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 adds the two percentage increases and stops, assumes area changes by the same percentage as one side, or calculates from percentages without identifying the original whole. 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 rectangle 10 cm by 20 cm has area 200 cm². Increase both dimensions by 10% and the new dimensions are 11 cm by 22 cm.
The new area is 242 cm², an increase of 42 cm². Relative to 200 cm², that is 21%, not 20%.
Adding 10% and 10% accounts for two strips but misses the small corner where both extensions overlap.
Multiplying scale factors captures the whole geometry: 1.10×1.10=1.21.
A percentage belongs to a specified original quantity. Ten per cent of length and ten per cent of width are not directly two pieces of area.
If only one dimension grows by 10% while the other stays fixed, area grows by exactly 10%. The cross-term appears only when both dimensions change.
Different rates work the same way. A 20% length increase and 5% width increase give factor 1.20×1.05=1.26, so area rises 26%.
Two decreases also multiply. A 10% reduction in each dimension gives 0.9×0.9=0.81, so area decreases 19%, not 20%.
An increase followed by a decrease needs signed factors. A 20% increase in length and 20% decrease in width give 1.2×0.8=0.96, a 4% area decrease.
The result can be checked with a convenient 100-by-100 rectangle, because percentage scale factors do not depend on the actual starting dimensions.
Units also expose the job: multiplying centimetres by centimetres produces square centimetres.
The safe routine is identify the original area, convert every rate to a factor, multiply factors, compare with 1 and verify with a numerical rectangle.
Core decision: When a rectangle’s length is multiplied by 1+p and its width by 1+q, its area is multiplied by (1+p)(1+q)=1+p+q+pq, where p and q are decimal rates. The pq cross-term represents the corner area created by both changes together. For decreases, use factors below 1 and compare the final area factor with 1.
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. Anchor the original whole
Percentage change in area must be compared with the original area, not one side or the new area.
Diagnostic question: What quantity represents 100%? Reliable response: Write A=LW before changing anything.
2. Convert rates to factors
An increase of p% becomes 1+p/100; a decrease becomes 1-p/100.
Diagnostic question: Is the new dimension larger or smaller? Reliable response: Choose a factor above or below 1.
3. Multiply dimension factors
Area is a product of length and width, so both scale changes multiply.
Diagnostic question: What multiplies L, and what multiplies W? Reliable response: Multiply the two factors rather than adding rates.
4. See the cross-term
Expanding (1+p)(1+q) produces pq in addition to p and q.
Diagnostic question: Which small region depends on both extensions? Reliable response: Name the corner overlap or use the algebraic product.
5. Convert factor to change
A factor of 1.26 means the final area is 126% of the original, hence a 26% increase.
Diagnostic question: How far is the factor from 1? Reliable response: Subtract 1 and convert to a percentage.
6. Verify independently
A convenient test rectangle makes the strips and corner measurable.
Diagnostic question: Does a direct area calculation reproduce the factor result? Reliable response: Use dimensions such as 100 by 100 or the given values.
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: Equal ten-percent increases
Task. Both length and width increase by 10%.
Reasoning. The factors are 1.1 and 1.1; their product is 1.21. The controlling idea is the original area as the whole, the separate scale factor for each dimension and the product of those factors. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Area increases by 21%.
Independent check. Use a 10-by-10 square: 100 becomes 121. 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: Different increases
Task. Length increases 20% and width increases 5%.
Reasoning. Multiply 1.20×1.05=1.26. The controlling idea is the original area as the whole, the separate scale factor for each dimension and the product of those factors. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Area increases by 26%.
Independent check. A 100-by-100 rectangle becomes 120 by 105. 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: Equal decreases
Task. Both dimensions decrease by 10%.
Reasoning. Multiply 0.9×0.9=0.81. The controlling idea is the original area as the whole, the separate scale factor for each dimension and the product of those factors. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Area decreases by 19%.
Independent check. 100 becomes 81, a loss of 19. 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: Increase and decrease
Task. Length increases 25% while width decreases 20%.
Reasoning. Multiply 1.25×0.80=1.00. The controlling idea is the original area as the whole, the separate scale factor for each dimension and the product of those factors. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Area is unchanged.
Independent check. For 20 by 10, new dimensions 25 by 8 still give 200. 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: One side fixed
Task. Length rises 15% and width does not change.
Reasoning. Factors are 1.15 and 1. The controlling idea is the original area as the whole, the separate scale factor for each dimension and the product of those factors. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Area increases by 15%.
Independent check. The cross-term is zero because q=0. 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: Find new area
Task. Original area is 300 cm²; factors are 1.2 and 1.1.
