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 English provide verified subject-specific continuation.
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This volume solves one precise learner problem: the learner sees the same plural noun after both expressions and chooses the same verb, without noticing whether the sentence treats the quantity as one total or refers to several members. 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
“The number of pupils is increasing” treats the total count as one quantity. The head of the subject is number, so singular agreement is the usual standard choice.
“A number of pupils are absent” means several pupils are absent. The sentence refers to multiple members, so plural agreement follows.
The following plural noun can distract the learner. In both examples, pupils is plural, but the determiner changes the meaning and the grammatical centre of the subject.
The definite article the points to a specific count: the number. We can ask what the number is, was, has become or appears to be.
The indefinite article a in a number of creates an idiomatic quantifier meaning several or many. We can often replace it with several and keep the plural verb.
A deletion or substitution test helps. Replace “a number of” with “several”: “Several pupils are absent.” Replace “the number of pupils” with “the total”: “The total is increasing.”
Tense does not change the distinction. “The number has fallen” remains singular, while “A number have left” is plural in the intended several-people reading.
The verb may sit far from the subject. Extra phrases such as in the two classes or after the competition do not change which expression controls agreement.
Meaning matters when number is used in another sense. “A number is written on the door” refers to one numeral, not the quantifier a number of. The complete phrase must be identified.
Questions and inversions can hide the link: “Has the number of entries changed?” still uses singular has. “Have a number of entries been rejected?” uses plural have.
Writers can sometimes avoid stiffness by using several directly, especially when the exact idiom might distract the reader. Clear meaning is more valuable than showing off a pattern.
The final check circles the determiner, paraphrases the subject as the total or several, identifies the finite verb and matches the verb to that meaning.
Core decision: Use singular agreement when the number of means one total or figure; use plural agreement when a number of means several members of the following plural noun group.
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. Circle the article
Locate the or a immediately before number.
Diagnostic question: Is the sentence naming one known total or several members? Reliable response: Do not begin with the plural noun after of.
2. Paraphrase the subject
Try the total for the number of and several for a number of.
Diagnostic question: Which replacement preserves the intended meaning? Reliable response: Write the paraphrase above the phrase.
3. Find the finite verb
Locate the tensed verb that shows agreement.
Diagnostic question: Which form changes between is and are, has and have, or was and were? Reliable response: Ignore infinitives and participles.
4. Match meaning and number
Use singular for one total and plural for several members.
Diagnostic question: What is actually doing or undergoing the action? Reliable response: Choose the verb after the paraphrase.
5. Check added phrases
Bracket location, time and descriptive phrases between subject and verb.
Diagnostic question: Did a nearby noun attract the verb incorrectly? Reliable response: Trace the subject–verb link across the interruption.
6. Reread the full sentence
Restore every phrase and confirm meaning, tense and style.
Diagnostic question: Does the sentence still report a count or a group of members? Reliable response: Rewrite with total or several if clarity improves.
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: Changing total
Task. Choose: “The number of entries is/are increasing.”
Reasoning. The subject means the total count. The controlling idea is whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Use is.
Independent check. Replace the subject with “The total.” 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: Several entries
Task. Choose: “A number of entries is/are incomplete.”
Reasoning. A number of means several entries. The controlling idea is whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Use are.
Independent check. Replace it with “Several entries.” 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: Has or have
Task. Complete: “The number of errors ___ fallen.”
Reasoning. One quantity has fallen. The controlling idea is whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Use has.
Independent check. Do not let errors attract have. 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: Several have left
Task. Complete: “A number of visitors ___ left early.”
Reasoning. Several visitors performed the action. The controlling idea is whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Use have.
Independent check. The paraphrase “Several visitors have left” is natural. 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: Past agreement
Task. Choose: “The number of books was/were recorded.”
Reasoning. The count is one recorded figure. The controlling idea is whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Use was.
Independent check. Contrast “A number of books were missing.” 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: Question form
Task. Choose: “Has/Have the number of teams changed?”
Reasoning. The subject remains the singular total despite inversion. The controlling idea is whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Use Has.
Independent check. Turn it back into a statement. 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: Long interruption
Task. Edit: “The number of pupils in the two afternoon classes are rising.”
Reasoning. The added location phrase does not change the singular head number. The controlling idea is whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. The number of pupils in the two afternoon classes is rising.
