How to Perform in PSLE | Learner’s Guide Vol 0680 | English, Mathematics and Science: Read By as Agent, Method, Deadline, Measurement Difference or Nearness From Context

CHAPTER 1 OF 12 · Orient · Back to contents

1. Why one short word creates many errors

The word by is short, frequent and deceptively powerful. In “written by Aisha,” it identifies an agent. In “by bus,” it identifies a method. In “by Friday,” it sets a deadline. In “increase by 4,” it gives an amount of change. In “8 cm by 5 cm,” it separates dimensions. In “by the window,” it locates something nearby.

Errors occur when a learner carries the first familiar meaning into a new subject. The spelling has not changed, but the relationship has. The solution is not to memorise a single definition. Build a small relationship map and use surrounding grammar, units, verbs and diagrams to select the local reading.

Before calculating or answering, replace by with a fuller phrase: “performed by,” “using,” “no later than,” “a difference of,” “multiplied with dimensions,” “near,” or “past.” If the paraphrase keeps the sentence coherent, it is evidence for the interpretation.

• Agent: who performed the action?
• Method or instrument: how was it done or measured?
• Deadline: no later than what time?
• Difference: how much did a value change or exceed another?
• Dimensions or operation: which quantities are related?
• Location or path: near, beside or past which landmark?

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CHAPTER 2 OF 12 · Model · Back to contents

2. The relationship map

Start with the governing verb. Passive forms such as was written often permit an agent by-phrase. Verbs such as travelled, sent, measured often permit method or instrument. Time commands such as submit by produce a deadline. Change verbs such as increase by name a difference.

Next inspect the noun after by. A person may be an agent; a bus, email or thermometer is more likely a means or instrument; Friday or 3 p.m. is a time boundary; a measured number with units may be a change; a landmark can be location or path.

Finally use the subject’s representation. A rectangle diagram makes “8 by 5” a dimension pair. An equation makes “divide 24 by 6” an operation. A passive Science sentence may use an instrument phrase. English grammar opens possible readings; subject knowledge chooses among them.

Ambiguity is sometimes real. “She stood by the bank” could describe location near a financial building or river edge; bank itself is ambiguous. Do not force certainty beyond the context. State the likely reading and identify the missing cue when necessary.

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CHAPTER 3 OF 12 · Model · Back to contents

3. Cross-subject representations

Use a four-column table: exact phrase, governing cue, relationship, paraphrase. For “by Monday,” the cue is a time noun, the relationship is deadline, and the paraphrase is “no later than Monday.” For “by 6 cm,” the cue may be a comparison or change verb plus units, and the paraphrase is “a difference of 6 cm.”

In Mathematics, attach units before deciding. “Multiply by 6” uses a dimensionless factor; “longer by 6 cm” uses a measurement difference; “6 cm by 4 cm” gives two dimensions. The same surface word does not select the operation by itself.

In Science, distinguish agent, instrument and process. “Measured by Lina” names the person; “measured by a thermometer” names the instrument; “dried by evaporation” names the process. A high-quality answer can often replace the by-phrase with an explicit clause.

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CHAPTER 4 OF 12 · Worked examples · Back to contents

4. Worked foundations

Worked case 0: agent in a passive sentence

Prompt. Interpret: “The model was built by Hana.”

Tempting reading. Reading by as near Hana. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. Here by Hana names the agent who performed the building.

Mechanism. The passive verb phrase was built describes what happened to the model; the by-phrase supplies the actor. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Rewrite actively: “Hana built the model.” Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 1: method or transport

Prompt. Interpret: “They travelled by bus and submitted the form by email.”

Tempting reading. Treating both phrases as deadlines. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. Both phrases express method: the means of travel and the means of submission.

Mechanism. A transport noun or communication channel after by often answers “How?” rather than “When?” Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Replace bus with 6 p.m.; the relation becomes a deadline. Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 2: deadline

Prompt. Interpret: “Submit the response by Friday.”

Tempting reading. Believing submission must happen only on Friday. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. The response must be submitted no later than Friday, subject to the stated context.

Mechanism. A time expression after by commonly sets an upper time boundary, not an exact appointment. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Contrast “by Friday” with “on Friday” and “from Friday.” Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 3: near or beside

Prompt. Interpret: “The seedlings were placed by the window.”