Reasoning. The area factor is 1.32. The controlling idea is the original area as the whole, the separate scale factor for each dimension and the product of those factors. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. New area is 396 cm².
Independent check. 396−300=96, and 96/300=32%. 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: Reverse missing rate
Task. Area rises 32% and length rises 20%; find width change.
Reasoning. 1.20×width factor=1.32, so width factor=1.10. The controlling idea is the original area as the whole, the separate scale factor for each dimension and the product of those factors. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Width increases by 10%.
Independent check. Multiply 1.2×1.1. 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: Addition trap
Task. A learner says 12%+8%=20%.
Reasoning. The correct factor is 1.12×1.08=1.2096. The controlling idea is the original area as the whole, the separate scale factor for each dimension and the product of those factors. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Area increases by 20.96%.
Independent check. The missing cross-term is 0.12×0.08=0.0096 or 0.96%. 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: Five and five
Case. Both sides rise 5%.
Analysis. Factor 1.05²=1.1025. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Explain the extra 0.25%. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 2: Fifty and fifty
Case. Both sides rise 50%.
Analysis. Factor 1.5²=2.25. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Compare 125% area increase with a mistaken 100%. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 3: Double both
Case. Both dimensions double.
Analysis. Area factor is 2×2=4. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. State the percentage increase. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 4: Halve both
Case. Both dimensions halve.
Analysis. Area factor is 0.5²=0.25. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. State the percentage decrease. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 5: Increase only length
Case. Length rises 30%, width fixed.
Analysis. Factor is 1.3. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Show why no cross-term appears. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 6: Decrease only width
Case. Width falls 12%, length fixed.
Analysis. Factor is 0.88. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Name the area decrease. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 7: Ten up, ten down
Case. Factors 1.1 and 0.9 multiply to 0.99.
Analysis. Area falls 1%. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Explain why equal rates do not cancel. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 8: Twenty up, twenty down
Case. Factors 1.2 and 0.8 multiply to 0.96.
Analysis. Area falls 4%. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Identify the product term. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 9: Original dimensions unknown
Case. Only percentage changes are given.
Analysis. The area percentage can still be found from factors. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Use a convenient assumed rectangle. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 10: Original area known
Case. Area is 480 cm² and factor 1.155.
Analysis. New area is 554.4 cm². Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Keep exact decimal work. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 11: Whole-number context
Case. Dimensions may be measurements with decimals.
Analysis. Fractional lengths and areas can be valid. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Do not round prematurely. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 12: Square special case
Case. A square side rises by p%.
Analysis. Area factor is (1+p)². Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Expand to 1+2p+p². State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 13: Perimeter contrast
Case. Both dimensions rise 10%.
Analysis. Perimeter rises 10% because it is linear in L and W. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Contrast with area 21%. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 14: Volume extension
Case. Three dimensions change.
Analysis. Volume uses three scale factors and more interaction terms. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Do not apply the area formula blindly. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 15: Negative result
Case. A factor below 1 means a decrease.
Analysis. Change is 1−factor. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Preserve the direction word. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 16: Factor 1.00
Case. The product equals 1.
Analysis. Area is unchanged despite side changes. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Give a compensating pair. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 17: Diagram strips
Case. Added length and width create two strips and a corner.
Analysis. The corner is the pq term. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Label each area region. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 18: Algebra route
Case. (L+pL)(W+qW) is expanded.
Analysis. Every term has area units. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Match terms to the diagram. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 19: Calculator display
Case. 1.2096 is read as 120.96% of original.
Analysis. The increase is 20.96%. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Do not report 120.96% increase. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 20: Complete audit
Case. Original whole, factors, product, direction and unit are recorded.
Analysis. The percentage statement has a traceable base. Notice that the answer depends on the original area as the whole, the separate scale factor for each dimension and the product of those factors; changing a decorative detail would not be enough to change the reasoning.
Challenge. Verify with direct dimensions. 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: Add rates and stop
What the learner may think. Ten plus ten gives a 20% area increase.
Why it fails. Area multiplies two changed dimensions and includes their interaction. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Multiply scale factors. Use this short test immediately: Where is the new corner area?
Misconception 2: Use one side as the whole
What the learner may think. Area percentage is compared with original length.
Why it fails. Area and length are different quantities and units. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Write original area explicitly. Use this short test immediately: What represents 100% area?
Misconception 3: Report the final factor as increase
What the learner may think. 1.21 means a 121% increase.
Why it fails. It means the final area is 121% of original, which is a 21% increase. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Subtract 1 before naming change. Use this short test immediately: How far from the original 100%?