Independent check. Use “the total is rising.” 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: Clear rewrite
Task. A number of participants are waiting sounds formal in context.
Reasoning. Several participants are waiting carries the same intended plural meaning. The controlling idea is whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of. This prevents a learner from choosing an answer merely because one word, number or observation resembles a remembered example.
Answer. Either can be correct; choose the clearer form for the audience.
Independent check. Agreement remains plural. 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: The number is
Case. The number of chairs is sufficient.
Analysis. One total is evaluated. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Replace with total. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 2: A number are
Case. A number of chairs are broken.
Analysis. Several individual chairs have the property. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Replace with several. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 3: The number has
Case. The number of responses has doubled.
Analysis. One count changed. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. State the earlier and later totals. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 4: A number have
Case. A number of responses have been removed.
Analysis. Several responses underwent removal. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Name the members. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 5: Was recorded
Case. The number of absences was recorded.
Analysis. The figure was recorded. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Contrast absent pupils. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 6: Were absent
Case. A number of pupils were absent.
Analysis. Several pupils were absent. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Use were correctly. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 7: Nearest noun trap
Case. The number of boxes is small.
Analysis. Boxes is plural but sits inside an of-phrase. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Circle the head noun. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 8: Quantifier reading
Case. A number of boxes are open.
Analysis. A number of functions like several. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Test substitution. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 9: Exact figure
Case. The number of votes is 240.
Analysis. A single numerical total follows. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Ask “What is the number?” State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 10: Unspecified members
Case. A number of voters are undecided.
Analysis. The members, not one count, are undecided. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Ask “Who is undecided?” State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 11: Question inversion
Case. Has the number changed?
Analysis. The auxiliary moves before the singular subject. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Restore the ordinary statement before choosing has or have. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 12: Plural question
Case. Have a number of files disappeared?
Analysis. Several files are the implied actors. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Rewrite it as a statement and identify the several files. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 13: There construction
Case. There are a number of reasons.
Analysis. The construction presents several reasons; direct wording may be clearer. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Rewrite as “Several reasons exist.” State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 14: One numeral
Case. A number is printed on the ticket.
Analysis. This is one unspecified numeral, not the quantifier a number of. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Identify the complete noun phrase. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 15: Numbers plural
Case. The numbers on the tickets are unclear.
Analysis. Numbers itself is plural. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Do not confuse it with the idiom. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 16: Large number
Case. A large number of pupils are attending.
Analysis. The expression still means many pupils. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Replace with many. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 17: Total emphasis
Case. The large number of pupils is surprising.
Analysis. The size of one total is surprising. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Explain the change in article. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 18: Style
Case. Several may be clearer than a number of in concise prose.
Analysis. Grammar and reader clarity can align. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Rewrite an example. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 19: Tense
Case. Agreement persists across present, past and perfect forms.
Analysis. The controlling meaning does not change with time. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Create three tenses. State the conclusion in one precise sentence, then add one sentence that names the evidence or relationship that makes it valid.
Deepening case 20: Final audit
Case. Article, paraphrase, head meaning, finite verb, interruption and full-sentence sense complete the check.
Analysis. Each catches a different attraction error. Notice that the answer depends on whether the grammatical subject is the single quantity called the number or the several people or things represented by a number of; changing a decorative detail would not be enough to change the reasoning.
Challenge. Audit five sentences. 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: Plural noun always controls
What the learner may think. Pupils or errors is plural, so the verb must be plural.
Why it fails. In the number of, the subject is the singular count. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Replace the subject with the total. Use this short test immediately: Would total take is?
Misconception 2: Number is always singular
What the learner may think. Any phrase containing number takes a singular verb.
Why it fails. A number of functions as a plural quantifier meaning several. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Test the several paraphrase. Use this short test immediately: Who performs the action?
Misconception 3: The articles are decorative
What the learner may think. Changing the to a does not affect grammar.
Why it fails. The article changes both meaning and agreement. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Circle the determiner first. Use this short test immediately: One total or several members?
Misconception 4: Nearest verb test
What the learner may think. Choose the form that sounds closest to the plural noun.
Why it fails. Sound can be pulled by attraction. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Trace the head meaning to the finite verb. Use this short test immediately: What is the core sentence?
