Fabulous World of Function- Unit Introduction

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SWBAT to identify, describe and analyze functional relationships (linear and non-linear) between 2 variables.

Big Idea

This lesson lays a strong foundation for the unit by introducing key unit vocabulary as well as the ever-important vertical line test.

Warm Up

7 minutes

For Warm Up problems today, I have included several concepts from previous grades. The first question asks students to determine the measure of a supplementary angle.  The second asks students to plot points on a coordinate plane, connect the points, then name the figure created. Plotting points will be especially useful during today's lesson when students must determine if a relation or graph is a function or not.  During Warm Up, I will move through the classroom looking for students who may struggle with plotting points so that I can strategically pair students with strong partners if needed. 

Lesson Introduction

6 minutes

In addition to the lesson objective, I have also included a proficiency scale for students. Our target level is a 3.0, but I want students to be aware of the other levels of performance as well. I also have this posted in the classroom for student reference.

Because of the amount of information included in this lesson, I have created a cloze note-taking template for students, which they will glue into their journals.  Students can then more easily follow along and fill in the essential information in the blanks. This will also become a reference tool for students as we progress through the unit.

Vertical Line Test

14 minutes

The vertical line test is an essential understanding that students must take away from today's lesson.  For this reason, I provide many examples on which students can build understanding. Instead of telling students what the vertical line test is, I show them three examples and ask them to work together to decide what the test is.  While the name is self-explanatory, it does not link directly to functions, so I ask students to look for patterns and notice similarities. Some classes may need more help in "seeing" the results of the test, so if no one volunteers that the vertical line crosses the graphs more than once, I circle those points on each graph and ask if anyone notices a pattern. Once students have articulated the rule, I check for understanding by showing the next three slides.

I then move to the following slides with tables and ask students how they might determine whether these represent functions or not. Some students return to the definition of a function, while others may suggest graphing the points.  This idea is pre-planned and animated within the Notebook, so when clicking on the page, a coordinate plane will appear as well as a vertical line for use in demonstration.  These samples lead directly to the relation and equation examples.

Work Time

12 minutes

Once students model basic understanding of the vertical line test, I distribute envelopes of six examples. For work time, student pairs must sort the cards into functions and non-functions.  I ask that at the end of work time they be able to explain why they sorted the cards the way they did.

When the timer sounds, I ask volunteers to share their finding for each of the cards (shown on the next six pages of the Notebook).  If there is discrepancy, I ask students to prove their thinking with explanation or demonstration. This allows students to critique the reasoning of others (MP 3).

At the end of Work Time, I ask students to complete a Ticket Out the Door to provide me feedback about their level of understanding of today's lesson.

Ticket Out the Door

6 minutes

For Closure of today's lesson, I ask students to give me feedback by completing a Ticket Out the Door that asks, "Matt says this relation is a function.  Do you agree with him?  Why or why not?" By looking at student responses, I will be able to determine each student's approach and level of understanding which will assist me in planning for subsequent lessons. For students who show a lack of understanding, I have time each morning when I can pull students from their advisory class for additional support.