Series route: This guide belongs to the complete PSLE Learner’s Guide volume directory. The original PSLE Learning Guide supplies the wider English, Mathematics and Science route, while PSLE Mathematics provide verified subject-specific continuation.
Find your route through this guide
This volume solves one precise learner problem: the learner divides a whole-number total by the wrong ratio number, ignores a remainder, rounds a fractional unit part into whole objects, or accepts a ratio allocation that no longer adds back to the stated total. The aim is not to memorise a slogan. It is to understand the mechanism well enough to recognise the idea when the wording, numbers, diagram or context changes. A Primary 6 learner should be able to explain the decision, perform it under time pressure, and detect a tempting answer that only looks familiar.
- Understand the mechanism before memorising a form.
- Study the worked examples and compare near-misses.
- Repair common misconceptions with targeted tests.
- Complete graded independent practice before reading the answers.
- Use delayed transfer and examination control to make the skill durable.
- Use the parent and tutor notes only after the learner has attempted the work.
The problem beneath the mistake
A red-to-blue ratio of 2:3 contains five equal ratio units in each complete scaled group.
If there are 40 counters altogether, one unit is 40÷5=8. The groups are 16 red and 24 blue.
If there are 41 indivisible counters and the exact ratio must be 2:3, one unit would be 8.2 counters. That cannot describe whole counters.
The remainder is not a small inconvenience to round away. It is evidence that the stated total and exact whole-number ratio are incompatible under the given conditions.
The divisor is the sum of the ratio numbers, not the larger number alone. A total covers all groups named in the ratio.
Ratio numbers are not automatically object counts. They describe relative units until the value of one unit is found.
A problem may allow continuous quantities such as mass or length. Then a fractional unit can be meaningful. The whole-number feasibility test applies when the context requires indivisible counts.
Some questions state only part of the whole. Before dividing, confirm that the total really covers every group in the ratio.
Three-part ratios work the same way. For 2:3:5, the whole contains ten equal ratio units.
Simplify a ratio when appropriate, but keep its relationship. The ratios 4:6 and 2:3 describe the same relative composition.
After allocation, add the groups and simplify their ratio. Both checks are needed because a plausible pair may pass one but not the other.
The safe routine is define the whole, add parts, test divisibility, find one unit, allocate, preserve whole-number conditions and verify total and ratio.
Core decision: For whole objects divided in the ratio a:b, the total represents a+b equal ratio units. Therefore the total must be divisible by a+b if every group count must be a whole number. Divide the total by the sum of ratio parts to find one unit, multiply by each ratio number, and verify that the group counts are whole, have the stated ratio and add back to the total.
A useful rule has three parts: a trigger, an operation and a check. The trigger tells you when the rule applies. The operation tells you what to do. The check tells you whether the result still matches the meaning of the question. Learners who remember only the operation often apply it in the wrong place; learners who remember only an example often freeze when the surface details change.
Mechanism: why the rule works
1. Define the whole
A ratio may compare two named groups without covering every item in a larger setting.
Diagnostic question: Does the stated total equal the sum of all ratio groups? Reliable response: Bracket exactly the groups included.
2. Add ratio units
The numbers in a:b count equal units assigned to each group.
Diagnostic question: How many unit parts make the compared whole? Reliable response: Calculate a+b, or the sum of all parts.
3. Test divisibility
For indivisible objects, one ratio unit must be a whole number.
Diagnostic question: Does total divide exactly by the part sum? Reliable response: Inspect the quotient and remainder before allocating.
4. Find one unit
Dividing the correct total by the part sum converts abstract ratio units into actual quantity.
Diagnostic question: What quantity does one unit represent? Reliable response: Attach the context label to the quotient.
5. Allocate by multiplication
Each group receives its ratio number times one unit.
Diagnostic question: Have all groups been calculated from the same unit? Reliable response: Multiply consistently.
6. Verify both conditions
A valid allocation must reproduce the total and simplify to the required ratio.
Diagnostic question: Do sums and relative parts both match? Reliable response: Run add-back and ratio checks.
Worked examples: make the decision visible
Do not race through these examples. Before reading each explanation, name the evidence that matters and the information that does not. Then compare the correct route with the tempting route. That comparison is where the transferable learning sits.
Worked example 1: Two groups fit exactly
Task. Red:blue=2:3 and total=45.
Reasoning. The part sum is 5, so one unit is 45÷5=9. The controlling idea is the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Red=18 and blue=27.
Independent check. 18+27=45 and 18:27=2:3. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption.
Worked example 2: Impossible whole count
Task. Pens:pencils=3:4 and total=50, with every item whole.
