My current boring, older-than-me textbook says that there are 10 tribes. My much more often updated teacher say that there are 12. And my friend who reads encyclopedias for fun says 13.
Ya'akov Avinu had twelve sons:
The fact is, there are twelve tribes, but technically Shevet Yosef is divided into two parts:
So when your friend says there are thirteen tribes, he isn't wrong per se, it's just a different way of counting the number of tribes. Because when you seperate Shevet Yosef into two tribes, then it makes thirteen not twelve.
However, some may still only count twelve tribes even when separating Shevet Yosef, because in Bereishit 48:5 we read that Ya'akov "took away" the birthright of Reuven and Shimon and gave it to Yosef's sons, Efrayim and Menasheh.
So it's merely a matter of perspective. Hope this answers your question.
As for the textbook saying there are ten tribes, it might be referring to the Ten Lost Tribes of Israel, who were sent into exile by the Assyrians.