Die Lehrerin erklärt allen Kindern die Aufgabe.

Die Lehrerin is the subject of the sentence — the person doing the action.

• die = the
• Lehrerin = female teacher

In this sentence, Die Lehrerin is in the nominative case, because she is the one who explains something.

German uses different articles depending on gender, number, and case, so die here is not just random — it matches the feminine noun Lehrerin in the nominative.

German often uses -in to form a specifically female job title or person noun.

• der Lehrer = the male teacher / teacher
• die Lehrerin = the female teacher

So Lehrerin tells you the teacher is female.

The plural is:

• die Lehrer = teachers (mixed group or masculine)
• die Lehrerinnen = female teachers

The verb is erklären = to explain.

Here it appears as erklärt because the subject is Die Lehrerin, which is third person singular: she explains.

Present tense of erklären:

• ich erkläre
• du erklärst
• er/sie/es erklärt
• wir erklären
• ihr erklärt
• sie/Sie erklären

So Die Lehrerin erklärt ... means The teacher explains ...

Also, German main clauses usually put the conjugated verb in second position, which is exactly what happens here.

Because erklären can take two objects:

• the person who receives the explanation
• the thing being explained

In this sentence:

• allen Kindern = to all the children → dative object
• die Aufgabe = the task/exercise → accusative object

So the structure is:

Die Lehrerin
erklärt
allen Kindern
die Aufgabe

= The teacher explains the task to all the children.

German often expresses to someone without using a separate word like to. Instead, it uses the dative case.

Because this phrase is in the dative plural.

The verb erklären takes the person receiving the explanation in the dative:

• jemandem etwas erklären = to explain something to someone

So:

• alle Kinder would be nominative or accusative plural
• allen Kindern is dative plural

There are two important changes here:

1. alle becomes allen in the dative plural
2. Kinder becomes Kindern — many masculine, feminine, and neuter nouns add -n in the dative plural if they do not already have one

So:

• nominative: alle Kinder
• dative: allen Kindern

Because die Aufgabe is the accusative object, and Aufgabe is a feminine noun.

For feminine singular nouns, the definite article is:

• nominative: die
• accusative: die
• dative: der
• genitive: der

So in this sentence:

• die Aufgabe is accusative
• that is why the article stays die

This is often confusing at first, because feminine nouns do not change from nominative to accusative in the article.

You know from the verb pattern and the article/endings.

With erklären, the usual pattern is:

• someone in the dative
• something in the accusative

In this sentence:

• allen Kindern has the clear dative plural ending
• die Aufgabe is the accusative object

A useful dictionary-style pattern is:

• jemandem etwas erklären

This means:

• jemandem = to someone → dative
• etwas = something → accusative

Learning verbs together with their case patterns is very helpful in German.

That is a very normal German word order when both objects are full noun phrases:

• dative object first
• accusative object second

So:

• Die Lehrerin erklärt allen Kindern die Aufgabe.

sounds natural and standard.

German word order can change for emphasis, though. You could also say:

• Die Lehrerin erklärt die Aufgabe allen Kindern.

That is still grammatical, but the emphasis feels a bit different.

A very common rule of thumb is:

• pronouns tend to come earlier
• if both objects are nouns, dative often comes before accusative

Yes, functionally it does.

English usually needs the preposition to:

• The teacher explains the task to all the children.

German often does not use a separate preposition here. Instead, the dative case itself shows that meaning:

• allen Kindern = to all the children

So when you see a dative noun phrase after verbs like geben, zeigen, erklären, sagen, it often corresponds to English to someone.

Because in German, all nouns are capitalized.

So:

• die Lehrerin
• die Kinder
• die Aufgabe

all begin with capital letters because they are nouns.

This is a general spelling rule in German, not something special about this sentence.

Yes — the best translation depends on context.

Aufgabe is a broad word and can mean:

• task
• exercise
• assignment
• problem or question in schoolwork

In a classroom sentence like this, die Aufgabe often means:

• the exercise
• the task
• the assignment

So you should choose the English word that fits the situation best.