Misconception 5: Questions use a new rule
What the learner may think. Inversion makes plural agreement safer.
Why it fails. The same subject controls agreement after the auxiliary moves. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Restore statement order. Use this short test immediately: Has or have after restoration?
Misconception 6: Never rewrite
What the learner may think. The idiom must be kept even if the sentence is dense.
Why it fails. Several or the total may communicate more clearly. The error feels efficient because it removes a decision, but it also removes the evidence boundary that makes the answer valid.
Targeted repair. Preserve meaning while simplifying. Use this short test immediately: Which paraphrase fits?
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: Recognition
Question. Choose: “The number of pages is/are fixed.”
Explained answer. Use is.
Why this answer earns trust. The subject is one total count. Transfer variation: Replace with “The total.”
Practice 2: Quantifier
Question. Choose: “A number of pages is/are missing.”
Explained answer. Use are.
Why this answer earns trust. The phrase means several pages. Transfer variation: Replace with several.
Practice 3: Perfect tense
Question. Complete: “The number of complaints ___ decreased.”
Explained answer. Use has decreased.
Why this answer earns trust. One figure changed. Transfer variation: Contrast several complaints.
Practice 4: Members
Question. Complete: “A number of players ___ improved.”
Explained answer. Use have improved.
Why this answer earns trust. Several players performed the action. Transfer variation: Name two possible players.
Practice 5: Interruption
Question. Correct: “The number of chairs in both rooms are enough.”
Explained answer. The number of chairs in both rooms is enough.
Why this answer earns trust. The location phrase does not change the singular total. Transfer variation: Rewrite with total.
Practice 6: Question
Question. Choose: “Has/Have the number of entries changed?”
Explained answer. Use Has.
Why this answer earns trust. Inversion does not change the singular subject. Transfer variation: Turn it into a statement.
Practice 7: Meaning contrast
Question. Explain the difference between “The number of errors is small” and “A number of errors are serious.”
Explained answer. The first evaluates one count; the second describes several errors.
Why this answer earns trust. Article and meaning control agreement. Transfer variation: Write a new pair.
Practice 8: Style
Question. Rewrite “A number of pupils are waiting” more directly.
Explained answer. Several pupils are waiting.
Why this answer earns trust. The meaning and plural agreement remain. Transfer variation: Keep the original in formal style.
Practice 9: Rule recall
Question. State the two paraphrases.
Explained answer. The number of means the total and takes singular agreement; a number of means several and takes plural agreement.
Why this answer earns trust. The paraphrases expose structure. Transfer variation: Recall after two days.
Practice 10: Transfer
Question. Edit a paragraph containing the number of, a number of, a large number of and the large number of.
Explained answer. Every verb matches one total or several members as intended.
Why this answer earns trust. Mixed practice prevents surface guessing. Transfer variation: Explain each article.
Delayed transfer: prove that the learning lasts
Transfer test 1: Meaning sort
Sort twenty subjects into total-count and several-member readings before seeing the verbs. 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 classification includes a total or several paraphrase. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter.
Transfer test 2: Delayed editing
After one week, repair agreement in questions and long interrupted subjects. 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 identifies article, finite verb and controlling meaning independently. If the criterion is not met, return to the smallest missing decision rather than repeating the entire chapter.
Transfer test 3: Own contrasts
Write four paired sentences that change only the article and verb. 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 pair changes meaning clearly without copying the article examples. 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 “Can you replace this with the total or with several?” before discussing the verb. Meaning first makes the grammar durable.
Use questions and long of-phrases only after the short contrast is secure. The purpose is to resist attraction, not to create unnecessary confusion.
Accept a clear rewrite with several when it preserves the intended meaning. Strong editing includes choosing a simpler structure.
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 is “the number of pupils” singular?
It refers to one total count, so the head idea is singular.
Why is “a number of pupils” plural?
It functions as a quantifier meaning several pupils.
Does the plural noun after of control the verb?
Not for the number of; the singular count controls agreement. In a number of, the phrase refers to several members.
What happens in a question?
The same rule applies even when the auxiliary moves before the subject.
Can I replace a number of?
Yes. Several is often a clear equivalent.
What is the fastest test?
Substitute the total for the number of, and substitute several for a number of; then match the verb to that meaning.
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 English 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.