The SPOSA model of teaching
This is problem-based teaching in the sense that the mathematical ideas grow out of work on the problem, rather than proceeding work on the problem.
Set the context. This step is often unnecessary. You might say where the problem comes from. (1-2 minutes)
Pose the problem, on an overhead transparency or, if students might want to mark up a copy of a diagram, on one handout per group. Clarify any terms that might be misunderstood, especially by ESL students. (5 minutes)
Observe, usually quietly, while groups work and selected students present their groups' ideas to the full class. As much as possible, sit to avoid being the center of attention. Ask clarifying questions if none of the students are doing so but you think some would benefit. (most of the class period, perhaps more than one class period)
Summarize the big ideas of the lesson, using complete sentences prepared in advance. Introduce terminology for concepts students have encountered. Have class pose extension problems. (5-8 minutes)
Assess what you have done, making quick notes about what you might have done differently, how you might have phrased the problem better, etc. Also make notes about what students have shown they understood. Students try other problems or write about what they've learned. (5-8 minutes)