У нашій родині різні покоління часто збираються за одним столом.

It is the locative case.

After the preposition у/в meaning in, Ukrainian normally uses the locative for location:

• у родині = in the family
• у нашій родині = in our family

Both words change to match that:

• нашій = locative singular feminine of наш
• родині = locative singular of родина

So this phrase is literally in our family.

Ukrainian often alternates у and в for euphony—to make pronunciation smoother.

At the start of this sentence, У нашій родині sounds very natural.
You could also say В нашій родині; the meaning does not really change.

So the choice here is mostly about sound, not grammar or meaning.

Because adjectives and adjective-like words in Ukrainian agree with the nouns they describe in gender, number, and case.

In this sentence:

• нашій родині

  • родині is feminine singular locative
  • so нашій must also be feminine singular locative

• різні покоління

  • покоління is plural here
  • so різні is plural nominative

• одним столом

  • столом is singular instrumental
  • so одним is also singular instrumental

English learners often notice this because English adjectives usually do not change form, but Ukrainian ones do.

That is a very common question.

Many neuter Ukrainian nouns ending in -ння have the same form in the nominative singular and nominative plural.
So покоління can mean either:

• generation
• generations

You know it is plural here because of the surrounding words:

• різні is plural
• збираються is plural

So різні покоління clearly means different generations.

збираються is the 3rd person plural present form of збиратися.

Here it means something like:

• gather
• get together
• assemble

The ending -ся is part of the verb. Historically it is reflexive, but in many verbs it is simply how the verb is normally used.

A useful comparison:

• збирати = to collect / gather something
• збиратися = to gather / get together or sometimes to get ready

So in this sentence, збираються means they gather / get together.

Because the sentence describes a habitual, repeated action:

• часто = often

For repeated or ongoing actions, Ukrainian normally uses the imperfective verb, here збиратися.

So:

• часто збираються = often gather

A perfective form such as зібратися would suggest a single completed event or a future completed event, not a general habit.

For example:

• Минулої неділі всі зібралися за одним столом.
  = Last Sunday everyone gathered at one table.

Here за takes the instrumental case, so:

• стіл → столом
• один → одним

So за одним столом means at one table or around one table.

This is a very common Ukrainian expression. It refers to people sitting or gathering together at the table.

Important contrast:

• за столом = at the table
• на столі = on the table

So this sentence is not saying the generations are on the table. It means they gather at/around the same table.

Literally, одним is the instrumental form of один = one.

But in this sentence it often carries a broader idea:

• at one table
• around the same table
• together at a single table

So it does not just count the table as one item. It also helps express unity and togetherness.

Yes. Ukrainian word order is fairly flexible because the endings show grammatical relationships.

The given order is very natural and neutral:

• У нашій родині — sets the context first
• різні покоління — gives the subject
• часто — adds frequency
• збираються за одним столом — gives the action and final image

You can move things around for emphasis, but the focus changes.
So this sentence is a good standard version for ordinary speech or writing.

Yes, you often could, but there is a nuance.

• родина often suggests a broader family, including relatives across generations
• сім’я often means the immediate family or household, though in many contexts it can also mean family in a broad sense

Because this sentence talks about different generations, родина fits especially well.

So:

• У нашій родині... sounds very natural here
• У нашій сім’ї... is possible, but may feel a bit narrower depending on context

Ukrainian has no articles, so there are no direct equivalents of a or the.

That means words like:

• родині
• покоління
• столом

appear without articles, and the exact meaning is understood from context.

English has to choose things like:

• in our family
• different generations
• at one table

Ukrainian simply uses the noun forms and lets context do the work.
In this sentence, одним helps make the image more specific: everyone gathers at one and the same table.