Reasoning. The part sum is 7; 50÷7 leaves a remainder. The controlling idea is the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. No exact whole-number allocation satisfies all stated conditions.
Independent check. Any rounding changes the total, ratio or both. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption.
Worked example 3: Three-part ratio
Task. A:B:C=2:3:5 and total=80.
Reasoning. The part sum is 10 and one unit is 8. The controlling idea is the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. A=16, B=24, C=40.
Independent check. Counts add to 80 and simplify to 2:3:5. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption.
Worked example 4: Continuous mass
Task. Two ingredients have mass ratio 2:3 and total mass 41 kg.
Reasoning. Mass can be fractional. One unit is 8.2 kg. The controlling idea is the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Masses are 16.4 kg and 24.6 kg.
Independent check. They add to 41 kg and have ratio 2:3. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption.
Worked example 5: Wrong divisor trap
Task. A learner divides 40 by 3 for ratio 2:3.
Reasoning. Three represents only the second group’s ratio units, not the whole. The controlling idea is the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Divide by 2+3=5.
Independent check. The corrected counts add back exactly. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption.
Worked example 6: Ratio not whole class
Task. Boys:girls=2:3 among club members, but the class total includes non-members.
Reasoning. The class total is not automatically the club total. The controlling idea is the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Use only the total explicitly covering boys and girls in the ratio.
Independent check. Check the population label. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption.
Worked example 7: Equivalent ratio
Task. Green:yellow=4:6 and total=35.
Reasoning. Simplify to 2:3; the unit sum is 5 and one simplified unit is 7. The controlling idea is the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Green=14 and yellow=21.
Independent check. 14:21=2:3=4:6. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption.
Worked example 8: Reverse feasibility
Task. Could 26 whole beads be split 5:8?
Reasoning. The part sum is 13; 26÷13=2. The controlling idea is the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Yes: 10 and 16 beads.
Independent check. 10+16=26 and 10:16=5:8. A good check approaches the conclusion from a different direction. Repeating the same steps more slowly may repeat the same hidden assumption.
Deepening lab: compare cases, conditions and limits
A method becomes independent when you can say where it applies, where it stops and which change would alter the conclusion. The cases below deliberately vary one structural feature at a time. For each case, pause before the analysis and predict whether the core rule remains available. Then name the exact condition that controls the decision. This is harder than repeating a worked solution, but it is also closer to what an unfamiliar examination item demands.
Deepening case 1: Total 30, ratio 1:2
Case. Three units fit ten times.
Analysis. Counts are 10 and 20. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Verify. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 2: Total 31, ratio 1:2
Case. Thirty-one is not divisible by three.
Analysis. Whole counts cannot fit exactly. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Explain the remainder. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 3: Total 0
Case. Zero whole objects can be allocated as zero and zero, but ratio interpretation may be undefined in some contexts.
Analysis. Read the question carefully. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Do not divide by zero ratio parts. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 4: Ratio 0:3
Case. One group is constrained to zero while the other carries the total.
Analysis. This is a special boundary case. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Check whether the context permits zero. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 5: Three groups
Case. Ratio 1:2:4 has seven units.
Analysis. Total must be a multiple of seven for whole counts. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Test 56. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 6: Simplified form
Case. Ratio 6:9 simplifies to 2:3.
Analysis. Both have the same feasible totals, multiples of five when scaled counts are whole. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Explain why fifteen ratio marks are redundant. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 7: Fixed total, changed ratio
Case. A total fitting 2:3 may not fit 3:4.
Analysis. Part sums change from five to seven. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Test total 40. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 8: Fractional people
Case. A quotient of 7.5 people is invalid.
Analysis. Context requires whole counts. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Do not round silently. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 9: Fractional length
Case. A quotient of 7.5 cm may be valid.
Analysis. Length is continuous. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Keep units. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 10: Remainder one
Case. A small remainder still breaks exactness.
Analysis. Exact ratio is a structural condition. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Do not dismiss it as close enough. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 11: Approximate ratio
Case. If the question permits an approximate ratio, optimisation becomes a different task.
Analysis. Exact and approximate are not interchangeable. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. State the tolerance. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 12: One group known
Case. If one group is 12 in ratio 2:3, one unit is 6.
Analysis. The other group is 18. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Do not use total division first. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 13: Difference known
Case. For ratio 5:3, the difference is two units.
Analysis. A difference of 14 makes one unit 7. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Find total. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 14: Sum known
Case. The total is the sum of all compared groups.
Analysis. Part-sum method applies directly. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Label the whole. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 15: Extra ungrouped items
Case. Some items are outside the ratio.
