My approach would likely be as follows:
Reserve time for questions. In my experience this will not actually take much of the time. Don't be afraid to not answer certain questions. For example, "what do you think is on the next test" is usually not wise to entertain. Unless you are writing the test and have a specific sense of how to use that question to leverage studying. For example, I will sometimes ask in return, "well, tell me something you're not done studying".
Prepare a few examples to give lecture style. Perhaps just 1/3 of the time for this, but it assures there is real content delivered. This could be at the beginning, middle or end, in fact all three of these can be rearranged as you see fit for your audience and setting.
Put all the students names on 3x5 cards. Write about 5-10 problems on the board and randomly select names to work those problems. Give them 10 or so minutes and emphasize that everybody should be trying to work through the problems to follow along. When the time is up, go through the problems critiquing both answers and presentation. Mark the cards with dates and short description for your record. Next time, go to new students, or for fun repeat to keep them on their toes. Eventually everybody comes up front to work problems in this fairly low-pressure setting. This works best if you have some course points to assign. If you have no influence over their grade then sadly I have not much hope. I mean, try talking to people anywhere about math for 2 hours when you have no control over their grade. You'll find yourself alone in a room long before the end. (statistically, people are rarely mathematicians, so the sentence before is said in that manner of thinking)
The benefit of 3. is it gives them incentive to work on the class regularly and it gives you a chance to warn against common mistakes and/or to show better ways to solve the given problems. Finally, it is probably useful for the students to see that everybody (for the most part) struggles with the material. Too often students refuse to ask questions because they think they are alone in their confusion. In fact, the confusion is the rule. Ideally, this process helps some of the students to start asking good questions. We probably need to teach them what is a "good question", but I'll leave that for another post.