Standard+1


 * ~ Home / ||~ Standard 1 / ||~ Standard 2 / ||~ Standard 3 / ||~ Standard 4 / ||~ Standard 5 / ||~ Standard 6 / ||~ Standard 7 / ||~ Standard 8 / ||~ Standard 9 / ||~ Standard 10 / ||

**Standard 1 **

**Teachers know the subjects they are teaching. **  The teacher understands the central concepts, tools of inquiry, and structures of the disciplines she or he teaches and can create learning experiences that make these aspects of subject matter meaningful for pupils

**Evidence1 **: EDT 674 – Graphing Absolute Value Functions Using an iPod Touch 

**Rationale 1 **: This lesson plan was created for my Advanced Algebra with Trig class. In this lesson, students learn how to graph absolute value functions by completing a guided investigation using a graphing calculator application for the iPod Touch. Students graph a series of absolute value equations and discover how each variable affects its corresponding graph. After completing this investigation, students need to create an audio recording using Audacity explaining what a, h and k represents in the standard equation for absolute value functions ( **)**. Also in their audio recording, students must identify the vertex, whether the graph opens up or down, and the rate of increase and decrease for two given equations.

This lesson on absolute value functions demonstrated the following mathematics and technology standards:

**Mathematics **

A.12.1 Use reason and logic to perceive patterns and identify relationships A.12.4 Develop effective oral and written presentations A.12.5 Organize work and present mathematical procedures and results clearly B.12.3 Perform and explain operations on real numbers (absolute value) F.12.2 Use mathematical functions in a variety of ways, including translating different forms of representing them and using appropriate technology to interpret properties of their graphical representations

**Technology **

<span style="font-family: 'Arial','sans-serif';">A.12.1 Use common media and technology terminology and equipment <span style="font-family: 'Arial','sans-serif';">A.12.4 Use a computer and productivity software to organize and create information <span style="font-family: 'Arial','sans-serif';">A.12.5 Use media and technology to create and present information <span style="font-family: 'Arial','sans-serif';">B.12.5 Record and organize information <span style="font-family: 'Arial','sans-serif';">B.12.6 Interpret and use information to solve the problem or answer the question <span style="font-family: 'Arial','sans-serif';">D.12.1 Participate productively in workgroups or other collaborative learning environments

<span style="font-family: 'Arial','sans-serif';">The goal of this lesson was for students to be able to make efficient and accurate graphs of absolute value functions. By completing the investigation, students should discover that the coordinates of the vertex is (h, k) and that a tells you whether the graph opens up or down and the rate of change from the vertex. From here on out, students should be able to just look at an absolute value function and identify the vertex, whether the graph opens up or down, and the rate of change from the vertex. Those are the three main parts needed to create a quick and accurate graph of any absolute value function.

<span style="font-family: 'Arial','sans-serif';">This lesson shows that I am able to use technology as a tool to help students gain a better understanding of math. After completing the investigation, students were able to correctly identify the vertex, whether the graph opens up or down, and the rate of change. I feel that since students were able to compare and contrast a few graphs at once on their graphing calculator, it made it easy for them to discover where these characteristics are located in the equation.

<span style="font-family: 'Arial','sans-serif';">I did use this lesson last year when covering absolute value functions and it worked pretty well. There were a few modifications, as I used graphing calculators instead of iPod Touches, since most of my students have a graphing calculator and not all have an iPod Touch. Also, I did not have access to computers, so students were not able to make an audio recording of what they learned. Instead, students needed to write or type out what they learned from the investigation.

**<span style="font-family: 'Arial','sans-serif';">KSD: **

**<span style="font-family: 'Arial','sans-serif';">1.K.1 The teacher understands the major concepts, assumptions, debates, processes of inquiry, and ways of knowing that are central to the discipline he teaches. ** <span style="font-family: 'Arial','sans-serif';">When learning how to graph different types of functions in math, it helps if students see accurate graphs of these functions using technology. Also, by using the graphing application, students are able to graph multiple functions, which allow students to compare and contrast the graphs of the different functions. This makes it easier for students to identify what each variable represents in absolute value functions, which allows them to be able to graph these functions correctly.

**<span style="font-family: 'Arial','sans-serif';">1.S.4 The teacher engages students in generating knowledge and testing hypotheses according to the methods of inquiry and standards of evidence used in the evidence. ** <span style="font-family: 'Arial','sans-serif';">As a class at the start of the lesson, I have students guess what they think each variable stands for in an absolute value function. After making their hypothesis, students test their guess by completing the guided investigation. By completing the guided investigation, students construct their own knowledge of absolute value functions, which usually results in a deeper understanding of the topic.

**<span style="font-family: 'Arial','sans-serif';">1.D.2 The teacher appreciates multiple perspectives and conveys to learners how knowledge is developed from the vantage point of the learner. ** <span style="font-family: 'Arial','sans-serif';">By completing the guided investigation on absolute value function, students construct their own knowledge rather than a teacher explaining how they work. Also, students learn math best when they see the math behind the topic and are able to make sense of it.