Shorter truth tables take some time to learn. Do not rush through them. Students need lots of examples to see how they work.
Make sure you and they understand the concept behind them. You are assuming that the argument is invalid (by making the premises true and the conclusion false). If this assumption leads invariably to a contradiction, then the argument cannot be invalid, so it must be valid. But if you can assume the argument is invalid and fill out all the truth values without any contradiction, you have shown that the premises can be true and the conclusion false, i.e. you have shown it to be invalid. Continue reading More Notes on Shorter Truth Tables