eduKateSG PSLE Learner’s Guide · Vol 0109
A Primary 6 performance guide for Mathematics. This guide teaches one precise examination job: Distinguish Constant Difference From Constant Multiplicative Change in Number Patterns. It is written for learners first, with a practical route for parents and tutors near the end.
Do not rush from two correct details to one incorrect conclusion. First identify the relationship that makes the details belong together.
Current examination context. This guide is aligned to the PSLE subject formats examined in 2026 as published by the Singapore Examinations and Assessment Board. Always use your school’s latest instructions and the official paper directions on examination day.
Use this guide as a performance route
Read Chapters 1 to 4 before attempting the worked cases. Then cover the repair notes and solve each case aloud or on paper. Return after two or three days for the delayed-transfer round. The aim is not to remember these examples. The aim is to recognise the same reasoning job when the wording, numbers, diagram or situation changes.
- Start by naming what the question is asking you to connect.
- Use the relationship test before writing a connector, operation or conclusion.
- Explain one worked case without looking at the repair.
- Practise a mixed case after a delay.
- Finish with the exam-control checklist, not with another rereading.
This volume does not replace specialist topic teaching. Use it to control performance at the point where knowledge must become an answer. For deeper teaching, follow the subject-owner link in Chapter 13.
Chapter 1: The exact job
Two patterns may both rise, yet they can grow by different rules. An additive pattern changes by the same amount: 7, 11, 15, 19 adds 4 each time. A multiplicative pattern changes by the same factor: 3, 6, 12, 24 doubles each time. The reliable method is to compare neighbouring terms twice: calculate differences, then test ratios when division is exact and meaningful. State the rule in words, test it on every shown step, and only then extend the pattern or build an expression.
The important shift is from recognition to control. Recognition says, “I have seen something like this.” Control says, “I can name the relationship, show why it fits, reject a tempting alternative and keep the conclusion inside the evidence.” PSLE questions often change the surface features while preserving the reasoning job. A learner who depends on remembered wording may freeze. A learner who understands the mechanism can rebuild the answer.
Use a four-part frame: objects—what two things are being connected; relationship—how they are connected; evidence—which detail makes that connection defensible; and scope—how far the conclusion may travel. If one part is missing, the answer may sound fluent while remaining logically weak.
Chapter 2: The learner’s move sequence
- Move 1. Write the term number beside each value so position and value do not become confused.
- Move 2. Find at least two consecutive differences; one matching pair is not enough proof.
- Move 3. If differences are not constant, test whether each term is multiplied by the same factor.
- Move 4. Check whether an alternating or two-stage rule fits better than forcing one operation.
- Move 5. State both the operation and its amount: add 6, multiply by 3, not merely increases.
- Move 6. Test the rule on every displayed transition before using it for a distant term.
- Move 7. For a diagram pattern, separate a fixed starting part from the repeated part added at each stage.
Practise the moves slowly until the order becomes stable. Speed should arrive by compression, not by skipping. During an examination, the full routine may take only a few seconds because each move has been rehearsed. During learning, say the moves in full so that a teacher or parent can diagnose the exact point where the reasoning changes direction.
Chapter 3: Why capable learners still lose marks
Many errors here are not failures of effort. They are category errors: the learner knows the details but assigns the wrong job to one of them. The repair is therefore more precise than “be careful”. Name the mistaken relationship, replace it with the legal one, and test the new relationship against the question.
- Misconception 1. Calling every increasing pattern an addition pattern. Repair it by returning to the objects–relationship–evidence–scope frame before adding any new information.
- Misconception 2. Finding one difference and assuming it stays constant. Repair it by returning to the objects–relationship–evidence–scope frame before adding any new information.
- Misconception 3. Using the term number as though it were the previous term. Repair it by returning to the objects–relationship–evidence–scope frame before adding any new information.
- Misconception 4. Confusing multiply by two with add two. Repair it by returning to the objects–relationship–evidence–scope frame before adding any new information.
- Misconception 5. Extending a rule that fits the first transition but fails the next. Repair it by returning to the objects–relationship–evidence–scope frame before adding any new information.
- Misconception 6. Ignoring a fixed part in a growing diagram. Repair it by returning to the objects–relationship–evidence–scope frame before adding any new information.
- Misconception 7. Using a ratio test when zero or non-whole ratios make the interpretation unsuitable. Repair it by returning to the objects–relationship–evidence–scope frame before adding any new information.
- Misconception 8. Calculating the next term correctly but stating the wrong general rule. Repair it by returning to the objects–relationship–evidence–scope frame before adding any new information.
