How to engage a large class? Teaching strategies that have worked for you
Clicker questions are nice. I use them. They break up the monologue, which is good. The change in mode "wakes the classroom up". They don't "take" much time. They give you feedback on whether something was clear or not. But the amount of active participation from the students is limited; just press A, B, or C. For harder question a lot of students choose not to participate (which is also a sign). 

An more intensive method I have used is to give students cards in different colors, and say all red students solve this question, all blue students that question, and all green students such question. After some time, they are asked to form groups of three, each a different color, and explain their answer to the rest. This is much more time intensive (it took about half the lecture), but the students are much more engaged. I was quite happy with the trade-off in that particular situation, but in many cases the cost of time would be just too big.