Learn Hardcore German: Die Kinder malen Gesichter auf jeden Luftballon, während wir die Tischdecke glatt ziehen. - The children draw faces on every balloon while we smooth out the tablecloth.

Luftballon is masculine: der Luftballon.
In the sentence, it is in the accusative singular because it follows the preposition auf expressing a direction/result (painting something onto a surface).

Masculine definite/indefinite articles and jeder in the accusative singular are:

der → den
ein → einen
jeder → jeden

So you get auf jeden Luftballon, not auf jeder Luftballon (which would be dative).

Why is the preposition auf followed by the accusative here?

Auf is a two-way preposition (Wechselpräposition). It takes:

dative for location (where something is),
accusative for direction or a change of state (where something is put / what something becomes).

Here, malen Gesichter auf jeden Luftballon describes an action that changes the state of the balloon (it becomes painted). This is treated like a direction/result, so we use the accusative: auf jeden Luftballon, not auf jedem Luftballon.

Compare:

Die Gesichter sind auf jedem Luftballon. (location → dative)
Die Kinder malen Gesichter auf jeden Luftballon. (resulting state → accusative)

Why is Gesichter plural when it says auf jeden Luftballon (each balloon)?

The plural Gesichter is used because more than one face is being painted in total. The sentence focuses on all the painting activity, not on “one face per balloon”.

Possible interpretations:

Each balloon gets one face → total faces = number of balloons.
Some balloons might get several faces.

German often uses the plural for the object of an ongoing action when it’s done repeatedly:

Die Kinder malen Bilder auf jedes Blatt. (They paint pictures on each sheet.)
Die Schüler schreiben Sätze auf jede Karte. (They write sentences on each card.)

You could say ein Gesicht auf jeden Luftballon to stress exactly one face per balloon, but the original is more general.

What is the role of während in this sentence?

Here während is a subordinating conjunction meaning while (indicating simultaneous actions).

Main clause: Die Kinder malen Gesichter auf jeden Luftballon,
Subordinate clause: während wir die Tischdecke glatt ziehen.

As a subordinating conjunction, während sends the finite verb to the end of its clause:

während wir die Tischdecke glatt ziehen

Während can also mean whereas (contrast) in other contexts, but here it clearly expresses that the two actions happen at the same time.

Why is the verb at the end in während wir die Tischdecke glatt ziehen?

Because während introduces a subordinate clause (Nebensatz). In German subordinate clauses, the conjugated verb always goes to the end of the clause.

Structure:

während (conjunction)
wir (subject)
die Tischdecke (object)
glatt ziehen (verb complex, at the end)

So we get: während wir die Tischdecke glatt ziehen.

In the main clause, the verb is in the second position:

Die Kinder malen Gesichter …

What kind of verb is glatt ziehen, and why is it written as two words here?

Glattziehen is a separable verb (trennbares Verb), built from:

ziehen (to pull),
glatt (smooth).

The basic meaning is to smooth out (by pulling).
In dictionaries you will see it as glattziehen (one word, infinitive). When conjugated in a main clause, the prefix separates:

Wir ziehen die Tischdecke glatt.

In a subordinate clause or infinitive construction, the parts come together at the end:

…, während wir die Tischdecke glatt ziehen.
Wir wollen die Tischdecke glattziehen.

So it’s one lexical unit, but its parts move depending on clause type.

Why is it die Tischdecke and not some other article or case form?

Tischdecke is feminine: die Tischdecke (the tablecloth).

In wir ziehen die Tischdecke glatt, die Tischdecke is the direct object of ziehen, so it is in the accusative singular.

Feminine nouns have die in both nominative and accusative singular, so:

Nominative: die Tischdecke liegt auf dem Tisch.
Accusative: wir ziehen die Tischdecke glatt.

Could you also say während wir die Tischdecke glätten instead of glatt ziehen?

Yes, but the nuance changes slightly.

glatt ziehen sounds more concrete and physical: you are literally pulling and smoothing the cloth with your hands.
glätten is more general “to make smooth” and can be a bit more neutral/formal (e.g. ironing a shirt: ein Hemd glätten).

Both are grammatically correct here; glatt ziehen fits very naturally when talking about a tablecloth being straightened by hand.

Can the order of the two clauses be reversed?

Yes. You can put the während-clause first. Then the main clause verb must still be in second position, which causes inversion:

Original: Die Kinder malen Gesichter auf jeden Luftballon, während wir die Tischdecke glatt ziehen.
Alternative: Während wir die Tischdecke glatt ziehen, malen die Kinder Gesichter auf jeden Luftballon.

Both versions are correct and natural. The choice depends on what you want to emphasize first.

Is the comma before während obligatory?

Yes. Während introduces a subordinate clause, so German spelling rules require a comma before it.

Die Kinder malen Gesichter auf jeden Luftballon, während wir die Tischdecke glatt ziehen.

If the während-clause comes first, you also need a comma at its end:

Während wir die Tischdecke glatt ziehen, malen die Kinder Gesichter auf jeden Luftballon.

Why is the present tense used here instead of something like “are painting” or “are pulling”?

German does not have a special grammatical progressive form like English am/are/is doing. The simple present covers:

general present,
habits,
and ongoing actions.

So:

Die Kinder malen Gesichter … can mean The children are painting faces … (right now).
Wir ziehen die Tischdecke glatt. can mean We are straightening the tablecloth.

Context tells you whether it’s a current, ongoing action or a general statement.

What is the difference between Luftballon and just Ballon?

Luftballon specifically means a party balloon / balloon filled with air or helium, the small ones used for decoration or children’s toys.
Ballon by itself is more general and often refers to a large balloon, for example:
- Heißluftballon (hot-air balloon),
- a big decorative balloon.

In everyday speech, Luftballon is the normal word for the kind of balloons children paint faces on, so it fits this context best.