Ten garnek jest duży, więc gotuję w nim zupę dla całej rodziny.

Because garnek is a masculine singular noun, and the demonstrative ten has to agree with it.

Polish demonstratives change for gender:

• ten = masculine
• ta = feminine
• to = neuter

So:

• ten garnek = this pot
• ta miska = this bowl
• to okno = this window

Agreement is very important in Polish.

Literally, ten means this.

Polish does not have articles like the or a/an, so sometimes English translations use the even when Polish uses no separate word for it. But in this sentence, ten garnek specifically points out a particular pot, so it is most naturally this pot.

Compare:

• Garnek jest duży. = The pot / A pot is big.
• Ten garnek jest duży. = This pot is big.

So ten adds emphasis or specificity.

Because it is the subject of the sentence, so it is in the nominative case.

In:

• Ten garnek jest duży

the thing being described is garnek, so nominative is used.

Its dictionary form is also garnek, so that is why it looks unchanged here.

Duży is the adjective big/large, and it has to agree with garnek in:

• gender: masculine
• number: singular
• case: nominative

Since garnek is masculine singular nominative, the adjective takes the matching form duży.

For comparison:

• ten garnek jest duży = this pot is big
• ta miska jest duża = this bowl is big
• to naczynie jest duże = this dish/container is big

Więc means so, therefore, or thus.

Here it connects the two ideas:

• Ten garnek jest duży
• więc gotuję w nim zupę...

So the logic is: the pot is big, so I cook soup in it.

In Polish, więc often appears after a comma, just like so in English:

• ..., więc ...

That placement is very natural.

Gotuję is the 1st person singular present tense form of gotować = to cook.

It means:

• I cook
• I am cooking

depending on context.

Why not the others?

• gotowałam = I was cooking / I cooked (female speaker, past)
• gotowałem = I was cooking / I cooked (male speaker, past)
• ugotuję = I will cook / I’ll cook completely

So gotuję is used because the sentence describes a present action or habitual situation.

Also, gotować is imperfective, which fits the idea of the activity itself, not the completed result.

Because w can take different cases depending on the meaning.

Here, w means in, describing a location, so it takes the locative case:

• w nim = in it

If there were movement into something, Polish could use w + accusative in some contexts, but that is not what is happening here.

So:

• gotuję w nim = I cook in it

is about location, not motion.

Also, nim is the locative/instrumental form of on/ono-type pronouns used after prepositions in this kind of context.

Nim refers back to garnek.

Instead of repeating the noun, Polish uses a pronoun:

• Ten garnek jest duży, więc gotuję w garnku...
• Ten garnek jest duży, więc gotuję w nim...

Both are possible, but w nim sounds more natural because it avoids repetition.

So nim = it, specifically in it.

Because zupa is the direct object of gotuję.

When a feminine noun is the direct object in Polish, it often goes into the accusative case:

• nominative: zupa
• accusative: zupę

So:

• Zupa jest dobra. = The soup is good.
• Gotuję zupę. = I’m cooking soup.

That is why the ending changes from -a to -ę.

Because the preposition dla (for) requires the genitive case.

So:

• rodzina = family
• dla rodziny = for the family

And because całej describes rodziny, it also has to be in the genitive feminine singular:

• cała rodzina = the whole family
• dla całej rodziny = for the whole family

So both words change because of dla.

It is the feminine singular genitive form of cały = whole / entire.

Some useful forms are:

• cały = masculine nominative singular
• cała = feminine nominative singular
• całe = neuter nominative singular
• całej = feminine genitive/dative/locative singular

Since rodzina is feminine, and dla requires genitive, you get:

• dla całej rodziny

Yes, absolutely.

• gotuję w nim = I cook in it
• gotuję w tym garnku = I cook in this pot

Both are correct.

The difference is mainly style:

• w nim is more natural when the pot has just been mentioned
• w tym garnku repeats the noun more explicitly and can add emphasis

So Polish often prefers the pronoun if the reference is already clear.

Not completely. Polish word order is more flexible than English, because case endings show grammatical relationships.

The given sentence is very natural:

• Ten garnek jest duży, więc gotuję w nim zupę dla całej rodziny.

But other orders are possible for emphasis, for example:

• Zupę gotuję w nim dla całej rodziny.
• Dla całej rodziny gotuję w nim zupę.

These are grammatical, but they shift the focus.

For a learner, the original version is the safest and most neutral word order.