As students enter, I ask them to cut out the graphs from their homework assignment (the activity from two lessons ago). After doing this, I have them group their graphs according to their generalizations. Next, I ask them to describe each grouping on a sticky note that is utilized as the “heading” for each category. I give the students the following example to help describe the activity:
Suppose you return from the farmer's market with a large bag of fresh produce. All of the produce shares the trait that it is home-grown, but within the bag are various sub-groups. How could we sort the bag of produce?
I ask the students to duplicate this grouping process with their graphs. Graphs that "open right" might be a category, as well as graphs that "open left"... It is important to emphasize to the students that there are a wide variety of possible groupings!
Once the student's groupings are ready, after 5-6 minutes, I ask the students to rotate the room in pairs and observe their peers' work. Having students move about in pairs promotes discussion between individuals (MP3) who might normally just float about the room haphazardly (you'll be surprised at how students just "float around the room" if you don't put them in pairs... they are really good actors!).
Following this rotation stage, I moderate a class discussion as we work to create a class consensus of the groupings that we saw. Although the students are likely already catching on to the translations of the graph, and how changes in the equation affect the shifts and shape, closing in this brief whole-class discussion helps to bring closure to the activity.
To close this lesson I'll use a four question exit quiz. From class to class, the four questions I ask may, and probably will, differ. I choose questions to address teaching points encountered during the class. There is no need to scramble for questions or make them up on the spot since I can use the pool of unanswered HAMGO questions to generate the quiz. It is important to remember which questions that you asked (or take a quick picture of the whiteboard) so that you do not get your classes confused!
At the end of the quiz, I also ask my students to complete the following "sentence starters":
One thing that is really clear to me is...
One thing that I would still like additional support on is...
Students' responses to these questions help me gauge the lesson's effectiveness and identify unresolved issues. The students readily respond to these prompts since they are presented in a non-threatening fashion, plus the feedback is also great reflection material for you as a teacher!