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:
Learning Prerequisite:
Students should be able to:
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.
The class activity is studentcentered. 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.
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:

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:
In terms of knowledge:


5 minutes 
1. Summarize the lesson.
2. Greeting 
1. Raise questions if they encounter setbacks 
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