G3 SEC English, Mathematics and Science | Learner’s Guide Vol 0164. A school library sends reminders before books are due. The reminder-assigned borrowers return more books on time than the comparison group. Did the messages cause the improvement? Before answering, readers must separate three groups that are easy to confuse: the borrowers assigned a reminder, the borrowers whose messages were successfully delivered and the borrowers who actually returned books by the deadline.
This is an original fictional EMS case. Its library records, borrowers, percentages, message prices and committee statements are learning examples, not authentic records or official SEAB examination questions. The 2027 SEC assesses English, Mathematics and Science through their own prescribed papers; this cross-subject workshop develops transferable reading, numerical and evidence-evaluation skills, not a new combined exam format.
1. Check the current G3 SEC assessment routes
The official SEAB 2027 G3 school candidate directory lists English Language as K300, Mathematics as K310 and combined Science subject pairs as K326, K327 and K328. The K300 English syllabus assesses comprehension, synthesis and accurate communication. The K310 Mathematics syllabus includes percentages, the interpretation of information and quantitative reasoning. The G3 Science syllabus includes evaluation of investigations, evidence and appropriate conclusions.
English K300 has Writing, Comprehension, Listening and Oral Communication. Each of the two Mathematics K310 papers lasts 2 hours 15 minutes and carries 90 marks, contributing 50 per cent each. For G3 paired Science, subject codes determine whether Physics, Chemistry or Biology theory papers are taken; Paper 1 and Paper 5 form part of the stated scheme. The present exercise is not a forecast of a particular paper.
A strong reader moves from the literal facts to a justified inference. A strong mathematician chooses the denominator that answers the actual question. A strong science learner asks what was controlled, which observations were complete and what evidence could still change the conclusion. Together they form a reliable method for judging the library trial.
2. The original fictional source packet
Source A — coordinator’s record. “We allocated 120 borrowers at random into two equal groups. Sixty were assigned to receive an extra message two days before books were due. Sixty followed our usual return procedure. We verified every borrower’s return status at the same deadline. Forty-two of the reminder-assigned group returned on time, compared with thirty-three in the usual-practice group.”
Source B — delivery audit. “Of the 60 message attempts, 51 were delivered and nine failed. Thirty-nine borrowers whose messages were delivered returned books on time. Three of the nine borrowers with failed deliveries also returned books on time. The fictional provider charges $0.12 for each message attempt, including an attempt that fails.”
Source C — student council’s draft announcement. “Reminders have proved that everyone will return books on time. Delivered reminders had 76.5 per cent on-time returns versus 55 per cent for the comparison group, so the messages guarantee a 21.5-percentage-point improvement for future years. We should double the reminders immediately.”
Source D — teacher’s reply. “The pilot is promising, but a short trial cannot guarantee what all future borrowers will do. If allocation was genuinely random, comparing the original assigned groups is important. We must check whether delivery problems, incomplete records, changes in school routines or different borrowers could affect the result.”
3. The meaning of each event matters more than the headline
Assignment is the decision to place a borrower in the reminder group or the comparison group. Delivery is the separate technical event of a message reaching a recipient. Return is a behavioural outcome defined as getting the loan back by the specified deadline. None of these three events is the same as another.
Source A reports 60 borrowers assigned reminders. Source B says only 51 of those messages arrived. A student who counts 51 as the group size has changed the question from what happens when the school attempts reminders to what happened among those it successfully reached. Both questions can be worth exploring, but they require separate denominators.
The main fictional packet assumes all 120 due statuses are known, so an on-time percentage may be computed without missing outcome records. A later separate hypothetical in this chapter will relax that assumption. Keep the primary data and the changed scenario distinct.
4. First compare the originally assigned groups
The reminder-assigned group had 42 verified on-time returns among 60 loans: 42/60 = 0.70 = 70 per cent. The usual-practice group had 33 on-time returns among 60: 33/60 = 0.55 = 55 per cent. Those are the primary policy-comparison rates.
Because the groups had equal sizes, the difference in counts, 42 − 33 = nine more observed on-time returns, corresponds directly to nine divided by 60, or a 15-percentage-point rate difference. If the groups had different sizes, the count difference alone could mislead.
