Today's Warm up is intended to take about 10 minutes for my students to complete and for me to review with the class. My students have worked with function notation before this lesson. We begin today's lesson with a review of how to evaluate a function, f(x) when given values for x. Then, students are asked to determine the value(s) of x that corresponds to a given output from a function.
In the video below, I demonstrate the strategy I use to teach graphing piecewise functions:
After reviewing the Warm Up with students, I hand each student an Activity called Running Errands from this website:
(last accessed 3-22-15)
I plan to have my students work on the activity individually for about 10 minutes. Then I will ask them to compare results with a table partner. For this activity the table partners are grouped homogeneously. I find that this helps my students to maintain the opportunity to think on their own, and share ideas with confidence.
While my students are working I am walk around the room monitoring their progress. Most of the students will be able to draw the five line segments on the graph associated with each of the five errands. However, I expect my students to have difficulty with the following elements of the task:
When students share their work, I will emphasize the precise use of function notation (MP6).
Here are some examples of my students' work on this task:
After the Using a Piecewise Function activity, I will work through a Guided Practice with students. I will lead this segment of the lesson so that we can focus on some of the difficulties that students experienced during the first half of today's lesson.
I will begin by working some of the problems on the worksheet while the students observe. Then, I will give them time to produce graphs on their own. Earlier, I had demonstrated how to read a function definition and graph a Piecewise Function. During the Guided Practice, I focus more on the last page of Graphing Piecewise Functions where students interpret a graph and write a piecewise function to describe it. The video below contains is an example of how I might do this with my students:
With about ten minutes remaining in the period, I give the students an Exit Slip to check for comprehension. Some of the issues I will look for in my students' work on this informal assessment are:
I have provided a copy of a correct graph in the resources.