A useful error log records the wrong relationship, not only the wrong final answer. Write, for example, “I treated sequence as cause,” “I treated a changing difference as a fixed factor,” or “I treated repetition as a control.” A named error can be noticed in a new context. “Careless mistake” is too vague to guide the next attempt.
Chapter 4: Worked cases with diagnosis and repair
Worked case 1
Situation. 5, 9, 13, 17
Tempting response. The values almost double at first.
Repair. Each neighbouring difference is 4, so the rule is add 4.
Why the repair works. Check 9−5, 13−9 and 17−13 before extending to 21. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 2
Situation. 3, 6, 12, 24
Tempting response. The difference is 3, so keep adding 3.
Repair. The differences change, but each term is twice the previous term.
Why the repair works. Use multiplicative language: multiply by 2. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 3
Situation. 2, 5, 10, 17
Tempting response. The pattern has no rule because differences change.
Repair. The differences are 3, 5, 7; the amount added itself increases by 2.
Why the repair works. Record first differences and then the change in those differences. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 4
Situation. 40, 35, 30, 25
Tempting response. A decreasing pattern cannot have a constant difference.
Repair. The constant difference is −5, meaning subtract 5 each time.
Why the repair works. Difference includes direction, not just size. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 5
Situation. Stage 1 has 5 tiles, stage 2 has 8, stage 3 has 11.
Tempting response. The stage number is multiplied by 3, so stage 4 has 12.
Repair. The visible totals add 3 each stage; stage 4 has 14 tiles.
Why the repair works. Separate the initial 2 tiles from 3 repeated tiles per stage. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 6
Situation. 4, 8, 16, 32
Tempting response. Add 4 because 4 to 8 changes by 4.
Repair. That rule fails immediately at 8 to 16. The constant factor is 2.
Why the repair works. A valid rule must survive all shown transitions. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 7
Situation. 6, 10, 18, 34
Tempting response. The additions are random.
Repair. Each term is doubled then 2 is subtracted: 6×2−2=10, 10×2−2=18.
Why the repair works. Test a two-operation rule consistently. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 8
Situation. 1, 4, 3, 6, 5, 8
Tempting response. There is no pattern.
Repair. Two interleaved sequences each add 2: 1,3,5 and 4,6,8.
Why the repair works. When odd and even positions behave differently, split them. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 9
Situation. A savings table shows $20, $35, $50, $65 after successive weeks.
Tempting response. Savings is multiplied by the week number.
Repair. The total increases by a constant $15 per week.
Why the repair works. Attach the difference to its unit and interval. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 10
Situation. A bacteria model shows 2, 6, 18, 54 in equal time intervals.
Tempting response. Add 4, then 12, then 36.
Repair. The constant factor is 3. The changing differences are a result, not the rule.
Why the repair works. Equal intervals make the factor comparison meaningful. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 11
Situation. A matchstick pattern has 4, 7, 10, 13 sticks.
Tempting response. The nth stage has 3n sticks.
Repair. The pattern is 3n+1 because stage 1 already contains 4.
Why the repair works. Test the expression on stage 1 and stage 2. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Worked case 12
Situation. 100, 90, 81, 72.9
Tempting response. Subtract 10 each time.
Repair. Each term is 90% of the previous term; the absolute decrease gets smaller.
Why the repair works. A constant percentage change is multiplicative, not a constant difference. The repaired response identifies the relationship rather than merely repeating both details. It also keeps direction intact: the first quantity or event is not silently exchanged with the second.
Independent check. Hide the repair and explain which word, number, comparison or observation carries the reasoning. Then change one surface detail. If your method still works, you are learning the job rather than memorising the case.
Chapter 5: Misconception diagnosis in real time
When an answer feels uncertain, do not restart the whole question immediately. Diagnose the smallest unstable step. Ask: Did I select the wrong pair of details? Did I name the wrong relationship? Did I reverse its direction? Did I use evidence that belongs to a different part of the question? Did I generalise beyond the tested or stated conditions? Each question points to a different repair.
Use the “because test” carefully. Read your answer up to the conclusion, add because, and supply the supporting relationship. If the words after because merely repeat the conclusion, the reasoning is circular. If they introduce information not found in the question, the answer is invented. If they name an exact comparison, mechanism or textual detail, the reasoning is likely becoming visible.
Next use the “could still be true?” test. Imagine that the first detail is removed. Could the second detail still occur? If yes, direct causation may be too strong. Imagine a different rule that fits the first example. Does it fail on the next example? If yes, your pattern rule was under-tested. Imagine the control produced the same result. Would the proposed factor still explain the difference? If not, the conclusion needs revision.
