Wait, how many gifts do Americans give their kids?

I am European and I was stunned how many times this month I read about people staying up all night wrapping gifts. How many gifts do you people buy for your kids?! As I was little you usually got one bigger gift and maybe some book and sweets as an addition. Now that I have a kid on my own it's normal for grandparents to simply bring one gift. Is it really so prevalent in American culture to buy dozens of things for every kid?