Tim Winn Curriculum 660 Lesson Plan: System of Equations - Addition/Subtraction Method Placement within Unit: This lesson is the first part of the second component of a three component unit plan. The overall unit focuses on single and multiple variable linear equations. The unit introduces, expands and compares y=mx+b equations. The first component is the introduction of single variable equations, the x in y=mx+b. The lessons will be focused on the understanding the Axioms of Equality, solving single equations through multiple methods and demonstrating the comprehension of theory through literal equations. This lesson plan takes the linear equation a step further by introducing a second variable into the equation. The only way to solve is to place the two variables into a system of equations. Through multiple methods, student will be able to solve each system to determine what the variables are for these specific equations. There will be a focus in relaying the message that most systems of equations are different and while one equation can be within two systems, the variables do not always have to be the same. Each system has unique attributes in relation to each linear equations and those attributes or variables can and will change in relation to other linear equations or in a different system of equations. This lesson plan will focus on the addition/subtraction solution method of solving system of equations. The following lessons will add the remaining methods, which are substitution and graphing solutions. The final component of the unit plan will focus on graphing solutions to linear equations. It will introduce the quadrants, slope and y-intercept. The final component will also be the jumping off point for future units on coordinate geometry and functions including domain, and range. Background: It is recognized that students gain more knowledge and understanding through experimentation, inductive thinking and conceptual control. This lesson will focus on a contructivism theory, which utilized these different approaches. The students will be provided leading questions to help stimulate critical thinking and problem solving. This lesson plan will allow the students to look upon their past experiences both personal and previous lessons to construct a logical outline and thought process to solve the real world examples and also the guided examples. The teacher will provide scaffolding as needed in the form of examples, prodding questions and assistance to specific questions. A key component to this lesson plan will be the peer interaction and reciprocal learning. During the initial introduction, the teacher will pose a real world question, building upon previous lessons and work. The teacher in a facilitator role will observe the individual responses or lack thereof from the students from the prodding/leading questions. From this observation, the class will be divided into smaller groups. The teacher will pass out numbers or colored card, each of these cards will represent the group. The groups will be blend students at different levels and also of different opinions of how to solve the problems. Within the groups, students will be able to provide assistance to students who have less of an understanding. There could also be a group of stronger student of differing opinions to work off each other and stimulate a greater degree of critical thinking.

Each group will also provide written documentation of their process. This process will be part of the formal assessment of the explanation and application of the lesson. Each process will be reviewed also as a class to bring all students to a certain level and also offer different perceptive and points of view for correct and useful processes. Massachusetts Curriculum Framework:  10.P.2: Demonstrate an understanding of the relationship between various representations of a line. Determine a line’s slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line, e.g., by using the “point-slope” or “slope y-intercept” formulas. Explain the significance of a positive, negative, zero, or undefined slope.  10.P.8: Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems.  12.P.9: Use matrices to solve systems of linear equations. Apply to the solution of everyday problems. Lesson Objectives: 1. As a result of this lesson, students will solve two variable by putting the equations into y=mx+b format.  In order to be successful, students must be able to solve single variable equations and understand.  In order to be successful, students will be able to reformat two variable equations to y=mx+b format through addition, subtraction, multiplication and division.  This objective is based on MA Curriculum Framework standard 10.P.2: Determine a line’s slope and x- and y-intercepts from a linear equation that represents the line. 2. As a result of this lesson, student will solve system of equations using the Addition/Subtraction method.  In order to be successful, students must be able to find the common multiplier number for both equations within the system of equation.  In order to be successful, students will be able to follow the 4 steps needed to accomplish the Addition/Subtraction method.  This objective is based on MA Curriculum Framework standard 12.P.9: Use matrices to solve systems of linear equations. Apply to the solution of everyday problems. 3. As a result of this lesson, student will demonstrate the ability to explain and solve real world type word problems based off specific method taught in this lesson.  In order to be successful, student s must be able format and apply the word problem into correct system of equation format.  In order to be successful, student s will be able to analyze and interpret the information in the word problem to conclude a specific solution.  This objective is based on MA Curriculum Framework standard 10.P.8: Solve everyday problems that can be modeled using systems of linear equations or inequalities. Apply algebraic and graphical methods to the solution. Use technology when appropriate. Include mixture, rate, and work problems.