Chapter 6: Practice progression from supported to independent
Do not begin with twelve mixed difficult questions. Build control in stages. Stage one is classification: label relationships without writing full answers. Stage two is completion: fill the missing connector, operation or comparison. Stage three is repair: correct a tempting response and explain the error. Stage four is independent production. Stage five is transfer after a delay.
- Round A — classification: take cases 1 to 4 and write only the relationship label.
- Round B — direction: draw an arrow or comparison sign showing which way the relationship runs.
- Round C — evidence: underline the smallest detail that supports the relationship.
- Round D — repair: rewrite each tempting response using no more words than necessary.
- Round E — variation: change the names, values, materials or setting while keeping the reasoning job.
- Round F — mixing: place one case beside a different relationship and decide which method belongs.
- Round G — explanation: teach the method to an imaginary classmate without reading the guide.
- Round H — timed use: allow a short, realistic decision window, then complete the final check.
Transfer prompt 1. Rebuild this situation with one important surface change: 5, 9, 13, 17 Keep the same reasoning job, but alter a name, number, setting, material or order. Write one wrong answer that a hurried learner might choose, then write the corrected answer and identify the relationship that makes it correct.
Transfer prompt 2. Rebuild this situation with one important surface change: 3, 6, 12, 24 Keep the same reasoning job, but alter a name, number, setting, material or order. Write one wrong answer that a hurried learner might choose, then write the corrected answer and identify the relationship that makes it correct.
Transfer prompt 3. Rebuild this situation with one important surface change: 2, 5, 10, 17 Keep the same reasoning job, but alter a name, number, setting, material or order. Write one wrong answer that a hurried learner might choose, then write the corrected answer and identify the relationship that makes it correct.
Transfer prompt 4. Rebuild this situation with one important surface change: 40, 35, 30, 25 Keep the same reasoning job, but alter a name, number, setting, material or order. Write one wrong answer that a hurried learner might choose, then write the corrected answer and identify the relationship that makes it correct.
Transfer prompt 5. Rebuild this situation with one important surface change: Stage 1 has 5 tiles, stage 2 has 8, stage 3 has 11. Keep the same reasoning job, but alter a name, number, setting, material or order. Write one wrong answer that a hurried learner might choose, then write the corrected answer and identify the relationship that makes it correct.
Transfer prompt 6. Rebuild this situation with one important surface change: 4, 8, 16, 32 Keep the same reasoning job, but alter a name, number, setting, material or order. Write one wrong answer that a hurried learner might choose, then write the corrected answer and identify the relationship that makes it correct.
Transfer prompt 7. Rebuild this situation with one important surface change: 6, 10, 18, 34 Keep the same reasoning job, but alter a name, number, setting, material or order. Write one wrong answer that a hurried learner might choose, then write the corrected answer and identify the relationship that makes it correct.
Transfer prompt 8. Rebuild this situation with one important surface change: 1, 4, 3, 6, 5, 8 Keep the same reasoning job, but alter a name, number, setting, material or order. Write one wrong answer that a hurried learner might choose, then write the corrected answer and identify the relationship that makes it correct.
Chapter 7: Delayed transfer that proves learning
Immediate success can come from short-term memory. Delayed transfer asks whether the method can be retrieved after the wording is no longer fresh. Close the guide. After forty-eight to seventy-two hours, solve four mixed prompts: one familiar case, one case with changed surface details, one case that uses a competing relationship, and one case from another subject. Mark the relationship before checking the final answer.
A strong delayed answer should survive three changes. First, the nouns may change. Second, the order of information may change. Third, irrelevant details may be added. If performance collapses, return to the smallest weak move rather than rereading everything. For example, practise only direction, only baseline choice or only control-versus-repeat classification.
One week later, use a blank-page retrieval check. Write the method, two common traps and one example from memory. Then compare with this guide. The differences show what is unstable. Correct them in a new colour and immediately use the repaired rule on a new question. Correction without renewed use often produces recognition, not durable control.
Chapter 8: Checking without simply repeating the first attempt
A useful check is independent of the first route. If you merely reread the answer with the same assumption, the same error may look correct twice. Check direction by reversing the sentence and seeing whether the meaning changes. Check a pattern rule against another transition. Check a scientific conclusion by naming the alternative explanation the comparison was meant to reduce. Check an English inference by separating what happened from why it happened.
- Objects check: Did I connect the two things the question actually asks about?
