Why are Miles and Alaska kicked out their World Religions class in "one hundred ten days before"? Where do they go?

When Dr. Hyde kicks Miles out of World Religions for looking out the window at the woods rather than listening to the lecture, Alaska tries to defend him, and is also kicked out. When class ends, they are joined by Chip and Takumi, the four of them wandering through the woods to a place Takumi calls The Smoking Hole.