Můj učitel miluje sport a často si s námi hraje v tělocvičně.

Because můj has to agree with učitel.

• učitel is a masculine singular noun.
• The possessive my is therefore můj in this form.

So:

• můj učitel = my teacher (male teacher)
• moje učitelka = my teacher (female teacher)

Czech possessives change form depending on the gender, number, and case of the noun they go with.

Usually yes.

• učitel = male teacher
• učitelka = female teacher

In some general statements, masculine forms can be used more broadly, but in a sentence about one specific person, učitel normally means the teacher is a man.

Because Czech does not have articles.

Unlike English, Czech usually does not use separate words for a/an or the. Whether something is definite or indefinite is understood from context.

So:

• můj učitel already clearly refers to a specific teacher because of můj
• sport does not need an article either

This is completely normal in Czech.

In Czech, sport is often used in the singular to mean sport in general.

English often says sports in this kind of sentence, but Czech commonly uses singular sport for the general idea.

So miluje sport means he loves sport as an activity or field in general.

It actually is in the correct case, but the form happens to stay the same.

The verb milovat takes the accusative case.
The noun sport is masculine inanimate singular, and in that pattern the accusative singular is the same as the nominative singular.

So:

• nominative: sport
• accusative: sport

Grammatically the case is different, but visibly the word does not change.

Both are 3rd person singular present tense, matching můj učitel.

• miluje = he/she loves
• hraje = he/she plays

Here the subject is můj učitel, so both verbs mean he loves and he plays.

Their infinitives are:

• milovat = to love
• hrát = to play
• hrát si = to play, have fun

Si is a reflexive word that is part of the expression hrát si.

This matters because:

• hrát often means to play a game, sport, instrument, role, etc.
• hrát si means to play in the sense of have fun, play around, or play with someone/something

So si hraje is not just random extra grammar. It changes the meaning of the verb.

Because they do different jobs.

• si belongs to the verb expression hrát si
• s námi means with us

So in si s námi hraje:

• si helps form the meaning plays / has fun
• s námi tells you with whom

They are not duplicates.

Because the preposition s meaning with requires the instrumental case.

The pronoun my changes like this:

• my = we
• nás = us
• nám = to us
• námi = with us / by us

So after s, you need námi:

• s námi = with us

Because v meaning in takes the locative case when it shows location.

The basic dictionary form is:

• tělocvična = gym

But after v, it becomes:

• v tělocvičně = in the gym

So the ending changes because of case.

Because si is a clitic, a short unstressed word that usually goes in the second position of the clause.

In this part of the sentence:

• a = and
• často = often
• si then comes very early, after the first real element of the clause

So často si s námi hraje is the normal neutral order.

A useful rule for learners is:

• short words like si, se, mi, ti, mu, by, etc. usually appear near the beginning of the clause, not later where English speakers might expect them.