- Relationship check: Is this sequence, cause, comparison, change, evidence, condition, control or contrast?
- Direction check: Have I reversed giver and receiver, cause and result, earlier and later, or factor and outcome?
- Evidence check: Can I point to the exact supporting detail?
- Scope check: Did I write all, always or only when the evidence supports that breadth?
- Unit and label check: Are values, people, variables and textual references still attached correctly?
- Answer check: Did I complete every requested part and then stop?
Chapter 9: Examination control under time pressure
In the paper, the method must be compact. Use a ten-second reset when a question produces two plausible answers. Stop writing. Box the requested outcome. Mark the two candidate details. Label the relationship in one or two words. Reject the option that changes direction, baseline, unit or scope. Then write the shortest complete answer.
If you remain uncertain, preserve marks by stating only what the evidence supports. A restrained answer is stronger than a dramatic explanation built from outside knowledge. In Mathematics, show the comparison that identifies the rule. In Science, name the changed factor and measured result. In English, attach the inference to an exact textual detail and avoid turning a possibility into certainty.
Do not spend unlimited time trying to rescue one relationship question. Mark it, move on, and return with a defined check. On return, do not reread passively. Perform one diagnostic action: test another transition, identify the connector, compare the control or rewrite the cause-and-result arrow. A specific check gives the second attempt a new route.
Chapter 10: A mini practice set
Mini-task 1. Read this situation: Stage 1 has 5 tiles, stage 2 has 8, stage 3 has 11. Decide which relationship must be named first. Explain why the tempting response—“The stage number is multiplied by 3, so stage 4 has 12.”—is unsafe. Then produce a precise answer using the repair principle without copying the wording above.
Mini-task 2. Read this situation: 4, 8, 16, 32 Decide which relationship must be named first. Explain why the tempting response—“Add 4 because 4 to 8 changes by 4.”—is unsafe. Then produce a precise answer using the repair principle without copying the wording above.
Mini-task 3. Read this situation: 6, 10, 18, 34 Decide which relationship must be named first. Explain why the tempting response—“The additions are random.”—is unsafe. Then produce a precise answer using the repair principle without copying the wording above.
Mini-task 4. Read this situation: 1, 4, 3, 6, 5, 8 Decide which relationship must be named first. Explain why the tempting response—“There is no pattern.”—is unsafe. Then produce a precise answer using the repair principle without copying the wording above.
Mini-task 5. Read this situation: A savings table shows $20, $35, $50, $65 after successive weeks. Decide which relationship must be named first. Explain why the tempting response—“Savings is multiplied by the week number.”—is unsafe. Then produce a precise answer using the repair principle without copying the wording above.
Mini-task 6. Read this situation: A bacteria model shows 2, 6, 18, 54 in equal time intervals. Decide which relationship must be named first. Explain why the tempting response—“Add 4, then 12, then 36.”—is unsafe. Then produce a precise answer using the repair principle without copying the wording above.
Mini-task 7. Read this situation: A matchstick pattern has 4, 7, 10, 13 sticks. Decide which relationship must be named first. Explain why the tempting response—“The nth stage has 3n sticks.”—is unsafe. Then produce a precise answer using the repair principle without copying the wording above.
Mini-task 8. Read this situation: 100, 90, 81, 72.9 Decide which relationship must be named first. Explain why the tempting response—“Subtract 10 each time.”—is unsafe. Then produce a precise answer using the repair principle without copying the wording above.
Mark each mini-task with four points: one for the correct objects, one for the relationship, one for supporting evidence or computation, and one for controlled scope. A final sentence can be polished later; first make the reasoning legal.
Chapter 11: Guidance for parents and tutors
Ask the learner to explain the relationship before correcting the final sentence. Questions such as “What are the two things?”, “How are they connected?”, “Which detail proves that?” and “How far can that conclusion travel?” reveal more than “Why is this wrong?” Keep the conversation neutral. The aim is to inspect a reasoning move, not to judge intelligence.
Use short mixed sets rather than long blocks of nearly identical questions. Two related examples help the learner notice the mechanism; a third example with a competing relationship tests whether the learner can choose. Return to the job after a delay. Record whether the learner needed a prompt and which prompt unlocked the answer.
Praise a visible move: preserving direction, testing a second difference, naming what the control removes, or using cautious language when evidence is limited. General praise can encourage, but precise feedback teaches. If a subject-specific knowledge gap appears, route the learner to the relevant canonical hub rather than stretching this performance guide into a replacement textbook.
Chapter 12: Frequently asked questions
How many differences should I check?
