Learn Hardcore Chinese: zhè gè lǎoshī zài jiā.

Correct: 这(个/位)老师在家。
Incorrect: 这(个/位)老师是家。 You can use 是 only in special emphasis patterns:
Contrastive focus: 他是在家 (He IS at home, not elsewhere).
The past-focus pattern 是…的: 他是在家里的 (used to emphasize where a past event/state held), not for a neutral present description.

Is 在 here a verb or a preposition?

Functionally it’s the main predicate meaning “to be located at.” Many grammars call it a “coverb,” but you can think of 老师在家 as Subject + Verb + Place.

Do I need the measure word 个 after 这?

Yes. With demonstratives (这/那) and countable nouns, you normally insert a classifier:

Standard: 这个老师
More polite: 这位老师 Using 这老师 without a classifier is colloquial in some regions; stick with a classifier in standard Mandarin.

Can I use 位 (or 名) instead of 个 here?

个: neutral, everyday.
位: respectful/polite for people; very natural with teachers: 这位老师.
名: formal/written, often with numbers (e.g., 三名老师). 这名老师 appears in news-style writing; in conversation it can sound stiff.

How do I pronounce 这个? Is 个 neutral here?

Yes, 个 is typically neutral tone in 这个: say “zhè ge.” Many speakers link it as “zhège.” A common colloquial variant pronounces 这 as “zhèi” before a classifier: zhèi ge. All are acceptable.

Is the sentence singular or plural?

Singular. 这 + classifier refers to one. For plural, use:

这些老师在家。
老师们在家。 Do not say 这个老师们 (mismatch of singular demonstrative and plural noun).

How do I turn it into a yes–no question?

Add 吗: 这位老师在家吗？
Use A‑not‑A: 这位老师在不在家？
Very casual speech may use rising intonation, but 吗 is the standard way.

How do I negate it?

这位老师不在家。 Pronunciation tip: 不 changes to second tone before fourth tones, so say bú zài.

Should there be 的 between 这 and 老师?

No. With demonstratives or numerals + classifier, don’t insert 的: 这个老师. Use 的 only when there’s an additional descriptive phrase: 这个新来的老师在家。

What’s the difference between 在家 and 在家里?

Both are natural. 在家 is slightly more general; 在家里 can emphasize “inside the home.” In most contexts they’re interchangeable. The same pattern holds for many places: 在学校/在学校里.

Can I drop 个 and say 这老师在家?

You might hear it in colloquial northern speech, but in standard Mandarin you should keep the classifier. If you want respectful tone, prefer 这位老师.

Where do time words go in this kind of sentence?

Typical order is Subject + Time + Location/Predicate:

这位老师今天在家。 If there’s also an action, put the location before the verb:
这位老师今天在家工作。 You can front the time for emphasis: 今天这位老师在家。

Is this 在 the same 在 used for the progressive (ongoing action)?

They’re related but used differently:

Progressive: 在 + Verb (e.g., 老师在看书 = is reading).
Locative: 在 + Place (e.g., 老师在家 = is at home). You can combine them: 老师在家看书; add 正在 for stronger “right now”: 老师正在家里看书.

Does 在家 mean “at one’s own home”? How do I say “at someone else’s home”?

Yes, 在家 means “at (the subject’s) home.” To specify another person’s home, add a possessor:

在他家/在她家/在王老师家。 在我的家 is possible for emphasis, but 在我家 is more natural.

Can I add 呢 at the end?

Yes: 这位老师在家呢。 呢 softens the tone and highlights a current, continuous state—often as an answer or when contrasting with another possibility.

How do I say “that teacher” instead?

Change the demonstrative:

那位老师在家。 Plural: 那些老师在家。

If I want to add a verb like “work,” where does it go?

Put the location before the verb:

这位老师在家工作。 Avoid 这位老师工作在家 in ordinary speech; it sounds unnatural unless used in special emphasis or formal written styles.

Why isn’t there an article like “the/a” before 老师?

Chinese has no articles. Demonstratives and classifiers handle specificity and number: 这个老师 = “this teacher.” A bare 老师 can be generic, definite, or plural depending on context.