Today instead of standardized practice test question today during the warm-up I put up the question "What does 4<x<8 actually mean?" This lead to a great conversation and showed me that although the students knew it was an "and" complex inequality, they had no idea of the real meaning. I actually had a couple students who had lightbulbs go off in their heads. I was able to extend this to inequalities in 2 variables and one student was able to connect the number line to the graph itself in terms of the closed circle is the same as the solid line while the open circle is the same as the dashed line. As a final step, I introduced some real world example and this same young man was able to relate the previous information in the discussion to the real world.
I decided that I would start off with a discussion question before we do the annotation because most of my students need to get used to changes in the daily routine. I think integrating discussion questions into the daily routine is going to help them do better in math because they will have a better understanding of the mathematical principal. I think when I start introduce new topics, I will give my usual reading assignment, then do a picture and annotate the photos to contain information on the material. It will be the mathematical equivalent of unpacking the standards. Unpacking the concept? That actually makes sense. We spend so much time teaching mechanics that we do not make sure they have a full understanding of the concept behind it. What do you think?