Learn Hardcore German: Der Bauer und die Bäuerin zeigen den Kindern stolz ihren neuen Traktor. - The farmer and the female farmer proudly show the children their new tractor.

Subject: der Bauer und die Bäuerin = they (two people).
In German, the verb must agree in number with the subject:
- er zeigt – he shows
- sie zeigt – she shows
- sie zeigen – they show

Since Bauer + Bäuerin = sie (plural), you must use zeigen.

Why is it den Kindern and not die Kinder?

Den Kindern is in the dative plural, because Kinder is the indirect object (the people to whom something is shown).

zeigen = to show something (direct object, accusative) to someone (indirect object, dative).
Pattern:
jemandem etwas zeigen = to show something to someone

In the sentence:

Direct object (accusative): ihren neuen Traktor
Indirect object (dative): den Kindern

Dative plural of die Kinder:

Nominative plural: die Kinder
Dative plural: den Kindern
(Most plural nouns add -n in the dative: den Kindern, mit den Freunden, bei den Eltern, etc.)

Why does Kinder get an extra -n in Kindern?

This is a regular dative plural ending.

Most plural nouns add -n in the dative:
- die Kinder → den Kindern
- die Freunde → den Freunden
- die Eltern → den Eltern (already ends in -n, so no extra -n)
- die Studenten → den Studenten (already ends in -n)

Rule of thumb:
In the dative plural, nouns normally end in -n, unless they already do.

Why is it ihren neuen Traktor and not ihr neuer Traktor?

Because Traktor is masculine accusative, and both ihr- and the adjective neu- must carry the accusative masculine ending -en.

Breakdown:

Traktor: masculine
Function in the sentence: direct object, so accusative
After a possessive (like ihr-, sein-, mein-), the endings work like after an ein-word.

Accusative masculine patterns with a possessive:

ihr
- -en → ihren
neu
- -en → neuen
Traktor stays the same

So you get: ihren neuen Traktor (their new tractor).

If Traktor were the subject (nominative masculine), it would be:

ihr neuer Traktor ist sehr groß.
(Their new tractor is very big.)

Does ihren mean “her” or “their” here?

In this sentence, ihren means “their”.

German ihr- is ambiguous without context:

ihr (singular feminine possessor) = her
- Das ist ihr Traktor. – That is her tractor.
ihr (plural possessor) = their
- Das ist ihr Traktor. – That is their tractor.

Here the owners are der Bauer und die Bäuerin (two people), so the possessor is they → their = ihr- in German.

The correct form ihren is simply ihr- with the accusative masculine ending -en.

Why is it neuen and not neu or neue?

Because neu is an adjective describing a masculine accusative noun after a possessive.

Pattern for adjectives after ein-/mein-/dein-/sein-/ihr- etc.:

Masculine nominative: ihr neuer Traktor
Masculine accusative: ihren neuen Traktor

In ihren neuen Traktor:

Traktor: masculine, accusative (direct object)
After a possessive, the adjective gets -en in this case:
- neuen Traktor

So neu → neuen here to match masculine accusative.

Why is stolz in the middle of the sentence? Can it go somewhere else?

Stolz is an adverb here (“proudly”), and German word order allows some flexibility.

Neutral, common order:

Der Bauer und die Bäuerin zeigen den Kindern stolz ihren neuen Traktor.

Other possible positions:

Der Bauer und die Bäuerin zeigen stolz den Kindern ihren neuen Traktor.
Stolz zeigen der Bauer und die Bäuerin den Kindern ihren neuen Traktor. (more emphatic, less neutral)
Der Bauer und die Bäuerin zeigen ihren neuen Traktor stolz den Kindern. (possible, but sounds a bit less natural)

General idea:
Adverbs like stolz typically go after the objects or between indirect and direct object, and speakers can move them to emphasize them.

Why is it Der Bauer und die Bäuerin and not just die Bauern?

Both are possible, but they are not exactly the same:

Der Bauer und die Bäuerin = The (male) farmer and the (female) farmer
→ explicitly one man + one woman.
die Bauern = the farmers (in general, plural), usually implies mixed or unknown gender.

If you say:

Die Bauern zeigen den Kindern stolz ihren neuen Traktor.
→ Some farmers (plural) show the children their new tractor; we don’t know or care about the exact genders.

The original sentence specifically highlights one man and one woman as a pair.

How is the feminine form Bäuerin formed from Bauer?

The feminine form Bäuerin is formed with two changes:

Add -in to make a feminine form of a job/role:
- der Lehrer → die Lehrerin
- der Arzt → die Ärztin
- der Student → die Studentin
Add an Umlaut to the vowel (where applicable):
- Bauer → Bäuerin (au → äu)
- Arzt → Ärztin (a → ä)

Plural forms:

Singular: die Bäuerin
Plural: die Bäuerinnen

What case is ihren neuen Traktor, and why?

Ihren neuen Traktor is in the accusative case because it is the direct object: the thing that is being shown.

Structure with zeigen:

jemand (subject, nominative)
zeigt (verb)
jemandem (indirect object, dative)
etwas (direct object, accusative)

In the sentence:

Subject (nominative): Der Bauer und die Bäuerin
Indirect object (dative): den Kindern
Direct object (accusative): ihren neuen Traktor

So ihren neuen Traktor must be accusative.

Why is Traktor capitalized?

In German, all nouns are capitalized, regardless of their position in the sentence.

der Traktor
die Kinder
der Bauer
die Bäuerin
der Stolz (noun) vs. stolz (adjective/adverb)

So Traktor, Bauer, Bäuerin, Kinder are capitalized simply because they are nouns.

How would the sentence change if only the male farmer showed the tractor?

Then the subject is singular masculine, so the verb and possessive change:

Der Bauer zeigt den Kindern stolz seinen neuen Traktor.

Changes:

zeigen → zeigt (because the subject is now singular)
ihren neuen Traktor → seinen neuen Traktor
(sein- = his; accusative masculine: seinen)

Grammar of the rest:

den Kindern stays dative plural
neuen Traktor stays accusative masculine with -en on the adjective.