There are two problems in Go that I would think might be appropriate (assuming that 9th grade == somewhere around about age 14).
The first, and the easiest to demonstrate because it's quickest, would be figuring out whether a move results in a group that is entirely surrounded and can be removed from the board.
The second, which builds on that, would be to implement a board on which two people can play, with the computer removing prisoners during play as above, but also spotting and not allowing other illegal moves such as suicide or repetition. Don't worry about the ruleset distinctions - just pick one and go with it.
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