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This unit explores systems of linear equations and inequalities in two variables and their application in solving real-life problems. Students will learn how to graph systems, solve them through different methods, and analyze their solutions. The unit includes hands-on activities and application of concepts using software tools.
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ESSENTIAL QUESTION • How do people approach their problems in life?
UNIT QUESTION • How do systems of linear equations and inequalities in two variables facilitate finding solutions to real-life problems and making decisions?
CONTENT QUESTIONS • What is a linear equation? • What is an inequality? • What are the systems of linear equations in two variables? • How do we solve systems of linear equations and inequalities in two variables? • How to graph system of linear equation and inequalities in two variables? • When can we say that linear equation has one solution? no solution? or infinitely many solutions?
TARGET STANDARDS • The learner demonstrates understanding of key concepts of systems of linear equations and inequalities in two variables.
LEARNING OBJECTIVES • At the end of the unit, the students will be able to: • describe systems of linear equations and inequalities using practical situations and mathematical expressions. • identify which systems of linear equations have graphs that are parallel, intersect and coincide. • graph systems of linear equations in two variables. • solve systems of linear equations by (a) graphing; (b) elimination; (c) substitution.
graph system of linear inequalities in two variables. • solve a system of linear inequalities in two variables by graphing. • solve problems involving systems of linear equations and inequalities in two variables.
UNIT SUMMARY In this unit, the students study systems of linear equations and inequalities involving two variables. It includes solving and graphing with the use of different strategies. Students draw systems of linear equations from real-life situation and graph each system through the use virtual manipulative like Geogebra or Geometer’s Sketchpad for efficiency and accuracy. Then, they perform role-playing real-life situations by video clip where systems of linear equations in two variables are applied. For the project, they design or sketch plan of an expanded school vegetable garden through the use of a software like likeGeogebra or Geometer’s Sketchpad
for efficiency and accuracy. Then, they perform role-playing real-life situations by video clip where systems of linear equations in two variables are applied. For the project, they design or sketch plan of an expanded school vegetable garden through the use of a software like Google Sketchup that demonstrates student’s understanding of systems of linear equations and inequalities in two variables. Then, they use the design or sketch plan of an expanded garden in formulating and solving problems involving systems of linear equations and inequalities in two variables.
CONTENT OF ACTIVITIES WEEK 1 Day 1 • Introduce the following Unit Question: How do systems of linear equations and inequalities in two variables facilitate finding solutions to real-life problems and making decisions? Day 2 • Pre-test (Multiple Choice Test through a Microsoft Word) Day 3 • Discussion for Lesson 1: Systems of Linear Equations an their Graphs
Day 4 • Teacher will facilitate the students as they practice manipulating the application of Geometers Sketchpad individually at the Computer room. Day 5 • Individual Performance Test about the Lesson 1 topic using the Geometers Sketchpad at the Computer room guided with scoring guide on problem solving.
WEEK 2 Day 1 • Discussion with for Lesson 2: Solving and Graphing Systems of Linear Equations Day 2 • Students will have an activity which deals with real life situation that involves linear equation and inequalities in two variables then solve using the Geometer’s Sketchpad and Math Type for writing equations.
Day 3 • Discussion for Lesson 3: Graphical Solutions of Systems of Linear Inequalities in Two variables. Day 4 The teacher will divide the students into five groups then they will be given a set of problems in Linear equation and Inequalities and let them generate their ideas through brainstorming on how they will describe and compare the graph of linear equation and inequalities through Geometers Sketchpad.
Day 5 • Journal Writing (type written) • Expressing Understanding of systems of linear equations in two variables • Expressing Understanding of finding solutions of systems of linear equations in two variables graphically and algebraically. • Expressing Understanding of systems of linear inequalities in two variables
WEEK 3 Day 1 • Questioning through an open forum regarding on the whole topic. Day 2 • They will be divided into 5 groups. Then, the teacher will present and discuss the Rubric on Design or Sketch Plan, Rubric on Problem Solving and Rubric on Explanation as they plan their project on sketch plan on expanded rectangular garden at least 1hectares. Day 3 • They work on designing their project through the use of Google Sketchup then formulate and solve problems guided.
Day 4 • Present and defend their project on sketch plan of the expanded rectangular garden atleast 1hectare by following the Rubric on Explanation through Powerpoint Presentation. Day 5 • Type written Reflection /Generalization of the whole topic.
