Lesson+Plan+3+(PPA+2)

Precalculus Section 2.1 (pt 1) 17 November 2008
 * Lesson 3 **

**Classroom and Student Characteristics Plan** The physical design of the classroom is one that allows for ample spacing of the students while still providing the instructor with accessibility to each student individually. The classroom was made for use as a science room. There are set desks on the sides of the room which allows for the execution of scientific experimentation when the class curriculum should require. In the middle of the room are several rows of desks for other students to work from. The students are concentrated in the forward sets of desks and work stations. The class is composed of twenty students in grades 11 and 12. In this group of twenty there are ten male students and ten female students. Many of the students are the children of individuals in the United States Air Force and have been assigned to this school for the time that his or her parents are stationed at the nearby base. This group does contain a few students with any developmentally inhibiting characteristics such as ADD. Few students have minor medical issues such as asthma, and one student is absent frequently due to a previous traumatic head injury. In the class of twenty there is one student of ethnic minority. No students are from a nation other than the United States. **Learning Targets:** **Washington State Math Standards:** This lesson is based on fulfilling the following set of items from the Washington State K-12 Mathematics Standards for Mathematics 1. M1.1.B. Solve problems that can be represented by linear functions, equations and inequalities. M1.2.C. Evaluate //f// (//x//) at //a// (i.e., //f// (//a//)) and solve for //x// in the equation //f// (//x//) = //b//. **Assessment Strategies:** The use of formative assessment will be utilized through questioning and activities during the course of the lesson. Students will be expected to interact and to contribute to the flow and structure of the class. The students will also be provided with exercises related to the new materials of the day to work out in the classroom and after class time if they are unable to complete it in class. Technology (i.e., graphing calculators) will be available for the students should they require them for remaining work. Learning Experience: ** //__Introduction__// – Students will be provided with a warm-up exercise to assist them in focusing their attentions and efforts to the subject at hand. This exercise will partially review old materials as well as bring about new ideas for the students to think about. The students will be asked to group the following items into different categories with justifications for their groupings: // f // (//x//) = 4//x//3 – 5//x// – ½ // g // (//x//) = 6//x//-4 + 7  // h // (//x//) = √ (9//x//4 + 16 //x//2) // k // (//x//) = 15//x// – 2//x//4 // l // (//x//) = 3//x//-5 + 17  // m // (//x//) = 19 The idea here is to get the students to group them in polynomial functions and non-polynomial functions. Items //f, k,// and //m// are such while //g, h,// and //l// are not. //__Guiding questions__// – Attempt to have the students develop their own definitions of polynomial functions through the following questions: What is common about the way that I grouped the opening functions? //One group had functions with negative exponents, and the other did not.// Why would //m//(//x//) be in the first group and not in the second? //It has no exponent at all so it is not in the negative group.// The first group is called “Polynomial Functions.” Write down how you would define this term. //The book loosely defines it as a function with real coefficients and not negative powers.// //__Class work__// – The class will build off of the definitions that they have developed in the warm-up exercise and the questions. The instruction needs to include the materials that will follow here. The ** degree ** of the polynomial is the highest power associated with //x//. Use this idea to rate the degrees of the three opening polynomial functions. The ** leading coefficient ** is the number before the //x// with the highest power. Use this idea to name the leading coefficients of the opening three polynomial functions. Today our concentration is on linear functions. “What is the degree of a linear function?” (1). The general form of such a function is //f//(//x//) = //ax// + //b//. “How else do we normally see this?” (//y//= //mx// + //b//). Linear functions must have be a slant line, being neither vertical nor horizontal. This means that it has an average rate of change or slope. Given the following points, find the average rate of change and write a function to relate them: (-1, 2) and (3, -2). (//f// (//x//) = -//x// + 1). //__Closure__// – Have the students complete **Exploration 1** on page 173. Provide 3-4 minutes for this and then go over the results as a class. //__Homework__// – Students will be asked to complete the following exercises from their textbooks on pages 182, 183 and 186: 1 – 12, 51, 52, and 77. The emphasis in the class is more on completion and less on accuracy since homework is for practice. //__ Assessment Rubric: __// // Learning Targets // The selected learning targets are drawn from the approved Washington state OSPI and have been designed to further the mathematical education and