Title: How to solve linear equation systems
Level: Second year secondary
Subject: Maths
Description:
The target of this didactic unit is to get the necessary skills in order to be able to solve any linear equation systems by different methods. This didactic unit will work on the human capacity of solving elemental equations based on real life.
Why solving linear equation systems is important?
This domain will be important for students to calculate unknown values during their daily life. For example, knowing how much each food costs in a certain purchase, the money earned by each person or the weight of certain objects.
1º SESSION (55 min)
ACTIVITY 1 (VISUAL TASK)
At the beguinning, we will start playing a video in order to show the importance of studying and solving systems of lineal equations by diferent ways. Also, we will teach the diferent aplications in our real life.
For this reason, we will need a video projector with a good conection to Internet. Audiovisual gadgets are very useful in order to start a new topic.
Link: https://www.youtube.com/watch?v=nok99JOhcjo&t=24s
2º SESSION (55 min)
ACTIVITY 1 (PRACTICAL TASK)
In this session, we are going to do several exercises to improve our Reading comprehension. For this reason, we will propose many exercises based in real life and their translation into equation systems.
At first, we will use the black board to explain the topic and propose some examples from the real life. Finally, we will use the class notes through the video projector.
ACTIVITY 2 (Using wxMAXIMA)
Students will carry out the following activities with wxMaxima in pairson each computer, simply by following the instructions given.
We are going to use wxMaxima to solve linear equations systems and to draw the associated straight lines onto a coordinate plane as a graphing method to find the solution of the system. Let's begin with this determined compatible system: x – 2y = - 4 3x + 2y = 12
3º SESSION (55 min)
ACTIVITY 1 (watching video projector)
In this sesión, we will teach how solving a equation system by the first method (Substitution method). Also, we will do several exercises by this way.
After that, we will play a video-tutorial through the video projector that helps us to understand this method.
Link: https://www.youtube.com/watch?v=l1xKkX7251w
ACTIVITY 2 (doing an exercise)
Example of an exercise by method of substitution
Calculate the values of the following system of equations.
x+y=5
2x-y=4
Finally, we will solve all dudes and ask pupils that do several exercises by this method.
4º SESSION (55 min)
ACTIVITY 1 (watching video projector)
In this session, we will learn to solve systems of equations by the second way (comparison method), also we will do several exercises by this way.
After that, we will play a video-tutorial through the video projector that helps us to understand this method.
Link: https://www.youtube.com/watch?v=ugdKRHrT_dI
ACTIVITY 2 (doing an exercise)
Example of an exercise by method of comparison
Calculate the values of the following system of equations.
x+y=5
2x-y=4
Finally, we will solve all dudes and ask pupils that do several exercises by this method.
5º SESSION (55 min)
ACTIVITY 1 (watching video projector)
In this sesión, we will teach how solving a equation system by the last method (elimination method). Also, we will do several exercises by this way.
After that, we will play a video-tutorial through the video projector that helps us to understand this method.
Link: https://www.youtube.com/watch?v=Tkrqrfkznoo&feature=youtu.be
ACTIVITY 2 (doing an exercise)
Example of an exercise by method of elimination
Calculate the values of the following system of equations.
x+y=5
2x-2y=2
Finally, we will solve all dudes and ask pupils that do several exercises by this method.
6º and 7º SESSION (55 min + 55 min)
ACTIVITY 1
We will work on consolidation, reinforcement and application of the unit.
We will use these 2 classes as a tutorial and to finish preparing students for the exam corresponding to the unit. We will use computers and the Internet for students to carry out different activities related to the teaching unit.
Link: http://www.math-play.com/System-of--Equations-Game.html
Link: http://www.math-play.com/equation-games.html
ACTIVITY 2 (GROUPAL TASK)
During the seventh session, tokens will be given to the students with exercises proposed for them to carry out in a group of 4 students.
8º SESSION (55 min)
ACTIVITY 1 (Unit exam)
In this session the students will present the proposed group tasks. Next, they will take the exam corresponding to the unit.
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