Keep the phrase “assigned to receive reminders.” Do not label the 70 per cent as a success rate among everyone whose message arrived, because the denominator includes nine failed deliveries. It measures the outcome of being assigned the policy in this fictional trial.
5. Percentage points are not the same as per cent relative change
Subtracting the two reported rates gives 70 − 55 = 15 percentage points. That is an absolute comparison of two percentages. The correct unit of the difference is percentage points, not an unnamed “15 per cent increase.”
To calculate a relative increase compared with usual practice, take the difference divided by the original 55 per cent: 15/55 × 100 ≈ 27.3 per cent. This is a different expression of the same gap. It uses the control rate as the reference baseline.
Both numbers can be useful if labelled precisely. “The reminder-assigned group had a rate 15 percentage points higher, equivalent to about 27.3 per cent higher relative to usual practice” makes the reference clear. Without a baseline, a percentage change is easy to misunderstand.
6. The delivered subset has a different denominator
Among the 51 successful deliveries, 39 borrowers returned on time. That conditional rate is 39/51 × 100 ≈ 76.5 per cent. Among the nine unsuccessful deliveries, three returned on time, giving 3/9 × 100 ≈ 33.3 per cent.
These rates describe genuine subsets of the assigned reminder group. They are mathematically valid. Yet the borrowers who received messages were not necessarily selected randomly from the 60 who were assigned reminders. Delivery may be associated with accurate contact details, attendance or organisational habits. Such traits could also be associated with library returns.
Therefore, comparing 39/51 directly with 33/60 is not the same as comparing the two originally assigned groups. The student council announcement uses a real percentage to support a more demanding causal conclusion than that percentage can justify.
7. Reconstruct the parent group from its subsets
The successful-delivery subgroup had 39 on-time returns, while the unsuccessful-delivery subgroup had three. Their sum is 42. Their subgroup sizes, 51 and nine, sum to 60. Both checks agree with the group totals in Source A.
This makes the fictional log internally consistent. In a real data audit, any disagreement would need to be resolved before interpretation. For example, 51 delivered plus nine failed cannot fit a claimed total of 58 attempts unless categories or records have different definitions.
A useful habit is to draw a simple hierarchy on scratch paper: assigned reminder group 60; delivered 51 with 39 on time; not delivered nine with three on time. It is not necessary to build a complicated chart. The hierarchy prevents mixing the numerators of one population with the denominators of another.
8. Random assignment protects a comparison only if it is honoured
Random allocation aims to prevent systematic sorting of borrowers by characteristics that already affect returns. A well-implemented assignment process makes the reminder and usual-practice groups more comparable at the beginning. In this fictional account, the coordinator says allocation was random, but a conscientious reader may still ask how that was done.
If the library worker chose more responsible borrowers for reminders, the policy group might have had better return rates even without messages. If the comparison group contained a large share of pupils absent on the due date, that would also affect outcomes. A source can say “random” without giving a complete audit of the actual procedure.
Randomisation is a method for supporting causal interpretation, not a magical guarantee of identical groups or perfect findings. For a small trial, chance imbalance remains possible, and the process must be implemented and recorded properly.
9. Delivery success is a post-assignment characteristic
Successful delivery happens after allocation. Whether a message arrives may depend on current contact data, network accessibility, or the borrower’s settings. The delivered recipients may therefore differ systematically from the undelivered recipients even though both were originally assigned to the same policy.
Imagine that borrowers who regularly update their school contact details are also more likely to keep track of due dates. Those borrowers may receive more messages and return more books, independently of the message itself. The fictional data do not prove that this happened. They show why it is an alternative explanation that should not be ignored.
The honest response is to distinguish descriptive association from a verified treatment effect. The delivered group had a higher on-time rate, but its membership was not a second randomised experiment.
10. What exactly does the school want to know?
A librarian may ask, “If we implement a reminder-attempt policy, will the proportion of books returned on time improve?” For that policy question, comparing assigned groups is a sensible first approach because unsuccessful deliveries are part of the practical implementation.
