Learn Turkish: Okula geç kalıyorum.

In English, we say we are late "for" a place, but in Turkish, you are late "to" a place. The suffix -a in okula shows direction towards the school.

I thought kalıyorum meant "I am staying". Why is it used here?

In Turkish, the set phrase for "to be late" is geç kalmak, which literally translates as "to stay late" or "to remain late". So, geç kalıyorum is the natural way to say "I am late" or "I am running late".

How do the suffixes on kalıyorum work?

It starts with the verb root kal (stay). We add the present continuous suffix -yor (like the English "-ing"). Because kal ends in a consonant, we need a connecting vowel, which is ı due to vowel harmony. Finally, the personal suffix -um means "I". Put together: kal-ı-yor-um.

Can I just use the word geç with a "to be" ending, like geçim?

No. While English uses "late" as an adjective with the verb "to be" (I am late), Turkish requires the action verb geç kalmak. Saying geçim would sound unnatural and incorrect here.