Tempting reading. Reading the window as an agent that placed the seedlings. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. Here by means near or beside the window.

Mechanism. The verb is active/passive-neutral about location, and the following noun names a place rather than a plausible actor in context. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Change to “The seedlings were placed by Amir” and explain the agent reading. Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

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CHAPTER 5 OF 12 · Worked examples · Back to contents

5. Mathematics and measurement cases

Worked case 5: difference in measurement

Prompt. A ribbon is 18 cm longer than another by 3 cm. What is the shorter length?

Tempting reading. Treating by 3 cm as a final length of 3 cm. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. The measurement difference is 3 cm, so the shorter ribbon is 15 cm.

Mechanism. In comparison language, by can introduce the amount of difference between two values. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Write the equation longer = shorter + 3. Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 6: multiplication dimensions

Prompt. Interpret: “A rectangular card measures 8 cm by 5 cm.”

Tempting reading. Subtracting 5 from 8 because by always means difference. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. The phrase gives two perpendicular dimensions, typically length and width: 8 cm × 5 cm.

Mechanism. Measurement conventions and the rectangle context turn by into a dimension separator. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Find area and perimeter, showing that the dimensions serve different formulas. Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 7: rate of change phrasing

Prompt. A plant’s height increased by 4 cm. If it started at 12 cm, what is the final height?

Tempting reading. Interpreting by 4 cm as “to 4 cm.” The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. The increase amount is 4 cm, so final height = 12 + 4 = 16 cm.

Mechanism. Increase by names the change; increase to would name the new value. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Rewrite the fact using “increased from 12 cm to 16 cm.” Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 8: division and grouping

Prompt. Interpret the instruction “Divide 24 by 6.”

Tempting reading. Reading 6 as a location or deadline. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. The instruction means 24 ÷ 6, asking how many groups of 6 or how much in each of 6 equal groups, depending on context.

Mechanism. The verb divide selects the mathematical operation reading. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Compare “increase 24 by 6” and explain why the operation changes. Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

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CHAPTER 6 OF 12 · Worked examples · Back to contents

6. Science and evidence cases

Worked case 9: evidence collected by an instrument

Prompt. Interpret: “The temperature was measured by a thermometer.”

Tempting reading. Saying the thermometer is a human agent with intentions. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. The by-phrase names the instrument or means used to obtain the measurement.

Mechanism. Passive structure invites an agent/instrument phrase; subject knowledge identifies a thermometer as a measuring instrument. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Rewrite as “A thermometer was used to measure the temperature.” Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 10: cause-like phrasing

Prompt. Interpret: “The wet cloth dried by evaporation.”

Tempting reading. Treating evaporation as a nearby place. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. The phrase indicates the process or means through which drying occurred.

Mechanism. Science vocabulary and the event relation make a process paraphrase coherent: drying occurred through evaporation. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Contrast “dried by the window,” where location is more likely. Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 11: passing a point

Prompt. Interpret: “The cyclist rode by the gate without stopping.”

Tempting reading. Assuming the cyclist stayed beside the gate. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. Here by can mean past the gate, supported by motion and “without stopping.”

Mechanism. A motion verb plus a landmark can produce a path reading rather than a static-nearness reading. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Compare “The bicycle stood by the gate.” Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

Worked case 12: mixed meanings in one instruction

Prompt. Interpret: “By 3 p.m., measure the 6 cm by 4 cm card by using a ruler.”

Tempting reading. Assigning one meaning to all three occurrences. The word by is familiar, so the mind may accept its first available meaning without checking the relation in the clause.

Controlled reading. The first sets a deadline, the second separates dimensions, and the third introduces method or instrument.

Mechanism. Each occurrence connects different constituents, so each must be resolved locally. Replace by with a fuller paraphrase and check whether the surrounding grammar and subject meaning remain coherent.

Transfer. Label them deadline, dimensions and method before following the instruction. Change one nearby word so that by takes a different meaning, then explain which cue forced the change.

Audit. Name the two things connected by by, label the relationship, preserve units where relevant, and reread the entire instruction.

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CHAPTER 7 OF 12 · Repair errors · Back to contents

7. Misconceptions and repairs

0. By always means near

Why it fails. Location is only one relation; passive agents, methods, deadlines, differences and dimensions are common. Repair the interpretation by paraphrasing the relation before calculating, answering or rewriting.