A technology provider might ask, “What happens when a borrower actually receives a message?” That question is harder to isolate using this packet, because the people who received messages were not independently assigned at random to receive them. Selecting only delivered recipients risks mixing the message’s effect with contact reliability.
The word “success” must always have an object. It might mean successful delivery, return by the deadline, reduced staff hours or lower overall cost. A claim such as “the reminder programme was 85 per cent successful” is vague unless it explains that 85 per cent refers to delivery attempts.
11. A positive observation is not a guarantee
At the same recorded deadline, 42 of 60 reminder-assigned borrowers returned on time, which leaves 18 who did not. The council’s “everyone will return” claim is already contradicted by its own trial data. Even among delivered recipients, 12 of 51 did not return on time.
Nor does a 15-percentage-point observed gap guarantee that future cohorts will have the same difference. School calendars, age groups, accessibility of the library and changes in behaviour can alter outcomes. A single pilot cannot establish a universal constant.
A reader can reasonably say the assignment comparison is encouraging if the recorded process was sound. The stronger claim that reminders caused precisely nine extra returns under all future conditions is not justified merely by the arithmetic.
12. Build an evaluation from facts, calculations and uncertainty
Classify a statement before putting it in a report. “Forty-two of sixty returned on time” is an observation in the fictional record. “Seventy per cent returned on time” is a calculation based on that observation. “The reminder policy will increase every future class’s return rate by 15 points” is an extrapolation requiring untested assumptions.
A clear final recommendation can use all three layers honestly: the observed comparison provides a reason to test a wider programme; the calculation quantifies the observed gap; the uncertainties explain what more evidence is needed before scale-up.
Do not label uncertainty as failure. The point of a pilot is often to learn whether an intervention is promising and which variables matter. A useful report gives the decision-maker a way to reduce uncertainty rather than pretending it does not exist.
13. Cost begins with the price unit
Source B states a fictional $0.12 charged per attempted reminder. There were 60 attempts, so the total modelled message charge was $7.20. This includes the nine attempts that failed delivery.
If a different hypothetical charging arrangement billed only the 51 successful deliveries, the charge at the same unit price would instead be $6.12. That is not the arrangement in the main source. It is a separate scenario that teaches students to pay attention to what is counted.
The cost calculation is simple, but a real decision would also need staff time, administrative maintenance and the value of a timely return. No actual Singapore commercial message prices or library charges are asserted here.
14. A tempting cost-per-extra-return ratio
The two equally sized assignment groups differed by nine observed on-time returns. Dividing the $7.20 attempt charge by nine gives $0.80 per extra observed on-time return in this trial’s naive comparison.
This is not an established causal cost-effectiveness figure. It assumes the nine-return gap is attributable to the reminder policy and that other costs are negligible. Even with randomisation, sampling variability and incomplete implementation complicate that inference.
The proper wording is conditional: “At the observed gap and fictional attempt cost, the simple comparison works out to $0.80 per extra on-time return, before other costs and without claiming the full gap is proven causal.” That sentence is more useful than a confident but unjustified advertisement.
15. If the delivery rate changes, the return rate may not change predictably
The fictional delivery rate is 51/60 = 85 per cent. If contact records improve, more messages could arrive, but the added recipients may differ from the earlier successful-delivery group. Do not multiply 76.5 per cent by a new delivery count and call it a guaranteed outcome.
A new reminder method could alter response behaviour too. More messages may help some readers, annoy others or simply be ignored. The packet contains no experiment comparing one reminder with two reminders, so the council’s proposal to double them is not supported by a measured dose-response result.
A useful extension trial would record the number of attempts, deliveries, message timings and outcomes separately. It could then examine what changed without forcing a conclusion from a single operational statistic.
16. A fairness check on the investigation
Both assigned groups should face the same definition of “on time,” the same observation window and comparable return procedures. If one group’s deadline were extended by a day, the resulting rates would not fairly estimate the extra reminder’s effect.
The library should also check that book types, loan lengths and access to drop-off locations were not systematically different. Random assignment helps, but the actual implementation and data collection still matter.
In Science-style evaluation, an improvement suggestion is strongest when it addresses a concrete weakness. “Use the same cutoff and record status for all participants” is more specific than “make the experiment better.” It identifies what must be controlled for a defensible comparison.
