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SWBAT identify and interpret the key features of graphs of relationships between two quantities.

Big Idea

Your students can look for key features of functions using algebraic calculations.

Set the Stage

10 minutes

I begin this lesson with the graph of a simple quadratic function projected on my whiteboard. (You could also just sketch it, but I like using the projector because the graph is more accurate and the axes actually match up properly!)  I challenge my students to look at this graph for features that help them make sense of the graph's characteristics, asking them to first observe silently, and then to pair-share what they've seen. (MP2)

While they're talking I walk around making my own observations about what my students are seeing and saying.  After a few moments I randomly select students to share what they've been discussing.  I'm looking for comments about the intercepts, minimum values, and what happens at the ends of the graph.  Some of my students will want focus on the transformations because they are pretty comfortable with those, but my goal for this unit is to get them to look beyond just the numbers and to start relating them to the patterns they see and to real-world applications. (MP7) I explain this further in my video

To raise the level of the mathematical discourse I have student who might just say  "It goes up at both ends" and "It's symmetrical"  go deeper by prompting them with additional questions such as, "What rate of change do you see and what does it mean about the structure?" or "What are the line/lines of symmetry that you see and how might the finished structure look?" 

We continue discussing the graph until everyone has had an opportunity to comment, then I tell my students that today they will get to exercise their brain power as they make observations about key features of other functions.

Put It Into Action

35 minutes

For this activity I have my students work independently to find intercepts, where the graphs are increasing or decreasing, maximum and minimum values, and other interesting features.  I choose independent work for this because it is one of the first lessons of the unit and I want to get a clear picture of where each student is in his/her understanding of the lesson. 

I distribute the Brain Power Worksheet and check for questions, then tell my students they will have about 25 minutes to complete this worksheet and that they should be prepared to share their work with the class.  (MP1, MP2)

As they work I walk around offering encouragement and assistance.  Some students will struggle with writing out what they observe so to help them I try to ask leading questions like "What points can you see?  What makes them important?  Now write down what you just said!"  When everyone is done or after about 20 minutes I remind my students that they need to be ready to share their work with the class. 

Before we begin the presentations, I explicitly share my expectation that each student should be checking their own work as we go over each problem and asking questions/offering appropriate critique.  Rather than just selecting students I know have corrrect and complete answers I randomly choose students and then let them pick which problems they want to talk about.  This allows for more interesting discussions and I think it also makes for better learning as students critique each problem and respond to each other. (MP3) .



Wrap It Up

5 minutes

To close this lesson I give each student a notecard and tell them to describe a real-world situation where knowing intercepts and other key features would be helpful.  This gives them a chance to reinforce the connection between key features and what they might represent. (MP7)  It also gives me a chance to get a snapshot of which students might need extra support.