Learn Hardcore Chinese: nà gè lǎoshī jīntiān tài máng le.

位 (wèi): more polite/respectful. Example: 那位老师…
名 (míng): often for professionals or in written style. Example: 那名老师… All are grammatical; 个 is the most casual.

Do I always need a measure word here? Is 那老师 okay?

In standard modern Mandarin, use a measure word: 那个老师/那位老师. 那老师 can appear in colloquial speech when 老师 functions like a title of address (“that Teacher [X]”), but in careful speech and writing, include the measure word.

What does the sentence-final 了 (le) do here? Is it past tense?

Here 了 is the sentence-final particle in the pattern 太 + Adj + 了, signaling a strong degree/exclamation. It’s not a past-tense marker. Contrast:

Aspect 了 after a verb: 他今天吃了饭 (completed action).
Sentence-final 了 with 太…了: 他今天太忙了 (so/too busy; strong emphasis).

Can I say 太忙 without 了?

Normally you keep 了: 太忙了 is the standard pattern. 太忙 alone often sounds abrupt or incomplete unless it’s part of a larger structure (e.g., 太忙，没时间去) or a very colloquial exclamation. For milder degree, use 很忙/挺忙.

Why is there no 是 (shì) before 忙?

Adjectives in Chinese can directly serve as predicates (they behave like stative verbs). You don’t use 是 before them. Say 他很忙/他太忙了, not 他是忙. Use 是 to link nouns: 他是老师.

What’s the nuance of 太 vs 很/非常/特别?

太…了: very strong, exclamatory; can imply “excessive,” though in daily speech it often just means “so/very.”
很忙: neutral “very busy.”
非常忙: stronger, slightly more formal “extremely busy.”
特别忙/挺忙的: colloquial; 特别 = “especially,” 挺…的 = “quite.”

Where should 今天 go? Is 今天那个老师… okay?

Time words usually go before the predicate, either at the start or after the subject. Both are fine:

那个老师今天太忙了 (subject first)
今天那个老师太忙了 (time first) They’re both grammatical; the difference is emphasis.

How do I turn this into a question?

Yes–no with 吗: 那个老师今天太忙了吗？
A-not-A: 那个老师今天忙不忙？
Confirmation with 是不是: 那个老师今天是不是太忙了？

How do I negate it naturally?

Use 不, often with 太 to soften:

那个老师今天不忙。 (not busy)
那个老师今天不太忙。 (not very busy; most natural) Avoid 太不忙 in neutral statements.

How do I say “those teachers …”?

Use the plural demonstrative:

那些老师今天太忙了。

Is 老师 a noun or a form of address? Can I add a surname?

Both. 老师 is a profession and also a respectful form of address. You can add a surname:

那位李老师今天太忙了。 (That Teacher Li…)

Pronunciation tips for this sentence?

那个: often pronounced nèi ge in colloquial speech; 个 is usually neutral tone (ge).
老师: lǎoshī (3rd + 1st).
今天: jīntiān (1st + 1st).
太: tài (4th).
忙: máng (2nd).
了: le (neutral). Both nà ge and nèi ge are heard.

I’ve heard 那个 used as a filler (“um”). Is that the same word?

Yes. Speakers often use 那个 (nèige) as a hesitation filler. It’s the same word, just stretched or repeated. Be cautious using it around English speakers as it can be misheard; try other fillers like 嗯 (èn/ǹg) in formal settings.

Could I say 很忙了? What does that mean?

很忙了 is grammatical but implies a change of state (“already very busy now,” compared to before). 太忙了 is an exclamatory intensifier, not mainly about change.

Why isn’t there a 的 between 那个 and 老师?

Demonstratives (这/那/这些/那些) + measure word go directly before the noun: 那个老师. Use 的 when a descriptive phrase modifies the noun:

那个很忙的老师… (“that teacher who is very busy…”)

Is 忙 an adjective or a verb? Can I say 我在忙?

忙 behaves like a stative verb/adjective. Predicate uses: 我很忙/我太忙了. Progressive activity: 我在忙 (“I’m busy [right now]”) is natural.

Can I drop 今天 if the time is obvious?

Yes. If context makes the time clear, 那个老师太忙了 is fine. You can swap 今天 for other time words (昨天/明天/下午/现在).

Any alternative emphatics similar to 太…了?

Yes:

忙死了 (“busy to death”; very colloquial)
忙极了 (“extremely busy”; a bit literary)
可忙了 (“so busy”; northern colloquial) All convey strong emphasis like 太忙了.