17. A separate missing-record example changes the question
Now consider an altered fictional scenario, not Source A, in which four of the comparison group’s 60 return statuses were unverified. Suppose 33 were confirmed on time and 23 confirmed late; four are unknown. The true number on time could be between 33 and 37, depending on the unknown outcomes.
The possible control on-time rate would therefore range from 33/60 = 55 per cent to 37/60 ≈ 61.7 per cent. Against a still-confirmed 70 per cent reminder rate, the gap could range from about 8.3 to 15 percentage points.
That is a bound under the altered scenario, not a probability interval or a claim that Source A omitted records. It shows why a missing value cannot automatically be treated as a late return. An incomplete outcome and a known failure are distinct observations.
18. Do not hide unknown records by changing denominators
Another temptation is to drop the four unknown records and report 33/56 ≈ 58.9 per cent, calling that the control success rate. The calculation describes returns among those with known outcomes; it does not necessarily represent all 60 assigned borrowers if missingness is related to behaviour.
Removing unknowns can change both the numerator and the population being described. If unknowns are more common among borrowers who return late, the complete-case rate may overstate the actual rate. If missingness has a different pattern, the direction of bias could differ.
A careful analysis either obtains the missing records, reports appropriate bounds, or explicitly states which subset is being analysed. Hiding the missingness behind a neat decimal makes the answer less trustworthy.
19. Show the difference between observation and projected future outcomes
The trial had a 15-percentage-point assigned-group gap. Under a strong, unverified assumption that the same gap applies to 100 comparable future loans, a simple projection would suggest 15 additional on-time returns. That is a mathematical extrapolation, not another observed outcome.
If future borrowers differ, if reminder delivery changes or if return conditions are altered, the projected difference may be larger, smaller or absent. Therefore it is more accurate to say “A constant-gap model projects 15 additional on-time returns per 100 comparable loans” than “Reminders produce 15 extra returns for every 100 borrowers.”
The word “model” is valuable because it tells the reader which conclusions depend on assumptions rather than already completed measurements.
20. A second trial tests whether the finding transfers
Imagine a separate follow-up pilot with 60 new borrowers assigned reminders and 60 controls. It records 36 and 34 on-time returns respectively. Those rates are 60 per cent and about 56.7 per cent, with a gap of roughly 3.3 percentage points.
That smaller gap neither proves the first trial was fabricated nor establishes that reminders are useless. It indicates that the observed difference was less stable across the two scenarios. A good investigator would compare participant characteristics, implementation, delivery reliability and timing, and consider the possibility of ordinary sample variation.
One additional study is helpful, but responsible decisions reflect the whole body of comparable evidence, not whichever result sounds most persuasive in a meeting.
21. Write the policy note in direct, accurate English
Original model: “The reminder-assigned group had a 70% on-time return rate, compared with 55% for usual practice. The difference was 15 percentage points, or about 27.3% relative to the 55% baseline. Only 51 of 60 attempted messages were delivered, so the 76.5% rate among successful recipients is not directly interchangeable with the assigned-group result. The trial is promising but does not prove a guaranteed future effect; the school should verify implementation, records and costs before expanding the policy.”
This note separates what happened from what it might mean. It does not blame the library or the student council; it treats their statements as claims that can be tested. It also allows decision-makers to see why the operational success rate is not the same as the behavioural outcome.
A candidate may need a shorter response in an actual examination. Follow the real task’s length, audience and context rather than copying this model wholesale.
22. Inspect loaded words in the announcement
The announcement uses “proved”, “everyone” and “guarantees”. Each makes the conclusion more sweeping than the data. A cautious revision could use “suggests”, “in this trial” and “subject to further testing”. Such language is not weak; it is precise.
Reporting the student council’s recommendation faithfully also means attributing the claim to its source. “The council argued for wider reminders” does not require the writer to endorse the argument. This connects to Volume 0161 on reported speech.
An evaluative answer may accept one part of a source and reject another. It can agree that 39/51 is approximately 76.5 per cent and disagree that the same number measures the randomised assignment effect. Identifying the precise break between arithmetic and inference demonstrates stronger understanding than dismissing the whole source.
