rather than rounded. The method explains the base-ten mechanism and prevents classification from an uncancelled denominator.

Delayed transfer. Apply after a delayed mixed fraction 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.

Contents · Previous · Next

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.

Contents · Previous · Next

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.

Contents · Previous