Im Wörterheft schreibe ich zu jedem Adjektiv ein Beispiel in der Einzahl und eins in der Mehrzahl.

Im is a contraction of in dem.

• in dem Wörterheft → im Wörterheft

This is very common in German, especially with in + dem. It works like English contractions such as do not → don't, except it is even more standard in everyday German.

Here, dem is used because Wörterheft is neuter: das Wörterheft.

Wörterheft is a compound noun:

• Wörter = words
• Heft = notebook / exercise book

So Wörterheft means something like vocabulary notebook or word notebook.

German often combines nouns into one word, so long compounds are very normal.

Because the sentence describes location, not movement.

German uses different cases after in:

• in + accusative for movement into something
• in + dative for being in something

Here the meaning is I write in the vocabulary notebook, meaning the writing happens there. That is location, so German uses the dative:

• in dem Wörterheft → im Wörterheft

If it meant movement, it would be something like:

• Ich lege das Blatt in das Heft. = I put the sheet into the notebook.

German main clauses usually follow the V2 rule: the finite verb must be in the second position.

So in this sentence:

• Im Wörterheft = first position
• schreibe = second position
• ich comes after the verb

That is why it is:

• Im Wörterheft schreibe ich ...

and not:

• Im Wörterheft ich schreibe ...

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

Zu jedem Adjektiv means for each adjective or for every adjective in this context.

Breaking it down:

• zu = to / for / concerning, depending on context
• jedem = every / each (dative form)
• Adjektiv = adjective

In this sentence, zu is being used in a sense like for or for each:

• zu jedem Adjektiv ein Beispiel schreiben = to write an example for each adjective

This is a common use of zu with notes, comments, examples, explanations, etc.

Because the preposition zu always takes the dative case.

So:

• das Adjektiv = nominative
• zu dem Adjektiv = dative
• zu jedem Adjektiv = to/for each adjective

The form jedem is the dative singular form of jeder with a neuter noun.

A quick pattern:

• masculine dative singular: jedem Mann
• neuter dative singular: jedem Adjektiv
• feminine dative singular: jeder Frau

Because eins here stands for ein Beispiel.

So the sentence means:

• ein Beispiel in der Einzahl und eins in der Mehrzahl
• one example in the singular and one in the plural

Instead of repeating ein Beispiel twice, German often replaces it with eins.

You can think of it as:

• ... one example in the singular and one in the plural

Here, eins is being used like one standing on its own.

When one stands alone as a pronoun, German usually uses eins.

Compare:

• ein Beispiel = an example / one example
  
  • here ein is directly before a noun
• eins = one
  
  • here it stands alone

So:

• Ich schreibe ein Beispiel.
• Ich schreibe eins.

That is why the sentence has:

• ein Beispiel ... und eins ...

They are the grammatical terms for singular and plural.

• die Einzahl = singular
• die Mehrzahl = plural

Literally:

• Einzahl = one-number
• Mehrzahl = multiple-number

You may also see:

• Singular
• Plural

Both sets of terms are used in German grammar explanations.

Because both Einzahl and Mehrzahl are feminine nouns:

• die Einzahl
• die Mehrzahl

After in with a location/state meaning, German uses the dative. The dative singular feminine article is der.

So:

• in der Einzahl
• in der Mehrzahl

This is similar to saying:

• in the singular
• in the plural

These are fixed grammar expressions.

Because this is a single main clause with coordinated elements, not separate clauses that require a comma.

The phrase:

• ein Beispiel in der Einzahl und eins in der Mehrzahl

just connects two parallel noun phrases with und:

• ein Beispiel ...
• eins ...

German normally does not use a comma before und in a simple structure like this.

Yes. German word order is flexible, as long as the verb stays in second position in a main clause.

For example, these are possible:

• Im Wörterheft schreibe ich zu jedem Adjektiv ein Beispiel in der Einzahl und eins in der Mehrzahl.
• Zu jedem Adjektiv schreibe ich im Wörterheft ein Beispiel in der Einzahl und eins in der Mehrzahl.
• Ich schreibe im Wörterheft zu jedem Adjektiv ein Beispiel in der Einzahl und eins in der Mehrzahl.

The meaning stays very similar, but the emphasis shifts slightly depending on what comes first.

Because Adjektiv is a noun here, not an adjective used to describe another noun.

It is the dictionary word das Adjektiv = adjective.

In the sentence:

• zu jedem Adjektiv

it is singular, so there is no plural ending. It is also in the dative singular after zu, but many neuter nouns like Adjektiv do not change their basic form in the dative singular.

So:

• nominative: das Adjektiv
• dative: dem Adjektiv

The article changes clearly; the noun itself stays the same.

Very natural, but a bit different from the most direct English structure.

A literal breakdown would be something like:

• In the vocabulary notebook write I for each adjective an example in the singular and one in the plural.

Natural English would say:

• In my vocabulary notebook, I write an example in the singular and one in the plural for each adjective.

So German is using:

• zu jedem Adjektiv = for each adjective

That structure is common and natural in German, even if English might place the phrase later.