understanding of all students in the state. The learning targets build on prior lessons of the equations of a line. They are designed to allow students to discover and interact with the sources and types of data needed to construct accurate equations for themselves using traditional methods learned previously as well as through technology. This will, as the course of study progresses, provide the students with a foundation for constructing more detailed equations for higher order functions and relations. These learning targets are designed for interactions in the world of mathematics. Many feel and believe that the posits of math are universally used and recognized. The information in the textbook is strictly numerically based. Some students might have difficulty understanding the field specific vocabulary of the lesson. However, since math is a language unto itself this is not limited to native foreign speakers. All students will be required to learn appropriate vocabulary to complete the assigned work. If any student requires further explanation times are provided for them to come and receive assistance individually. // Assessment Strategies // The assessment of this lesson will be of two types. First will be the formative assessment of the in-class discussions. The class size will permit that many student will be given the opportunity to have questions answered and working in small groups allows for the development of ideas in each student’s zone of proximal development as discussed by Piaget. The second assessment, found in the form of the homework, is designed to be evaluated on completion more than accuracy. The homework is merely practice based on the idea that exposure to information is the only way to gain proficiency with it and to then grow stronger. The major obstacle in this assignment will be the development of technological skills. The students are gaining a proficiency in this area through continued development of calculator skills in the class. // Learning Experiences // The learning goals and objectives for this lesson have been designed to be accommodating to different peoples across cultures. The items that are taught in this lesson and the skills that are refined in the world of algebra do not adhere to any one peoples or ethnic past. The inclusion of math as a staple of learning in every culture is evidence of this pan-cultural aspect of the discipline. The terminology of math is, at times, unique to its own study and will permit both native speakers and English learners to expand their understanding of the language and be better prepared to encounter different terminology out of their time in school. There are no students, however, in this class that are in the process of learning English as a second language. The demands placed in the students for the execution and completion of this lesson and the accompanying assignment should not cause any undo stress on students with learning needs or on 504 plans. The students in the class that do have 504 plans are given extra time to complete their assignments if it is so noted in their plans. The lesson is designed to teach people of all cultures and linguistic backgrounds how to speak and communicate in terms of mathematics. The example exercises and homework problems create a basis for later exploration in applying the formulaic models into application of actual situations and the ability to discuss these items in mathematical terms. A brief introduction of such application will be provided in the lesson. By encouraging the students to interact through the instruction process and to assist one another in the discovery, the lesson will assist in the development of learning communities in the classroom and will help the students to come to see that they have the ability to do the work and to find results on their own. // Family Interactions // Parents have full access to grades and assignments on the school’s website and have been provided with contact information for the class. Any parent wishing to be so informed is welcome to all materials needed for their child’s success.
 * Instructional Plan **
 * Grouping:** Students will be encouraged to participate in class discussion on the new materials and to ask questions to clarify misconceptions. During the in-class exercises the students will be permitted to work together to solve the problems. The teacher will circulate the room to encourage dialogue and to assist in answering questions. Students will be encouraged to keep notes for later reference and to complete his/her work for both in-class material and the assigned homework.
 * Prerequisites:** This lesson is the beginning of a new chapter in the book. The materials covered in this section will be a continuation of the materials that were learned in both the first chapter and previous mathematics courses.
 * Students are to be evaluated on the basis of the completion of the work, not on the accuracy. ||  5 All assigned exercises are complete with explanations and show care in the work.  ||  4 Most items are complete or all are complete with short justifications.  ||  3 Half of the work is complete or all work with only answers and no justifications.  ||  2 Few items have been attempted and no validation is present.  ||  1 Minimal work has been done with no explanations.  ||
 * Instructional Plan Rationale **