Check every displayed neighbouring pair. At minimum, two equal differences are needed before the pattern is plausible.
What if both addition and multiplication seem to work once?
Use later transitions. A rule must fit all given terms, not only the first pair.
Can a pattern decrease multiplicatively?
Yes. Multiplying by a factor between zero and one produces decay, such as multiplying by 0.9.
What is a second difference?
It is the difference between first differences. It can reveal a steadily changing amount added.
Should I always find a formula?
No. Use a formula only when the question asks for a distant term or general rule and you can verify it.
Why label term numbers?
Because term 5 is a position, while its value may be 21 or another number.
How do diagram patterns differ?
A diagram often has a fixed core plus a repeated unit. Count both.
What is the final check?
Substitute an early term into your rule and verify the next term independently.
Chapter 13: Your next route
Continue through the permanent PSLE Learning Guide for the wider sequence of learner-performance guides. For deeper subject teaching, use the Mathematics Learning Hub.
This batch is designed as a connected route. Next, read Vol 0108, Vol 0110 and Vol 0111. WordPress may publish these dated URLs; the links are kept as stable base-slug routes and can resolve through the site.
Your completion test is simple: can you meet a new question, name the relationship before reaching for an answer, show the supporting detail or calculation, and keep the conclusion within its proper scope? If yes, move to a mixed paper. If not, return to the first unstable move and practise that move alone.
Reinforcement: twelve explain-and-transfer drills
Drill 1. 5, 9, 13, 17 First, classify the relationship without solving. Second, explain why “The values almost double at first.” attracts a hurried learner. Third, use this repair principle: Each neighbouring difference is 4, so the rule is add 4. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 2. 3, 6, 12, 24 First, classify the relationship without solving. Second, explain why “The difference is 3, so keep adding 3.” attracts a hurried learner. Third, use this repair principle: The differences change, but each term is twice the previous term. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 3. 2, 5, 10, 17 First, classify the relationship without solving. Second, explain why “The pattern has no rule because differences change.” attracts a hurried learner. Third, use this repair principle: The differences are 3, 5, 7; the amount added itself increases by 2. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 4. 40, 35, 30, 25 First, classify the relationship without solving. Second, explain why “A decreasing pattern cannot have a constant difference.” attracts a hurried learner. Third, use this repair principle: The constant difference is −5, meaning subtract 5 each time. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 5. Stage 1 has 5 tiles, stage 2 has 8, stage 3 has 11. First, classify the relationship without solving. Second, explain why “The stage number is multiplied by 3, so stage 4 has 12.” attracts a hurried learner. Third, use this repair principle: The visible totals add 3 each stage; stage 4 has 14 tiles. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 6. 4, 8, 16, 32 First, classify the relationship without solving. Second, explain why “Add 4 because 4 to 8 changes by 4.” attracts a hurried learner. Third, use this repair principle: That rule fails immediately at 8 to 16. The constant factor is 2. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 7. 6, 10, 18, 34 First, classify the relationship without solving. Second, explain why “The additions are random.” attracts a hurried learner. Third, use this repair principle: Each term is doubled then 2 is subtracted: 6×2−2=10, 10×2−2=18. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 8. 1, 4, 3, 6, 5, 8 First, classify the relationship without solving. Second, explain why “There is no pattern.” attracts a hurried learner. Third, use this repair principle: Two interleaved sequences each add 2: 1,3,5 and 4,6,8. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 9. A savings table shows $20, $35, $50, $65 after successive weeks. First, classify the relationship without solving. Second, explain why “Savings is multiplied by the week number.” attracts a hurried learner. Third, use this repair principle: The total increases by a constant $15 per week. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 10. A bacteria model shows 2, 6, 18, 54 in equal time intervals. First, classify the relationship without solving. Second, explain why “Add 4, then 12, then 36.” attracts a hurried learner. Third, use this repair principle: The constant factor is 3. The changing differences are a result, not the rule. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 11. A matchstick pattern has 4, 7, 10, 13 sticks. First, classify the relationship without solving. Second, explain why “The nth stage has 3n sticks.” attracts a hurried learner. Third, use this repair principle: The pattern is 3n+1 because stage 1 already contains 4. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.
Drill 12. 100, 90, 81, 72.9 First, classify the relationship without solving. Second, explain why “Subtract 10 each time.” attracts a hurried learner. Third, use this repair principle: Each term is 90% of the previous term; the absolute decrease gets smaller. Fourth, create a different example in which the tempting response would actually become correct, and state what extra evidence, value or control would be needed. This final variation matters because it teaches conditions, not slogans.