Graphing Absolute Value Functions (Day 1 of 2)

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Objective

SWBAT graph absolute value functions on a coordinate plane.

Big Idea

Students will observe the how changing values in an absolute value function transform the appearance of the graph.

Do-Now

10 minutes

Students will complete the Do Now. While students are working, I will circulate around the room passing back the graded exit cards from our last class. After about 4 minutes, I will ask students to switch their Do-Now with a partner, and we will review each other's responses together as a whole class. Some of my students will benefit from a slow walkthrough of plotting coordinate points on plane. To help refresh students, for each point I will start at the origin and have students say aloud for each point (right/left, up/down).

Next a student volunteer will read today's objective,  "SWBAT graph absolute value functions on a coordinate plane".

I will ask students to recall from their previous math classes the meaning of absolute value. The majority of my students knew that is was something that was "always positive", but couldn't exactly recall what it was, or what it was used for. 

We will briefly discuss as a whole group that absolute value is a measurement of the distance that is number is from zero. I will stress to students that it yields a positive number. For example, I can not run negative three miles around a track (even if I run backwards).

While students consider my running skills, I will point their attention to the number line that is hanging up on the wall in my classroom. I will use this representation to quickly quiz the whole group on the absolute value of various integers (-11, -4, 5, 4, 11, 18, -20). After I call out each number, I will use a pointer to count back to zero to reiterate to students that we are simply naming the distance the number is from zero.

Introduction to Absolute Value Function

15 minutes

We will start the next section of class by graphing the parent absolute value function:

f(x) = |x|

To do this, we will continue using the table and graph on the top of the Guided Notes. I will select x values, and students will use the definition of absolute value to determine the output values for the function. Then, I will ask students to plot the points from the table and to talk with a partner about the resulting shape of the function.

After giving students time to talk with a partner about this interesting graph, I will bring the class together. I will ask several students to describe the shape of the graph. Then, I will ask students to explain why the graph has the shape that it does. I will encourage them to use the definition of absolute value to justify their reasoning. I will ask probing questions about its symmetry, its minimum point, etc.


Whole Group Investigation + Discussion

30 minutes

I think it is important for students to make a visual connection to Absolute Value Functions before introducing the general formula. In order to accomplish this, we will spend at least 15 minutes making predictions about the appearance of absolute value functions and then evaluating our predictions using a graphing calculator.

I ask my students to record their observations in the chart on the bottom of their Guided Notes titled "What_happened_to_the_Vertex?" Later, with the whole group, I will use this Desmos to show students the effects of a transformation on a function, using Absolute Value as our example.

For each row in the table, we will graph both examples together. Next, I will ask students to create their own absolute value functions and to call out the equations aloud to the group. As students are calling out their examples, I will ask students to make a prediction about the location of the vertex then graph the function before displaying the end function on the screen. Once students understand how each individual transformation affects an absolute value functions in isolation, we will complete the summary box.

Next, students will use the knowledge that they gained from our whole group discussion to match the equations of absolute value functions with their graphic representation. Students will be asked to refer to their summary sheet in order to make predictions about absolute value function with multiple transformations.

Partner Practice: Versatiles

15 minutes

Students will practice finding the vertex and writing the equation of an absolute value function using this versatile handout. Students will work individually or in pairs on this versatile hand out. After 10 minutes, we will review responses aloud as a whole group.

Closing

10 minutes

To wrap up today's lesson, I will ask students to discuss what we have discovered about absolute value functions. Then I will ask students to make a prediction about why the x-coordinate of the vertex is located on the opposite of its sign when graphed on a plane.

Students will then complete an Exit Card.