Diagnostic prompt. What question does the by-phrase answer: who, how, when, where or how much? A correct final answer with an incorrect paraphrase is unstable and needs another contrast case.

1. By a date means on that exact date

Why it fails. A deadline reading usually permits completion earlier, whereas on identifies the date itself. Repair the interpretation by paraphrasing the relation before calculating, answering or rewriting.

Diagnostic prompt. Would Tuesday satisfy “by Friday”? Explain. A correct final answer with an incorrect paraphrase is unstable and needs another contrast case.

2. Increase by equals increase to

Why it fails. By names the change amount; to names the final value. Repair the interpretation by paraphrasing the relation before calculating, answering or rewriting.

Diagnostic prompt. Write start + change = final with the given numbers. A correct final answer with an incorrect paraphrase is unstable and needs another contrast case.

3. Every passive by-phrase is a person

Why it fails. A by-phrase may name an instrument, method or process as well as an agent. Repair the interpretation by paraphrasing the relation before calculating, answering or rewriting.

Diagnostic prompt. Can the noun intentionally perform the action, or is it a tool/process? A correct final answer with an incorrect paraphrase is unstable and needs another contrast case.

4. Dimensions should be added immediately

Why it fails. An “8 by 5” rectangle supplies two dimensions; the required operation depends on area, perimeter or another demand. Repair the interpretation by paraphrasing the relation before calculating, answering or rewriting.

Diagnostic prompt. Which formula does the question ask for? A correct final answer with an incorrect paraphrase is unstable and needs another contrast case.

5. One sentence uses one meaning of by

Why it fails. Different occurrences can have different local relations. Repair the interpretation by paraphrasing the relation before calculating, answering or rewriting.

Diagnostic prompt. Label each by-phrase independently in a multi-clause instruction. A correct final answer with an incorrect paraphrase is unstable and needs another contrast case.

6. A nearby noun alone decides meaning

Why it fails. Verb type, units, discourse purpose and subject representation all contribute. Repair the interpretation by paraphrasing the relation before calculating, answering or rewriting.

Diagnostic prompt. What broader clause makes the reading coherent? A correct final answer with an incorrect paraphrase is unstable and needs another contrast case.

7. Paraphrasing wastes time

Why it fails. A two- or three-word paraphrase prevents larger calculation or comprehension errors. Repair the interpretation by paraphrasing the relation before calculating, answering or rewriting.

Diagnostic prompt. What short replacement preserves the relation? A correct final answer with an incorrect paraphrase is unstable and needs another contrast case.

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CHAPTER 8 OF 12 · Examination control · Back to contents

8. Examination control

Use the BY check: Bind the word to the two things it connects; Yield a short paraphrase. Then perform the subject action. This takes seconds and protects against executing the wrong operation or answering the wrong relation.

• Box the complete by-phrase.
• Underline the governing verb or comparison.
• Circle units or time expressions.
• Write a two- or three-word paraphrase above the phrase.
• Check the diagram, equation or sentence structure.
• Perform the operation or answer only after the relation is fixed.
• If two readings remain plausible, state what context is missing.

Stop rule. Stop interpreting when the paraphrase fits grammar, units and subject representation. Do not keep cycling through every dictionary meaning once the evidence converges.

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CHAPTER 9 OF 12 · Practice · Back to contents

9. Independent practice I

Practice 0: “The poem was written by Mei.” What does by express?

Explained answer. It introduces the agent, Mei, who wrote the poem. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Rewrite in active voice. Return later and write a paraphrase before the final answer.

Practice 1: “Finish the graph by noon.” Must it be finished exactly at noon?

Explained answer. No. In the ordinary deadline reading, it must be finished no later than noon. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Contrast with “finish the graph at noon.” Return later and write a paraphrase before the final answer.

Practice 2: “The path passes by the pond.” What relation is likely?

Explained answer. The path goes near/beside the pond; in a motion context it may also suggest passing the landmark. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Change the verb to ends and reconsider. Return later and write a paraphrase before the final answer.

Practice 3: A mass decreases by 7 g from 25 g. Find the final mass.

Explained answer. 25−7=18 g. The 7 g is the amount of decrease. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Rewrite using “decreases to.” Return later and write a paraphrase before the final answer.

Practice 4: A page is 21 cm by 15 cm. Find its area.