23. Design a useful error ledger
After solving the case, classify mistakes into six types: wrong denominator; percentage-point confusion; assignment-versus-delivery confusion; missing-status handling; unjustified causal language; and cost per attempt versus cost per delivery. Each requires a different repair.
For example, 39/60 is a numerator-denominator mismatch if the question asks for the success rate among delivered recipients. Calling 70 − 55 a “15 per cent increase” is a units-of-comparison problem. Claiming that a delivered-only subgroup comparison proves the treatment effect is an evidence-design mistake.
Record one corrected example in each category and revisit it with new numbers. The aim is not to remember this particular library story forever. It is to recognise the same reasoning structure when a new paper uses buses, plants, surveys or household bills.
24. Thirty-two original EMS worked questions
Use the complete main fictional trial unless a question explicitly changes its assumptions. These are new learning exercises, not an official answer key. Every explanation identifies the population or evidential condition that gives a number meaning.
Practice 1
Question. How many borrowers were assigned in total?
Worked answer. 120. Why: Two groups of 60 were assigned before outcomes. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 2
Question. What is the denominator for the reminder policy comparison?
Worked answer. 60. Why: The assignment group includes unsuccessful deliveries. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 3
Question. Compute 42/60 as a percentage.
Worked answer. 70%. Why: It is the assigned-reminder on-time rate. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 4
Question. Compute 33/60 as a percentage.
Worked answer. 55%. Why: It is the usual-practice on-time rate. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 5
Question. Find the absolute difference.
Worked answer. 15 percentage points. Why: Subtract 55 from 70. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 6
Question. Find the relative increase over 55%.
Worked answer. About 27.3%. Why: Divide the 15-point gap by the 55-point baseline. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 7
Question. How many more on-time returns were observed across equal groups?
Worked answer. Nine. Why: 42 minus 33. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 8
Question. How many messages were delivered?
Worked answer. 51. Why: Source B gives delivery separately from assignment. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 9
Question. How many attempted messages failed delivery?
Worked answer. Nine. Why: 60 minus 51. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 10
Question. Find the message delivery rate.
Worked answer. 85%. Why: 51/60. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 11
Question. Find the on-time rate among delivered recipients.
Worked answer. About 76.5%. Why: 39/51, not 39/60. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 12
Question. Find the on-time rate among undelivered recipients.
Worked answer. About 33.3%. Why: 3/9. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 13
Question. What does 39 + 3 represent?
Worked answer. 42 on-time returns. Why: It reconstructs the assigned reminder group’s successful returns. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 14
Question. What does 51 + 9 represent?
Worked answer. 60 reminder attempts. Why: It reconstructs the assigned group size. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 15
Question. Can 39/51 replace 42/60 in an assignment-based comparison?
Worked answer. No. Why: Successful delivery is a post-assignment subset. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 16
Question. What bias may arise from comparing 39/51 with 33/60?
Worked answer. Selection bias. Why: Contact reliability may be related to return behaviour. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 17
Question. What is the fictional cost of 60 attempts at $0.12?
Worked answer. $7.20. Why: Attempts, not deliveries, are billed. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 18
Question. What if the service billed only 51 deliveries at $0.12?
Worked answer. $6.12. Why: This is a different hypothetical charge convention. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 19
Question. What is $7.20 divided by nine observed extra returns?
Worked answer. $0.80. Why: It is a simple descriptive ratio, not a proved causal cost. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 20
Question. Do the data show every assigned borrower returned on time?
Worked answer. No. Why: Only 42 of 60 did. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 21
Question. Does a delivery rate of 85% mean an on-time return rate of 85%?
Worked answer. No. Why: Delivery and return are different outcomes. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 22
Question. Name one variable to keep comparable between the groups.
Worked answer. The return deadline. Why: Different cutoffs would alter the outcome comparison. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 23
Question. Name one possible source of selection after assignment.
Worked answer. Up-to-date contact information. Why: It can affect who actually receives a message. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 24
Question. Can the packet show the effect of sending two reminders?
Worked answer. No. Why: It did not compare one reminder with two. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 25
Question. In a separate altered case, 33 of 60 control returns were on time and four are unknown. Minimum true rate?
