Der Lehrer nickt kurz, seufzt dann leise und sagt, dass wir weitermachen sollen.

Because der Lehrer is third-person singular: he.

The verb nicken becomes:

• ich nicke
• du nickst
• er/sie/es nickt
• wir nicken
• ihr nickt
• sie/Sie nicken

So Der Lehrer nickt means the teacher nods.

The same pattern appears with:

• seufzt from seufzen
• sagt from sagen

All three verbs agree with the same subject, der Lehrer.

Because German, like English, does not need to repeat the subject when the same subject continues across coordinated verbs.

So:

• Der Lehrer nickt kurz, seufzt dann leise und sagt ...

means:

• The teacher nods briefly, then sighs softly and says ...

It would be unnecessary to repeat der Lehrer before each verb unless you wanted special emphasis.

They are adverbs.

• kurz = briefly / for a moment
• dann = then
• leise = quietly / softly

They describe how or when the actions happen:

• nickt kurz = nods briefly
• seufzt dann leise = then sighs softly

Their placement is natural German word order, but it is not always translated word-for-word into English.

dass means that and introduces a subordinate clause.

Here:

• ... und sagt, dass wir weitermachen sollen.

This means:

• ... and says that we should continue.

German often uses dass in places where English sometimes keeps that and sometimes leaves it out.

Compare:

• German: Er sagt, dass ...
• English: He says that ... / He says ...

In German, dass is very common and often required in this type of sentence.

Because dass creates a subordinate clause, and in German subordinate clauses the conjugated verb typically goes to the end.

So instead of:

• wir sollen weitermachen

you get:

• dass wir weitermachen sollen

This is one of the most important word-order rules in German.

A quick comparison:

• Main clause: Wir sollen weitermachen.
• Subordinate clause: ..., dass wir weitermachen sollen.

Because this clause contains:

• a main infinitive: weitermachen = to continue / to carry on
• a modal verb: sollen = should / are supposed to

With modal verbs, German often uses this structure:

• subject + infinitive + modal verb

So:

• wir weitermachen sollen

literally looks like:

• we continue should

but naturally means:

• we should continue

In a subordinate clause, both verbs move toward the end, with the infinitive before the modal.

Mostly yes, but sollen has a slightly broader range than English should.

It can mean:

• should
• are supposed to
• are meant to

In this sentence, the teacher is telling the group what they are expected to do next, so sollen suggests instruction or expectation.

So the idea is something like:

• that we should continue
• that we are supposed to continue

Both are reasonable depending on context.

Because weitermachen is a separable verb:

• weitermachen = to continue / to carry on

Its parts are:

• weiter = further / on
• machen = do / make

In some forms, the prefix separates:

• Wir machen weiter. = We continue.
• Der Lehrer sagt, dass wir weitermachen sollen.

In the infinitive, and before another verb like a modal, it stays together as weitermachen.

Because in German, subordinate clauses are separated by commas.

So:

• ..., sagt, dass wir weitermachen sollen.

The comma marks the start of the dass clause.

This is standard German punctuation and is much more obligatory than in English, where comma usage before that is usually different.

Because der Lehrer is the subject of the sentence — the person doing the actions:

• nickt
• seufzt
• sagt

Subjects are in the nominative case in German.

So:

• der Lehrer = nominative singular masculine

If the teacher were an object instead, the article might change, for example:

• Ich sehe den Lehrer. = I see the teacher.

But here the teacher is the subject, so it stays der Lehrer.