Learn Turkish: En hızlı koşucu ilk noktayı üçe çeyrek kala geçti. - The fastest runner passed the first checkpoint at a quarter to three.

This phrase uses the dative case plus the word kala. Üç (three) gets the dative suffix -e to become üçe (to three). Çeyrek means "quarter", and kala comes from kalmak (to remain). Literally, it translates as "with a quarter remaining to three".

I am confused by "geçti" at the end. Aren't we learning to use "geçe" for time?

That is a very tricky part of this sentence! The verb geçmek (to pass) is doing double duty in your Turkish studies. In a time expression like "at a quarter past three", you use its special form geçe (as in üçü çeyrek geçe). However, in this sentence, the time expression uses kala (to), and geçti is simply the main verb of the sentence, meaning the runner physically "passed" the checkpoint.

Why does "nokta" (checkpoint) have the -yı ending?

Nokta is the direct object of the verb geçti. Because it refers to a specific, defined place ("the first checkpoint"), it requires the accusative case. Since nokta ends in a vowel, we add the buffer letter -y- followed by the accusative suffix -ı, making it noktayı.

Why don't we use var here, like "üçe çeyrek var"?