Content+-+Math

Overview
In this session, you will navigate through an Algebra I lesson aligned to Common Core that is supported with and through technology.

During navigation of this lesson, you will consider and apply how you can effectively infuse technology to both support student learning and your instructional practices. This lesson is meant to serve as a model for you to create your own technology enhanced lesson. You, along with your colleagues, will engage in reflective discussions about this lesson and as a result, you will glean innovative practices for technology integration in a 1:1 mathematics classroom.

Participants will be able to:

 * Identify and discuss the various components of an effective learning experience supported by technology in a 1:1 setting associated with the Mathematics Standard - Analyze Functions Using Different Representation.
 * F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
 * e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
 * F.IF. 8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
 * b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.


 *  Explore and leverage Geogebra, while considering its use for both learning (demonstrating understanding/mastery) and teaching mathematical concepts.


 * Reflect and apply pedagogical methods, strategies, and tools appropriate in a mathematics 1:1 classroom.

I. Experiencing the Lesson (50 minutes)
__Consider the following questions as we go through this lesson:__
 * How does this classroom experience compare with your typical classroom experience?
 * What technology is being used in this lesson? Does it enhance the learning process?
 * If I were a student, what would I enjoy about this technology infused lesson/activity? Would it engage me and why?

<span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; vertical-align: baseline;">__Title of the Lesson__ <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">Exploring Exponential Functions

<span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; vertical-align: baseline;">__Essential Question__ <span style="background-color: #ffffff; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">How do the parameters a and b of an exponential function in the form y = a*b^x <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;"> change the graph of a function?

<span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; vertical-align: baseline;">__Learning Outcomes__
 * <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">The learner will be able to relate parameter changes to graphical transformations
 * <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">The learner will be able to identify between exponential growth and decay

<span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; vertical-align: baseline;">__Prior Content Knowledge__
 * <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">How the parameters m and b of linear function in the form y=m*x+b change the graph a function

<span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">Click here to begin the lesson. Exploring Exponential Functions

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">Take 10 minutes to reflect and answer the following questions and read through other participants' postings. We will then take time to delve into each of these questions in whole group discussion.


 * <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">How does this classroom experience compare with your typical classroom experience?
 * <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">What technology is being used in this lesson? Does it enhance the learning process?
 * <span style="background-color: transparent; color: #000000; font-family: 'Trebuchet MS'; font-size: 15px; text-decoration: none; vertical-align: baseline;">If I were a student, what would I enjoy about this technology infused lesson/activity? Would it engage me and why?

<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">You may work individually or with a partner. You will be creating a technology-enhanced lesson aligned with Common Core.

>>
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">Use this template (word document) to guide your planning. [[file:LessonPlanTemplate.doc]]
 * Choose from one of the following Common Core Standards to align your lesson:
 * A-REI.6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
 * F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
 * a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
 * F-TF.2. Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">Visit GeogebraTube to find a pre-made file to use in your lesson. If you create an account, you may log in, edit existing files, and save them in a collection.
 * A-REI.6 - Systems of Equations (or you can search "equations" for more files)
 * F-IF.7a - Expore the Linear Graph (or you can search "linear functions" for more files), Translating Quadratics in Vertex Form (or you can search "Quadratics" for more files)
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">F-TF.2 - Unit Circle and Trigonometry (or you can search "Unit Circle" for more files)


 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">When you are finished, share your lesson plan here.

IV. Conclusion (10 minutes)
<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">Share out and explain the lessons you have created. Discuss the following questions:
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">How does technology enhance teaching and learning Common Core?
 * <span style="font-family: 'Trebuchet MS',Helvetica,sans-serif; font-size: 120%;">What have you learned that you can take back to your schools and share with other teachers?

Next Steps.... Return to your Agenda to access the next session.
Video Tutorials on Using Geogebra Algebra Geometry Teaching Mathematics
 * Additional Resources: **