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SWBAT calculate the average rate of change of a function over a specified interval. SWBAT interpret the average rate of change of a function over a specified interval.

Big Idea

Just what does that change mean? Your students build understanding of rate of change as they calculate then interpret their work for each other.

Set the Stage

5 minutes

I begin this lesson with the same function on the board that we began with yesterday:

f(x) = 0.2x^2. 

This time I ask my students to work with their back partner to determine the rate of change for this function without specifying which section of the graph to consider. (MP1) I do this intentionally to see how my students handle this, because it should be review from previous classes.  After a few minutes or when discussion dies down, I ask for volunteers to post their solutions on the board.  We critique any solutions posted, with a focus on whether they fit for the whole function. (MP3) This allows my students to realize that some functions do not have a single rate of change on their own, instead of just hearing it from me.   

Put It Into Action

45 minutes

I explain to my students that today they will work independently to calculate the average rate of change for several problems (from both tables and equations).  I distribute the worksheet then ask if there are any questions and tell my students they have about 30 minutes to complete their work. (MP1, MP2) As my students work I walk around offering encouragement and assistance as needed. Some students may struggle with determining which points to use even with the restricted domain.  For them I try to ask questions like, "What pattern do you see when you graph the points in the table?" or "Have you tried setting your calculator window to the given domain?"  As everyone finishes or after 30 minutes I tell my student that they will now have an opportunity to share their solutions with several classmates, one at a time.  I have them start with their front partner, then rotate to a new partner after they complete the discussion of two problems. (MP2, MP3)  I walk around observing but when my students ask me to determine who's answer is correct I instead let them sort it out themselves asking leading questions if necessary.


Wrap It Up

5 minutes

We close this lesson with a whole class discussion of what rate of change means in the broader context we've explored today.  I explain the my reasoning for making this a whole class activity rather than individual exit ticket in my video.  When we reach a class consensus about rate of change I post it on the board and suggest that my students add it to their notes.