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Write notes back and forth with a friend. Ask personal questions or entertaining questions such as "would you rather be attacked by a lion or an alligator and why." This is risky and you might get caught doing this, try at your own risk. You can also play hangman or tic tac toe on paper. You may want to have more than one game going at once so that you don't have to pass the paper as frequently. Be sure to be discreet about your note passing. Don't write anything in your note that you wouldn't want your teacher (and possibly your parents) to read in case she sees you and takes your note away. Playing a game like sudoku or a crossword puzzle can keep your mind active while the class is going on. You can be engaged with an activity but quiet at the same time. Try different puzzle games until you find one you like. You can find a book of puzzles or print them from the internet. Doodling can be a way to let loose while still listening to the teacher. Doodle on paper, preferably not a desk or chair. Meditating can be a relaxing way to entertain yourself silently. Breathe deeply in and out. Focus on deep, regular breaths but don't breathe too loudly. Sit straight in your seat with both feet flat on the ground. Place your hands in a neutral position on your desk. Clear your mind and focus on a happy, quiet thought. Meditate with your eyes open, but don't focus your vision on any particular thing in the room. Practice filling yourself with emptiness, then with a single idea or emotion.
Pass notes with a friend. Play a game by yourself. Doodle in class. Meditate silently in your seat.