I Heard Lightbulbs

I heard lightbulbs go off.

After today, I am pretty sure there are few greater sounds.  Today, was day 2 of adding and subtracting rational expressions.  Yesterday was a bit of a scare as most students were very lost and I was unsure of how to deal with the situation.  The full story can be found here, but in short: I decided to assign the full homework assignment even though I had not adequately addressed all the topics in the assignment.  This was something that I stressed over for the rest of the day.  Was this a good decision? How am I going to answer all of their questions tomorrow? 

I decided that the best way to address class for day 2 would be to start with questions only on the stuff that I covered and then go on to better teach the new information.  I figured there would be a ton of homework questions.  When I asked who had questions, nearly everyone raised their hand.  When I asked who had questions on the LCM section from the homework, all the hands went down except for one.   I went over that problem on the overhead.  Next, I put the class into learning teams of 4 and had them sit in their groups.  I explicitly went through the steps for solving an addition problem and then had them work in teams on some example problems.  I randomly picked students to come up to the overhead with their team and teach the class the problem.  After this, I told them to work together in their teams to answer any other homework problems. After about five minutes, I asked the class if they still had questions.  No one did! 

At this point, I knew that I had made some good decisions.  I walked around the room while they worked with their teams and I heard a ton of math related conversations.  They were truly engaged and they were doing a great job of supporting each other.  This is what I mean by, "I heard lightbulbs."  I heard a ton of, "Oh!" "I get it" "Oh, so that's where I went wrong." "Wait, I can do this." It was awesome.  Also, the fact that no one had questions by the end spoke to the productivity that occurred in the groups.  True, a few students worked individually and some did ask me questions as I walked around, but in general they worked really well and I was grateful to have chosen this collaborative approach.

Following the group work, I asked the class to tell me the steps for subtraction problems.  They were confident in answering my questions, they worked well on the example problem, and then I gave them their homework assignment.  The assignment included addition and subtraction problems and I added a few LCM problems to keep them sharp.  This time, I was fully confident that the class was in a good place.  I was so excited that my lesson plan was a success. 

Originally, I intended to include a worksheet activity where rational expressions and geometry are combined.  This did not work out as we did not have time.  I feel as though this "running out of time" phenomenon is going to be a common theme as my teaching career progresses.  However, I showed the substitute my activity, she loved it, and she told me she is going to assign it for homework over the weekend so that I can collect it on Monday and see how the students do.  Check it out: 

Students use these dimensions to answer questions
about the perimeter, area, or circumference of different shapes on the house

Students receive this worksheet (mine were black and white and they got to color if they wanted)

Oh, and by the way, the cookie bars were a huge hit :)