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# Yung Chuek Ho's Lesson Plan

Lesson Plan

Class: F2A

Duration: 30 minutes

Chapter: Linear Equations in Two Unknowns

Topic: Consistency of systems of linear equations

Learning Objectives:

Students should be able to plot graph of linear equations (i.e. Ax + By + C = 0) on a rectangular coordinate plane. At the same time, students are allowed to solve simultaneous linear equations in two unknowns graphically and algebraically.

Learning Aims:

Students should be able to:

1. understand and find three types of solutions in solving systems of linear equations.

1. determine the consistency of systems of linear equations.

Learning Prerequisite:

Students should be able to:

1. plot graph of linear equations on a rectangular coordinate plane.

1. understand any points on the line is a solution of an equation with two unknowns.

1. interpret the intersection point of two straight lines on graph is the solution of the system of linear equations.

Features of The Lesson:

1. Flipped Classroom The flipped classroom video lasts for 2 to 3 minutes. The purpose of video is revision. In the video, it is reminded that any points on the graph of a straight line is a solution and hence we have infinitely many sets of solutions. After that, it is recalled that the intersection point of two straight lines on graph is the solution of the system of linear equations. Examples are given in illustrations and students are asked to pause in answering questions. At the end of video, two set of simultaneous linear equations, in which the answer is no solutions and infinitely many solutions, are given to students as challenging questions and it brings first glance to the concept of consistency of system of linear equations.

1. Classwork

The class activity is student-centered. Indeed, the topic is interesting because it overthrows students’ thought every system of linear equations in two unknowns must have a unique solution. It is expected that students discover the ‘truth’ by themselves, which it is possible that a system of linear equations having no solutions and infinitely many solutions. It follows that students can determine the consistency of system of linear equations. Geogebra and worksheet are set in achieving the above purpose. Students work in a group and follow instructions to use Geogebra plotting graphs of linear equations, eventually to attempt questions on the worksheet. Ideally, students should notice the relationship between inconsistency of the system and parallel lines of two graphs of linear functions, as well as, that between infinitely many solutions of the system and overlap of two graphs of linear functions.

1. Teacher’s Guidance

In order to facilitate the learning progress, one has to pay effort in the use of teaching language. The role of a teacher is a guider, not a lecturer. As mentioned, students are to discover by themselves, they are inspired and motivated by the teacher. Before the classwork, the teacher may ask questions like “Is it true that all system of linear equations having a unique trivial solution?” and invite students giving responses with rational support. In the middle of class activity, students may have some interesting findings, but they fail to connect their findings with prior knowledge. For example, the teacher may say “What is the properties of parallel lines?” Students may response like “There is no intersection point”. Then the teacher may ask if there is no intersection points, what does it mean to the solution of the system. Apparently, the teacher guides students in connecting different ideas and achieving expected learning outcomes. Lesson Flow:

The rundown of lesson is listed below.

 Minutes Teacher’s actions Student’s response 5 minutes 1.Recall content in the flipped classroom and propose last two questions mentioned at the last of video. 2.Ask students for their response. 3.Raise students’ attention. 1. Give response to the teacher. 2. Write down notes. 10 minutes 1.Distribute iPads and worksheets 2.Guide students to produce three sets of plotting graphs using Geogebra. 3.Inspire and encourage students attempting questions. 4.Answer students’ questions when they encounter setbacks. In terms of knowledge: Explain the relationship between graphs of linear functions and the number of solutions in the system of linear equations. Introduce concepts of “no solutions” and ‘infinitely many solutions” 1.Produce three sets of graphs of linear functions using Geogebra. 2.Discover the relationship between special properties of two lines and the solution to the system. 3.Raise questions if they encounter setbacks 4.Discuss with classmates. 10 minutes In terms of activity: Guide students to finish questions in Part B using Geogebra. Inspire and encourage students attempting questions. Answer students’ questions when they encounter setbacks. In terms of knowledge: Introduce consistency of system of linear equations Ask students how to check the consistency of the system of linear equations without solving. Finish questions using Geogebra. Raise questions if they encounter setbacks Discuss with classmates. 5 minutes 1. Summarize the lesson. 2. Greeting 1. Raise questions if they encounter setbacks

DMU Timestamp: November 27, 2019 01:26

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