Some days we do Desmos activity builder lessons and work with Fathom. Other days we collect data as a class and ask "What do we notice?" These classes often fly by for me and I am guessing my students find it that way, too. Why? Because they are engaged in what they are learning.
However, there is sometimes a need for direct instruction. Within a class where the primary teaching method is direct instruction, I ask students questions and also have them work at their desks to solve problems. Under our previous bell schedule, a class might have 10 - 25 minutes of direct instruction. And within those 40 minute class periods, there was also time for a warm-up, reviewing homework questions and time for individual work on problems similar to the ones done together in class. Students are also engaged in this class, but 25 minutes of direct instruction is the upper limit for my students with this more passive learning style.
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Zoning out identification technique: Ask a question. Call on student. Student answers a totally different question or admits outright "I wasn't paying attention."
A few days ago I read a brief blog post on doing board work, called "Should Math Students Be at the Board Working?" A simple idea really. Give students problems to do in small groups at the board. Since I normally have students do problems at their desks or have individual students put homework problems on the board, this was a quick and easy fix to my problem of keeping students engaged.
After reviewing one problem from the previous day and comparing its solution to a similar problem, we went over the homework by having students put the problems on the board. One problem was assigned per table and I already had the problems put on the board. I told the students that after about 20 or 30 seconds, I would say "switch" and someone else would have to write on the board. This made sure everyone participated in getting the problem on the board and there was definitely more engagement by all students in the learning. I could hear students in each group discussing the solution and correcting each other's errors. After the problems were up, we reviewed the strengths seen in each of the solutions. The energy of putting the problems up on the board and having students discuss them carried us through into the direct instruction component of the lesson which lasted about 20 minutes. Not too bad for a Friday afternoon at 3 PM.