Worked answer. 55%. Why: At least 33/60 were on time. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 26
Question. In that altered case, maximum possible control rate?
Worked answer. About 61.7%. Why: At most 37/60 were on time. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 27
Question. In that altered case, what is the smallest gap to 70%?
Worked answer. About 8.3 percentage points. Why: 70 − 61.7, approximately. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 28
Question. What does 33/56 measure if four unknowns are excluded?
Worked answer. The confirmed-on-time rate among recorded outcomes. Why: It does not automatically equal the rate among all assigned borrowers. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 29
Question. In a separate later trial, 36/60 versus 34/60 produces what absolute gap?
Worked answer. About 3.3 percentage points. Why: 60% minus 56.7%. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 30
Question. Does a smaller second-trial gap prove the first was false?
Worked answer. No. Why: Different groups, conditions and sampling variation may matter. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 31
Question. What evidence would strengthen a scale-up decision?
Worked answer. Verified allocation, complete outcomes, delivery data, costs and replication. Why: These test different weak links. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
Practice 32
Question. Write a defensible conclusion.
Worked answer. “Reminders were associated with a higher on-time return rate among assigned borrowers in this fictional trial.” Why: It reports the observation without universalising or guaranteeing causation. State whether the answer is a directly recorded observation, an exact calculation, or a conditional inference when writing a full explanation.
25. Change one assumption and watch the answer change
First change the reminder group’s size to 80, keeping 42 on-time returns. The rate becomes 42/80 = 52.5 per cent, below 55 per cent. The observed count is still 42, but its meaning changes because the population is larger. Second, switch the pricing unit from attempted to delivered reminders and recalculate total cost under that new policy.
Third, introduce uncertain return statuses instead of known late outcomes. Give a range rather than hiding missing data. Fourth, let a new cohort have worse message-delivery reliability: the operational reach may change even if the underlying impact of a received reminder stays similar.
These extensions teach students to treat numerical results as functions of the conditions. A defensible conclusion can change when its inputs change; that is a strength of transparent analysis, not a reason to abandon the method.
26. A practical seven-day revision sequence
Day one: label assignment, delivery and return in the packet. Day two: calculate all fractions and check their denominators. Day three: practise absolute rate differences versus relative changes using a different baseline. Day four: audit the successful-delivery subset and explain why it is not a second randomised group.
Day five: calculate the two fictional billing arrangements and write the cost unit next to each number. Day six: examine missing records and construct possible bounds. Day seven: draft a committee briefing, then underline every sentence that describes a guarantee, prediction or unverified cause. Rewrite those sentences at the strength justified by the source.
This study plan is a suggestion, not an examination requirement. It should complement direct practice for K300 English, K310 Mathematics and the Science combination the learner actually takes.
27. Internal learning connections and official source owners
Go to the G3 SEC learner-guide route for examination preparation and the PSLE Learning Guide for earlier reasoning foundations. The Secondary English Hub supports source-faithful sentences; the Mathematics Hub covers comparison, rates and denominators; the Science Hub develops fair experimental reasoning.
Volume 0160 on misleading combined rates addresses a different statistical trap: aggregation can hide subgroup patterns. This chapter focuses on the distinction between random assignment and the subset actually reached. For accurate claim attribution, see Volume 0161; for mathematical restrictions, see Volume 0162.
The official examination descriptions remain in the SEAB 2027 G3 directory. This original workshop is neither a paper prediction nor an official marking guide.
28. The conclusion must keep its denominator
The assigned-reminder group had 42 of 60 loans returned on time, a 70 per cent rate. Usual practice had 33 of 60, or 55 per cent. The difference was 15 percentage points. The successful-delivery subgroup had a separate 39/51 on-time rate. Those statements are all mathematically coherent because their populations are named.
The fiction offers a promising policy signal, but does not prove that every future borrower will comply, that sending more reminders will always work, or that the entire observed gap has been established as a universal causal effect.
The habit to keep is a strict one: define the group, select the correct denominator, distinguish operation from outcome and state only what the evidence supports. That simple discipline makes English clearer, Mathematics more reliable and Science conclusions more honest.