Explained answer. 21×15=315 cm². By separates the two dimensions. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Find perimeter and explain the different operation. Return later and write a paraphrase before the final answer.

Practice 5: “The parcel was sent by courier.” What does by express?

Explained answer. It expresses the method or service used to send the parcel. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Replace courier with Tuesday. Return later and write a paraphrase before the final answer.

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CHAPTER 10 OF 12 · Practice · Back to contents

10. Independent practice II

Practice 7: “The bulb was controlled by a switch.” Agent or instrument?

Explained answer. The switch functions as a controlling device/instrument in the system, not a human agent. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Name the human agent in a new sentence. Return later and write a paraphrase before the final answer.

Practice 8: “Divide 56 by 7.” What operation is selected?

Explained answer. 56÷7=8. The verb divide controls the mathematical reading. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Compare “multiply 56 by 7.” Return later and write a paraphrase before the final answer.

Practice 9: “The tree grew by 12 cm to 85 cm.” What was its starting height?

Explained answer. 85−12=73 cm. By gives the change; to gives the final value. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Rewrite using from, by and to accurately. Return later and write a paraphrase before the final answer.

Practice 10: “A bench stood by the door.” What does by express?

Explained answer. Static location: the bench was near or beside the door. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Change stood to moved and discuss possible ambiguity. Return later and write a paraphrase before the final answer.

Practice 11: Identify three meanings: “By Monday, send the 4 by 6 card by post.”

Explained answer. Deadline; dimensions; method. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Write a new sentence with agent, difference and location meanings. Return later and write a paraphrase before the final answer.

Practice 12: Why should units stay attached to “by 5” in Mathematics?

Explained answer. Units reveal the quantity being changed and help distinguish a measurement difference from a bare multiplier or label. The controlling evidence comes from both the words around by and the subject’s representation.

Delayed-transfer variation. Compare “increase by 5 cm” with “multiply by 5.” Return later and write a paraphrase before the final answer.

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CHAPTER 11 OF 12 · Transfer · Back to contents

11. Delayed transfer and proof

On day one, sort by-phrases into relationship categories. On day three, remove the category labels and write paraphrases. On day seven, solve mixed English, Mathematics and Science items in which two meanings occur in the same sentence.

Prove an interpretation by substitution. Replace by with the proposed fuller phrase and reread. “Submit no later than Friday” preserves the deadline. “The model was built near Hana” does not preserve the ordinary agent meaning of the original passive sentence.

Create contrast pairs that change only one cue: “stood by the gate” versus “rode by the gate”; “measured by Ana” versus “measured by a ruler”; “increase by 5” versus “increase to 5.” Contrastive practice teaches the cue that causes the relationship change.

Seven-day test. Label twelve unseen by-phrases, including at least two agents, two methods, two deadlines, two measurement relations, two locations and two mixed cases. Give a paraphrase and one rejected alternative for each.

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CHAPTER 12 OF 12 · Transfer · Back to contents

12. Family guidance, FAQs and next routes

Guidance for parents and tutors

Do not ask only “What does by mean?” Ask “What relationship does it express here?” The word has several legitimate uses, so the learner needs a local decision rather than a universal one-line definition.

When correcting, point to the governing cue. A useful exchange is: “What verb controls this phrase? What noun follows by? What do the units or diagram show?” Fade the prompts as the learner begins to ask them independently.

Frequently asked questions

Is by always a preposition?

It commonly functions as a preposition in the cases taught here, but the learning goal is the relationship expressed in context, not a label in isolation.

Does by Friday include Friday?

In ordinary deadline use it means no later than Friday, but practical instructions may specify a time zone, closing time or submission rule. Read the full instruction.

Why is increase by different from increase to?

By gives the amount of change; to gives the final value. From gives the starting value.

How do I read 8 by 5?

In a rectangle or page-size context it usually gives two dimensions. Use the question’s demand to decide whether to multiply for area or add sides for perimeter.

Can a by-phrase name a tool?

Yes. “Measured by a thermometer” names an instrument or means. In a passive sentence, not every by-phrase is a human agent.

What if two readings are possible?

Use the wider sentence, diagram and subject context. If ambiguity remains, state the plausible readings and the cue needed to choose.

Next routes

Continue through the English, Mathematics and Science hubs, or return to the series directory.

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