Analysis. Subtract or isolate them only if explicitly stated. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Protect scope. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 16: Rounding temptation
Case. 8.2 counters is rounded to 8.
Analysis. The new counts total 40, not 41. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Show the contradiction. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 17: Different rounding
Case. One group rounded up and another down.
Analysis. The ratio changes even if total is preserved. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Check both conditions. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 18: Unit table
Case. List group, ratio units and actual amount.
Analysis. A table exposes consistent scaling. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Fill one-unit row. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 19: Bar model
Case. Equal-width unit bars represent ratio units.
Analysis. The complete bar count equals the part sum. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. Mark the total bracket. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 20: Feasibility statement
Case. No exact solution is a valid mathematical conclusion.
Analysis. It follows from indivisibility and remainder evidence. Notice that the answer depends on the defined whole, the sum of ratio units, the requirement for whole objects and the exact add-back check; changing a decorative detail would not be enough to change the reasoning.
Challenge. State which condition conflicts. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Finish the lab with a blank-page recall. Write the rule, its conditions, one confirming example, one near-miss and one independent check from memory. Compare that page with the article only after finishing. If the rule is correct but the condition is missing, the learning is not yet safe: an overgeneralised rule can produce confident errors. If the condition is correct but no example can be generated, practise construction rather than rereading.
Common misconceptions and targeted repairs
Misconception 1: Divide by the larger ratio number
What the learner may think. For 2:3, divide total by 3.
Why it fails. The total contains both groups, so it spans five units. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Add all ratio parts first. Use this short test immediately: What does the bracketed total cover?
Misconception 2: Ratio numbers are counts
What the learner may think. 2:3 always means two objects and three objects.
Why it fails. Ratio numbers are relative units that can scale. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Find the value of one unit. Use this short test immediately: Could 20:30 represent the same ratio?
Misconception 3: Round fractional people
What the learner may think. 8.2 people is close enough to 8.
Why it fails. Whole-object exact ratios do not permit silent rounding. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Use divisibility as a feasibility gate. Use this short test immediately: Do rounded groups still meet both checks?
Misconception 4: A remainder can be assigned anywhere
What the learner may think. Place the leftover object in either group.
Why it fails. Adding it changes the exact ratio. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. State incompatibility or follow an explicit exception rule. Use this short test immediately: What is the new simplified ratio?
Misconception 5: Every total is the ratio whole
What the learner may think. Use the class total for a ratio comparing club members.
Why it fails. Some items may lie outside the named groups. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Define the population before calculating. Use this short test immediately: Do ratio groups exhaust the total?
Misconception 6: Add-back alone is enough
What the learner may think. Any pair adding to the total is valid.
Why it fails. The pair must also have the stated relative relationship. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Check both sum and simplified ratio. Use this short test immediately: Does 17+28=45 prove 2:3?
Graded independent practice
Attempt each item without looking ahead. Write one line that identifies the controlling evidence before writing the final answer. Items 1–3 check recognition, 4–7 require explanation, and the later items change the surface form so that memory alone is insufficient.
Practice 1: Part sum
Question. How many ratio units are in 4:7?
Explained answer. 11.
Why this answer earns trust. The whole contains both groups. Transfer variation: Extend to 2:3:4.
Practice 2: Feasibility
Question. Can 55 whole objects fit ratio 4:7?
Explained answer. Yes.
Why this answer earns trust. 55 is divisible by 11. Transfer variation: Find the counts.
Practice 3: Allocation
Question. Split 55 in ratio 4:7.
Explained answer. 20 and 35.
Why this answer earns trust. One unit is 5. Transfer variation: Check both conditions.
Practice 4: Impossible count
Question. Can 56 whole objects fit ratio 4:7 exactly?
Explained answer. No.
Why this answer earns trust. 56 is not divisible by 11. Transfer variation: State the remainder.
Practice 5: Three groups
Question. Split 72 in ratio 1:3:5.
Explained answer. 8, 24 and 40.
Why this answer earns trust. There are nine units, each worth 8. Transfer variation: Verify sum.
Practice 6: Continuous quantity
Question. Split 10.5 m in ratio 2:5.
Explained answer. 3 m and 7.5 m.
Why this answer earns trust. Seven units make 10.5 m, so one is 1.5 m. Transfer variation: Keep measurement units.
Practice 7: Scope
Question. Why might a class total be unusable for a boys:girls sports-team ratio?
Explained answer. The ratio may cover only team members, not the whole class.
Why this answer earns trust. The whole must match the compared groups. Transfer variation: Identify the needed total.
Practice 8: Error audit
Question. A learner gets 8.2 counters per unit and rounds. Diagnose.
