Lesson+Plan+1

 ** Lesson Plan 1 **       strong questions - well done.   
 * ** Date **
 * October 21, 2009
 *  ** Math emphasis/objective **
 * The class has learned how to solve systems of linear equations using two techniques. This lesson will introduce an additional technique, the linear combination method. Students will also learn how to determine which solution method is appropriate for a given system of linear equations.
 *  ** Essential Questions **
 * What are three methods for solving systems of linear equations in multiple unknowns? What situations would be appropriate for using each of these techniques?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">** Standards **
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> The Pennsylvania state standards for mathematics are presented in [|www.pde.state.pa.us/k12/lib/k12/MATH.pdf] . This document includes several standards related to systems of equations. According to Section 2.8.11, “Algebra and Functions”, a student should be able to formulate systems of equations to model problem situations, identify whether systems of equations are consistent or inconsistent, analyze and explain systems of equations, and select and use an appropriate strategy to solve systems of equations.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> ** Assessment (formative and summative) **
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Students will be solving practice problems individually and in groups. Student participation in the initial lecture question and answer period and in the review of the practice problems will form part of their assessment. They will also be assessed on their activities during group time and their willingness to present the consensus solution of the group.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> ** Materials/Handouts **
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> A “Warm Up Exercises” worksheet Warm Up Exercises
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> A handout for the lesson [| Lesson Plan 1]
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> A homework sheet [|Homework]
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> **Content review** --- 15 minutes
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> “Warm Up Exercises” work sheet
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 10 minutes to complete
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> 5 minutes to review
 * <span style="color: windowtext; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">**Active Teaching** --- 15 minutes
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Review PowerPoint handout using overhead projector
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> For first example, solve using other methods and then solve using linear combination
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Why would we use linear combination rather than the other methods?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> What are the advantages and disadvantages of the linear combination method?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Can we use the other solution methods if we want to?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Review checking the answer
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> When the values for the variables are substituted into the equation, do all equations results in true statements?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Do the answers make sense?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">** Explore and Apply ** --- 30 minutes
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Groups
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Students will work in their existing heterogeneous work groups. These groups, typically with 3 to 5 students of various abilities, have been in place since the beginning of the school year. Students are required to participate in these groups until at least the end of the first quarter. At the end of each quarter, new groups will be formed.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Materials
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> One student from each group will obtain enough personal whiteboards, markers, and erasers for everyone in their group.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Group Activities
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> A system of equations will be presented on the board. Each student in each group will be required to solve the system using the substitution method. After a few minutes of working, each group member will compare their answer with others in the group. To conclude this problem, a random student from the first group will be called upon to give the class their group answer. That person will then select a representative from the next group to give their answer. This process will be repeated until the answers from all groups have been discussed. If all groups agree, we will move onto the next problem. If not, we will discuss the differences and will attempt to come to a whole class consensus.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> A second system of linear equations will be presented on the board. Similar to the first problem, each member of each group will solve this problem. However, each group will be assigned a different solution method to use. As in the first problem, answers from each group will be compared and discussed before moving onto the third problem.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> The final problem will be to solve another system of linear equations. However, for this problem, students will be permitted to select the solution methodology they wish to use. A group may only use one technique, so there will be a few extra minutes for the group to decide on the most appropriate method. When groups are presenting their solutions, they will be required to justify their method selection.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Materials
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> In each group, the student who distributed the materials at the beginning of the group activity will select another group member to return all materials to the appropriate storage location.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">** Whole class work review/discussion ** --- 15 minutes
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> We will discuss the various methods for solving a system of linear equations.
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> What are the methods to solve a system of linear equations?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> What are the advantages and disadvantages of each method?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Is there a single, right method of solution for a given system of linear equations?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> Can any of the solution methods be extended to systems of equations with 3 unknowns?
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;"> ** Homework ** --- 5 minutes
 * <span style="color: #000000; font-family: Arial,Helvetica,sans-serif; font-size: 130%;">Homework worksheet will be distributed at the end of class.