First of all, the paper with footprints is called the marauder's map, which was invented by Harry's father and his friends. Later, this thing was confiscated until the Weasley brothers stole it.
It was a holiday at the beginning of the movie, and Harry was still at his uncle's house. He is very unpopular in his uncle's house. He is regarded as a magic monster. Besides, Harry is not allowed to use magic in front of ordinary people outside school. That book is not a marauder's map, but an ordinary book (you can read it carefully. The marauder's map is made of parchment, which Harry couldn't have got at that time. Ha used the wand to emit fluorescence, which alarmed his uncle, who came to check the situation. Harry is also a little naughty or just playing tricks on his uncle ~
In this new semester, students can go to Hogsmeade village on weekends, but only if their parents agree to sign it, and Harry's uncle didn't sign it for him, so he can't go. So he tried to sneak out in an invisibility cloak ... The Weasleys decided to help him and gave him the map ~
You may not have played the game Harry Potter, but if you have, you will realize that Hagrid's hut (the one where you look at the pumpkin) is at a certain distance from the stone tablet on the top of the mountain. The distance from the hut to the top of the mountain can save Buckbeak (the bird). This is magic, as the headmaster said, how mysterious and powerful time is, how wonderful magic is, and everything is going just right ~
This is my favorite Harry Potter series. Although it is different from the original, I personally think it has been changed very well!
I hope my answer can help you ~