If you need a ML book as a teacher, Machine Learning – The art and science of algorithms that make sense of data, is definitely the one you need. It covers most ML algorithms, divided by genre (tree, rule, ensemble, etc.). From a teaching point of view, the book is quite comprehensive. From a practical point of view, some chapters can be skipped as too theoretical.
The perspective taken by Peter Flach, the author, is very different from most data mining and data science books. The focus is on math and stats rather than business problem solving. Worth a read if you need to get the theoretical concepts behind ML algorithms.