Die Lehrerin legt die Kreide auf den Tisch.

In German, all nouns are capitalized, not just proper names.

So in this sentence:

• Lehrerin = teacher
• Kreide = chalk
• Tisch = table

That is a standard spelling rule in German.

The ending -in usually marks a female person in German.

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

The sentence uses Lehrerin, so it specifically means a female teacher.

Because both nouns are feminine singular.

• die Lehrerin is feminine
• die Kreide is also feminine

In German, the article depends on the noun’s gender, number, and case.

Here:

• die Lehrerin is nominative feminine singular because it is the subject
• die Kreide is accusative feminine singular because it is the direct object

A useful thing to notice: for feminine singular nouns, the article is die in both nominative and accusative. So even though the grammatical role changes, the article looks the same.

Because Tisch is a masculine noun, and here it is in the accusative case.

• nominative: der Tisch
• accusative: den Tisch

The phrase auf den Tisch shows movement toward the table, so German uses the accusative there.

This is one of the most important article changes to learn:

• der → den for masculine singular in the accusative

Because auf is a two-way preposition (Wechselpräposition). These prepositions can take either:

• accusative for direction / movement toward a place
• dative for location / position in a place

Here, the chalk is being put onto the table, so there is movement to a destination:

• auf den Tisch = onto the table

If the chalk were already there and you were just describing its location, you would say:

• auf dem Tisch = on the table

So the contrast is:

• Die Lehrerin legt die Kreide auf den Tisch. = The teacher puts the chalk onto the table.
• Die Kreide liegt auf dem Tisch. = The chalk is lying on the table.

Because the subject is die Lehrerin, which is third person singular: she.

The verb legen is the infinitive, meaning to lay / put. In the present tense, it changes like this:

• ich lege
• du legst
• er/sie/es legt
• wir legen
• ihr legt
• sie/Sie legen

So with die Lehrerin = she, the correct form is legt.

In a normal German main clause, the finite verb usually comes in second position. This is often called the V2 rule.

In this sentence:

• Die Lehrerin = first element
• legt = second element
• die Kreide auf den Tisch = the rest

So the structure is: Subject + verb + other parts

German can move other elements to the front too, but the finite verb still stays in second position. For example:

• Die Lehrerin legt die Kreide auf den Tisch.
• Auf den Tisch legt die Lehrerin die Kreide.

Both are grammatical, but the second one emphasizes auf den Tisch.

Because it is the direct object of the verb legen.

Ask yourself: what is the teacher putting?

• She is putting the chalk

That makes die Kreide the thing directly affected by the action, so it goes in the accusative case.

In this sentence:

• Die Lehrerin = subject, nominative
• die Kreide = direct object, accusative
• auf den Tisch = prepositional phrase showing destination

This is a very common question.

• legen = to lay / put something somewhere
  
  • transitive: it takes an object
• liegen = to lie / be lying
  
  • intransitive: it does not take a direct object

So:

• Die Lehrerin legt die Kreide auf den Tisch.
  The teacher puts the chalk onto the table.

• Die Kreide liegt auf dem Tisch.
  The chalk is lying on the table.

A useful pattern:

• legen = action of placing something
• liegen = resulting position

Yes, but the meaning would change.

• auf den Tisch = onto the table, with movement toward it
• auf dem Tisch = on the table, location only

So compare:

• Die Lehrerin legt die Kreide auf den Tisch.
  She puts the chalk onto the table.

• Die Lehrerin legt die Kreide auf dem Tisch.
  This would normally sound wrong for the intended meaning, because legen describes placing something somewhere, so German expects the destination with accusative.

If you want location, you usually use a different sentence, such as:

• Die Kreide liegt auf dem Tisch.

German often chooses different verbs depending on the object’s position.

• legen = to lay something down, so it ends up lying
• stellen = to stand something up, so it ends up standing
• setzen = to set someone/something into a sitting position

With Kreide (chalk), the natural idea is that it is placed so that it lies on the table, not stands upright. So legt is the normal choice.

That is why:

• Die Lehrerin legt die Kreide auf den Tisch. sounds natural.

Here it is singular: the chalk.

German Kreide is usually an uncountable or mass noun in many contexts, similar to English chalk. But depending on context, it can also refer to a piece of chalk.

The article die here does not mean plural, because:

• the verb is singular: legt
• the meaning is one item or chalk as a substance/object

So in this sentence, learners should understand die Kreide as singular feminine.

A helpful breakdown is:

• Die Lehrerin = subject
• legt = verb
• die Kreide = direct object
• auf den Tisch = prepositional phrase showing where the object is being put

So the pattern is:

Subject + verb + object + place/destination

That is a very common German sentence pattern.