1 + 1 = 2

1.  Timers are awesome.

 Put a timer over the top of a problem (if you use PPT or Keynote) with an opacity of 50%, and give the students 1, 2, or 3 minutes to try the problem.  I intially called this "Silent See What You Know", but eventually dropped that headline and just used the timer, and they understood the rules.  I get about 50% of students strongly engaged during the timer session, and the other 50% are at least silent.

When I am using the timer, I do not let them ask me a question, or any of their friends a question.  I tell them if they are confused, then just spend the time being confused.  

Students tend to believe there are only two states of learning:  1.  Not knowing how to do the problem.  2.  Knowing how to do the problem.  They don't realize there are a bunch of intermiate steps inbetween those two states.  This timer section of the class is meant for them to discover those extra steps.  When the timer is up, I call for all answers, and don't care if they are right or wrong.  I praise them all for getting to a solution, for getting pencil to paper.

2.  Do things in small chunks. 

Do a couple examples, then have the students do one problem.  Then go over that problem.  Then have them do one more problem as a pair/share.  Then go over it in front of the class.  Then give them three more problems.  Have those problems are the board and ask students who are done fast to put their work on the board.  Have the class set up in small time intervals, rather two long intervals ( I show you how to do it, then you do it).

My first year I would introduce the concept with a few examples, and then give them problems #1-10.  The result would be that I would spend too much time talking at the start, and then they would too much time to work, which due to shorter attention spans, caused a lot more conversation than work.