4. As a result of this lesson, students will demonstrate the ability to work within groups and communicate a specific process within their own terminology and thought process.  In order to be successful, student s must be able interact in a social and professional manner with students of varying levels.  In order to be successful, student s will be able to explain and demonstrate their ability to solve specific problems using a process developed within group work. Materials and Resources: This lesson will require the following:   

Examples of System of equations. Real world word problem example. PowerPoint Presentation of Method Steps.

  

Pencils and paper. Website resources. Handout of Method Steps.

Procedures: 1. What is a system of equations? Using Problems with a Point’s Lemonade Stand example. Have students begin to format the problem’s equation into y=mx=b format. 2. Ask the students their views and opinions on how to set the problem and possible solutions. Based on the students responses and physical queues, divide the class up into small groups varying on students’ skills and understanding. Walk around the class and hand out different color or number cards. The number cards will determine which group the students are in. The teacher will sort the groups based on comprehension of the problems. 3. Facilitate the introduce System of Equations, solving two variable solutions through the use of multiple linear equations. Explain the first method of the unit will be:  Addition/Subtraction Method - This lesson will focus on using basic math to having one variable equal zero. 4. Describe and demonstrate the steps needed to accomplish the first method: 1. Multiple one or both equations by a common denominator to make the number in front of one of the variables the same in both equations. 2. Add or subtract the two equations to eliminate one variable. Focus on carrying the same procedures out through the equation regardless of signs 3. Solve for the first variable. 4. Insert the value of the first variable in one of the equations to solve for the second variable. 5. Check work - Put the first and second variables into the second equation, which should also equal. 5. Provide examples of different types of problems. Define each type of problems in definite sets and allow the student to characterize each set.  Simple multiplication number.  More complex multiplication numbers needed for equaling the equations out. o Provide some best practices on how to find the multiplication number.  First and Second variables on the same side.  The second variable has a value.  Unsolvable equations - equations are equal. 6. Allow the students to work within groups to provide peer interaction and reciprocal learning. Have each group define their own Addition/Subtraction process.

7. Compare each groups Addition/Subtraction Process, provide insight and help to groups as needed. 8. Reintroduce the real world problems within the group and gauge the student’s current approach to the problem with the new understanding of system of equations. 9. Solve the real world problem. Assessments:  Informal Assessment: o During the introduction of the lesson plan, the teacher will gauge an oral assessment of the class’ current level of applicable algebra through the introductory real world question. o The teacher will work directly with each group to evaluate the level of comprehension. The teacher will provide more time with students who solve at a slower rate and students who have learning disabilities or are on IEPs.  Formal Assessment: A differentiated homework assignment will be provided to students. The students will be assessed on a minimum proficiency of the following types: o Simple multiplication number will require a 90% minimum proficiency. o More complex multiplication numbers needed for equaling the equations out will require a 75% minimum proficiency. o First and Second variables on the same side will require an 80% minimum proficiency. o The second variable has a value will require a 75% minimum proficiency. o Unsolvable equations where the equations are equal will require an 85% minimum proficiency.  Group Process Documentation: Each group, which were determined by the varying skill and comprehension during the pre-lesson discussion, will create a process document to solve specific problems given in class. This group project will explain the step by step process in the student’s own words and action. This will give the students the opportunity to demonstrate the understanding, provide an organized process for at home practice and also provide peer interaction and tutoring opportunities. Homework/Extension of the Lesson: Students will be given extended individual practice for homework based on various types of problems also a similar real world problem. The problems will range from 10-20 problems depending on the student’s need and ability. The homework will be differentiated to reinforce the lesson based on the student’s ability to solve and explain the set of problems. Students who have demonstrated a high ability will be challenged with more difficult problems. Students on IEP or in need of accommodations will have a work load better suited to their levels. Due to the differentiation, this homework will be used as the formal assessment. Accommodations: Students with reading disabilities will have the problems explained directly to them. An MP3 explanation of the steps will be available for play back during the homework or individual practice sessions. Students with learning disabilities will also be given a website or Excel Sheet helping to organize the problems. The student will be able to enter the individual variables or linear equation into the spreadsheet and the information will be organized into a format that better fits the student’s needs. For situations where a computer is not available, a graphical organizer will be available prompting

students at each step with specific questions to help organize the information and to help advance the student through the problem. Students will also work within group based on the overall class needs and time allotment of the lesson. The groups will be based on the different strengths and personalities within the class. Student more advanced will be mixed with students in need of more individual help. The group work will also be part of the assessment process to promote teamwork and also provide peer to peer interaction and assistance.