Lesson


 * LESSON PLAN**

**Algebra II** **- Transformations of Functions**

__**Objective**__: Students will be able to understand how different symbolic aspects of an equation of a function result in transformations from the parent function. Students will obtain this understanding through an analysis of quadratic functions, square root functions, and absolute value functions.

__**Standards:**__ __ACT__ -Identify characteristics of graphs based on a set of conditions or on a general equation such as //y// = //ax//2 + //c// MDE -A2.1.3 Represent functions in symbols, graphs, tables, diagrams, or words, and translate among representations. -A2.2.2 Apply given transformations to parent functions, and represent symbolically. NCTM -Understand relations and functions and select, convert flexibly among, and use various representations for them -Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions;

__**Prerequisites:**__ Students entering into this lesson need to be competent with graphing. It is not imperative that students have a deep understanding of each of the functions examined. However, there needs to be a clear understanding how points are plotted on the coordinate plane for functions. Additionally, students need to be capable of substituting in inputs, obtaining outputs, and creating ordered pairs.

__**Materials:**__ Laptops (One per group) with internet to access and applet Video Introduction Worksheet

__**Accommodations:**__ There are no direct problems presented to students. Therefore, providing select students with less complex problems is not an option. This lesson is an exploration and students will be placed in pairs. Students will be partnered so that students who lack a strong mathematical base will be placed with students who have proven to master many algebraic concepts. The only other accommodation being made is for those with visual impairments. Students can zoom in with the web browser which will enable the text of the directions and the actual applet to be more visible for students with visual impairments.

__**Instructional plan:**__ As previously mentioned, students will be placed in pairs to explore transformations of functions. Each pair will be given a worksheet, which will require students to make and test conjectures and understand patterns between different families of functions. The teacher should circulate the room to clarify direction and provide guidance. Students may have difficulty with the applet. Therefore, I created a screen cast to discuss the basics of the applet prior to following the directions in the worksheet:

media type="custom" key="14128362"

It is crucial that there is time devoted to reviewing the answers from the activity and providing rational for the answers. Teachers should devote at least half of a period to defining the relationship between the various manipulations of the equations and the subsequent transformation of the graph. Furthermore, the teacher should use tables and substitution to demonstrate to student why the graphs are shifted up, down, left, right, or reflecting. The depth of this discussion is contingent upon the level of the students, thus this discussion must be planned and implemented by each teacher, to best address the specific needs of his/her students.

__**Assessment**__: Part III of the worksheet will serve as a formative assessment for the teacher to use to gauge student understanding. This will assist in planning the debriefing after the activity. After questions are addressed and the students have a relational understanding of why certain manipulations of a function lead to transformations, the students should be presented with another assessment to measure their progress. The assessment available for download below tests students on their instrumental understanding of the activity, as well as their relational understanding of transformations. Furthermore, the questions are diverse in nature. Some deal with the symbolic representation of mathematics, others require a written explanation, and other questions revolve around the graphical representations of transformations. This provides teachers with a holistic view of student understanding from the lesson.