You have to go inside the school and use the bubble gum, so that a teacher will send you into detention. Before you chew it, get the blueprint from Nate's overstuffed locker, and also make a stink bomb in the Science Room (mix blue and yellow and heat it) so you can scare off the teacher.
(see related question)
On Big Nate's island
big nate island has lots of gum included!
You eat it.
all you have to do to get a pack of gum is: on Big Nate Island you have to collect all of the big nate comic book pieces.
On Big Nate island, you have to go into the Komix Shop, and talk to the guy, then find all of the Big Nate comic pieces, assemble them, and give them to him. Then he'll give you gum. *Various kinds of "effects" using gum are also available in the Store, but do not have anything to do with Big Nate Island.
chew it in school and go to detention
get some gum in a mini-game from nate and go to the school.then go to detention and chew the gum
You stand outside the detention room door, and since a sign says "No gum-chewing", chew the gum. Once you do, a teacher will stand by you and say, "I smell gum! Get in there!"
Chew the bubble gum
There is a sign that says that you cant chew gum in the school. You can get the gum from the man who wants the comics. Once you find them he will give you the gum. If you chew the gum in the school than you go to detention.
To get the gum in Big Nate Island, you must complete the comic sheet and give it to the man in a tan shirt. You can find him in the "Klassic Komix" store. When you start the island you must go to him first so he can give you a piece of the comic. After you've completed the comic, give it to him and he'll give you gum.
You just chew bubble gum then the teacher yells at you.