Explained answer. The total is incompatible with an exact whole-count ratio.
Why this answer earns trust. Rounding hides a feasibility failure. Transfer variation: Show which check breaks.
Practice 9: Reverse test
Question. A split is 18 and 27. Does it fit 2:3 and total 45?
Explained answer. Yes.
Why this answer earns trust. It adds to 45 and simplifies to 2:3. Transfer variation: Find one unit.
Practice 10: Routine
Question. State the ratio-total routine.
Explained answer. Define whole, sum parts, test divisibility, find one unit, allocate, protect whole-number conditions, add back and simplify ratio.
Why this answer earns trust. It catches scope and feasibility errors. Transfer variation: Apply to 3:5 with total 64.
Delayed transfer: prove that the learning lasts
Transfer test 1: Feasibility cards
Sort totals into possible and impossible for several whole-number ratios before calculating groups. Do this after a delay, without rereading the worked examples. The purpose is to test retrieval and decision-making, not immediate imitation.
Success criterion. Every decision uses divisibility by the part sum. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter.
Transfer test 2: Context switch
Compare people, counters, mass and length ratio problems. Do this after a delay, without rereading the worked examples. The purpose is to test retrieval and decision-making, not immediate imitation.
Success criterion. The learner states when fractional units are valid. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter.
Transfer test 3: Delayed reverse design
After two days, create a total that fits 3:4:5 and one that cannot. Do this after a delay, without rereading the worked examples. The purpose is to test retrieval and decision-making, not immediate imitation.
Success criterion. Both choices are justified by the twelve-unit sum. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter.
Examination control
1. Read the job before the story. Underline the command and the noun it governs. “Explain the change,” “state the word,” “find the fraction” and “identify the evidence” are different jobs even when the surrounding context is similar.
2. Separate given information from remembered information. Use only the facts supplied for the current task plus secure subject knowledge. Do not let a previous question, a familiar worksheet or an expected pattern silently become new evidence.
3. Write enough working to expose the decision. A marker or teacher should be able to see the relationship that justifies the answer. Extra sentences are not automatically stronger; the strongest working is concise, relevant and checkable.
4. Reserve a different-route check. For language, read the sentence for meaning and grammar. For mathematics, estimate or reverse the operation. For science, check the claim against the stated observation and a conservation or fair-test principle.
5. Stop when the requested job is complete. Unrequested speculation can contradict a correct answer. Add detail only when it explains the mechanism or satisfies another explicit part of the question.
Under time pressure, use a compact four-part margin routine: trigger → evidence → operation → check. Trigger names the feature that activates the method. Evidence identifies the exact words, values or observations allowed. Operation performs the language, mathematical or scientific step. Check asks whether the final statement answers the requested job, preserves units or referents, and avoids a stronger claim than the evidence supports.
A compact error log
After practice, do not record only “careless mistake.” Name the broken decision. Useful labels include trigger missed, evidence imported, relationship reversed, referent lost, unit dropped, operation correct but job wrong, and check repeated the same route. Add one prevention cue beside the label. A short accurate log is more useful than a long emotional account because it tells the learner what to do on the next item.
Review the log after two days and again after a week. Reattempt only one or two representative items first. If the method transfers, move to a mixed set. If it fails, repair the exact link between trigger and operation. This spacing matters because a solution can feel obvious while it is still visible and disappear when the page is closed.
Notes for parents and tutors
Ask what the total covers before asking for a calculation.
Use counters or equal bars to make the sum of ratio units visible.
Treat a remainder as mathematical evidence, not a cue to round whole people or objects.
The adult’s most useful question is not “Why were you careless?” but “Which decision did the evidence require?” Ask the learner to point to the controlling word, value, relationship or observation. If the learner can explain that link, reduce support. If the learner cannot, model one example and then change the surface details for the next attempt.
Frequently asked questions
Why add the ratio numbers?
They count all equal ratio units in the compared whole.
Must the total always be divisible by the part sum?
Only when the exact ratio applies to indivisible whole objects and the total covers all ratio groups.
Can a fractional unit ever be valid?
Yes for continuous quantities such as mass or length.
What if there is a remainder?
No exact whole-number allocation satisfies all stated conditions unless the question provides another rule.
How do I check the answer?
Add all groups and simplify their ratio.
What is the fastest routine?
Whole, part sum, divisibility, one unit, allocation, two checks.
Next routes
Return to the complete volume directory to locate the series, use the original PSLE Learning Guide for the foundation route, and continue through PSLE Mathematics for verified subject guidance. The next useful task is a mixed set in which this idea is sometimes relevant and sometimes irrelevant; that is the point at which a learner must choose, not merely copy.