Students will learn several strategies for solving Hashi (Hashiwokakero) puzzles. Wikipedia has listed some basic strategies. Lead your students to discover the strategies for themselves. Do not outright tell your students the strategies, that would spoil all the fun! You should give your students puzzles that'll help them discover strategies for themselves. You can generate puzzles here, if you like.
TODO: List exactly which strategies students should learn. Also, at what age can students begin solving these puzzles? I have placed it here as my best guess.
Conclude by leading this investigation:
Siteswap (juggling number patterns)