Misconception 4: Equal up and down cancel
What the learner may think. A 20% rise and 20% fall cancel.
Why it fails. They apply to different dimensions as factors 1.2 and 0.8. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Multiply, then compare. Use this short test immediately: Is the product exactly 1?
Misconception 5: Round before multiplying
What the learner may think. Convert 1.2096 to 1.21 too early in every problem.
Why it fails. Premature rounding can distort later quantities. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Keep exact factors until the final required precision. Use this short test immediately: What precision is requested?
Misconception 6: Area and perimeter scale alike
What the learner may think. Both are properties of the same rectangle, so their percentage changes match.
Why it fails. Area is a product; perimeter is a sum. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Identify the formula before choosing factor logic. Use this short test immediately: Is the target linear or multiplicative?
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: Equal increase
Question. Both dimensions rise 20%. Find area change.
Explained answer. 44% increase.
Why this answer earns trust. 1.2²=1.44. Transfer variation: Show the 4% cross-term.
Practice 2: Different increase
Question. Length rises 10%, width rises 30%.
Explained answer. 43% increase.
Why this answer earns trust. 1.1×1.3=1.43. Transfer variation: Check with 10 by 10.
Practice 3: Equal decrease
Question. Both fall 20%.
Explained answer. 36% decrease.
Why this answer earns trust. 0.8²=0.64. Transfer variation: Compare with mistaken 40%.
Practice 4: Mixed
Question. Length rises 50%, width falls 20%.
Explained answer. 20% increase.
Why this answer earns trust. 1.5×0.8=1.2. Transfer variation: Use direct dimensions.
Practice 5: Unchanged
Question. Length rises 25%, width falls by what percentage for unchanged area?
Explained answer. 20% decrease.
Why this answer earns trust. Required width factor is 1/1.25=0.8. Transfer variation: Multiply to 1.
Practice 6: New area
Question. Original area 250 cm²; factors 1.1 and 1.2.
Explained answer. 330 cm².
Why this answer earns trust. Area factor 1.32. Transfer variation: State increase amount too.
Practice 7: Reverse
Question. Area factor 1.56; one dimension factor 1.2. Find other.
Explained answer. 1.3, a 30% increase.
Why this answer earns trust. 1.56÷1.2=1.3. Transfer variation: Multiply back.
Practice 8: Explain cross-term
Question. Why is 8%+5% insufficient?
Explained answer. It misses 0.08×0.05=0.004, or 0.4%, created by both extensions.
Why this answer earns trust. Area includes their interaction. Transfer variation: Draw strips and corner.
Practice 9: Perimeter contrast
Question. A square side rises 10%. Compare perimeter and area changes.
Explained answer. Perimeter rises 10%; area rises 21%.
Why this answer earns trust. Perimeter scales once, area scales twice. Transfer variation: Use side 10.
Practice 10: Routine
Question. State the two-dimension routine.
Explained answer. Define original area, convert each rate to a factor, multiply, compare product with 1, convert to percentage and verify numerically.
Why this answer earns trust. It protects the whole and cross-term. Transfer variation: Apply to two decreases.
Delayed transfer: prove that the learning lasts
Transfer test 1: Factor table
Create a table of length factor, width factor and area factor for six mixed changes. 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 area factor equals the product and the direction is named correctly. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter.
Transfer test 2: Strip diagram
Draw an original rectangle, two extension strips and the corner for different positive rates. Do this after a delay, without rereading the worked examples. The purpose is to test retrieval and decision-making, not immediate imitation.
Success criterion. Each region corresponds to 1, p, q or pq times the original area. 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, invent one pair that increases area, one that decreases it and one that preserves it. Do this after a delay, without rereading the worked examples. The purpose is to test retrieval and decision-making, not immediate imitation.
Success criterion. All three are verified by factor products and direct dimensions. 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 is the 100% whole?” before discussing any percentage change.
Use a 10-by-10 or 100-by-100 rectangle to make the two strips and corner visible.
Require both a factor calculation and one direct-dimensions check before increasing speed.
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 can’t I just add the percentages?
Because area is the product of two changed dimensions; multiplying factors creates an additional cross-term.
What is the cross-term?
It is pq, the product of the two decimal change rates, represented geometrically by the added corner.
What if only one side changes?
The unchanged side has factor 1, so no cross-term remains and area changes by the same rate as that side.
Do equal increase and decrease rates cancel?
Not generally; for rate p the product is (1+p)(1−p)=1−p².
How do I state a factor of 1.32?
The final area is 132% of original, so the increase is 32%.
What is the fastest check?
Multiply dimension factors, then test with a convenient rectangle.
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.