Contextualization

The equations with two variables, also known as systems of equations, are essential tools in mathematics and can be applied in a variety of practical situations in our daily lives. They allow the solution of problems where more than one variable needs to be considered, such as in the calculation of costs, planning of routes, evaluation of econometric scenarios, among others.

The ability to solve these systems of equations and to intuitively understand the representation of these systems in the Cartesian plan is a fundamental skill in fields as varied as physics, economics, engineering and computer science. Thus, the importance of this subject for the academic education of students, as well as for their training as citizens able to understand and interact with the world around them, becomes clear.

In this project, you will deepen your understanding of these concepts by exploring equations with two variables in a practical and playful way. But make no mistake, as entertaining as this may sound, the workload will be quite high. You will work in groups and will also have the opportunity to develop important skills such as teamwork, time management, communication and problem solving.

At the end of this project, we hope that you will be able to draw up and solve equations with two variables related to your immediate context, and that you will be able to represent them using the Cartesian plan.

Preliminary Study

To begin with, you need to understand the fundamental concepts on the subject well. Here are some reliable sources where you can study and go deeper:

1. Khan Academy: The Khan Academy has a whole section dedicated to the study of Equations with two variables.
2. SOS Professor: SOS Professor has a detailed explanation on First-Degree Equations with Two Variables.
3. Textbook: A good reference book that you can use is "Fundamentals of Elementary Mathematics" by Gelson Iezzi and Carlos Murakami.

These sources will be useful for you to understand and go deeper into the subject. However, remember: dialogue and discussion are fundamental for learning. Therefore, whenever you have any questions, do not hesitate to ask and discuss them with your colleagues and teacher.

Practical Activity - "Planning of an Interdisciplinary School Event"

Project Objective

The objective of this project is to apply the concepts of equations with two variables in the planning of an interdisciplinary school event. The event will be a science fair, where the groups will have to plan all the activities, costs and logistics involved.

Detailed Description of the Project

Each group of 3 to 5 students will be responsible for planning a booth for the school science fair. To do so, they will have to consider: material required, costs, labor, lead time for each activity, among other aspects.

The completion of this project will require more than twelve working hours per student and will involve concepts from more than one discipline, such as Mathematics and Management, in addition to developing technical and socio-emotional skills.

Materials Required

To carry out the project, you will need:

1. Paper and pencil for initial sketches and calculations
2. Computer with internet access for research and more complex calculations
3. Material for making the booth (to be defined by the groups)
4. Calculator

Step by Step

1. Definition of the booth theme: The first step is to define the subject that the booth will deal with. This can be something related to science, mathematics, history, art, etc.

2. Drawing up the equations: Once the theme has been defined, the group must draw up two equations that represent the costs and time required to complete the project. For example, one equation might represent the cost of materials and another the cost of labor.

3. Planning of the booth: With the equations ready, the group must plan all the activities necessary to set up the booth, considering the costs and time previously calculated.

4. Execution of the project: After planning, the group must execute the project, always paying attention to meeting the forecasts made by means of the equations.

Note: Throughout the process, it is important that the group keep a detailed record of all activities, discussions and decisions made. This record will be essential for the preparation of the report at the end of the project.

Project Deliverables

After the event, each group must submit a written report including:

1. Introduction: The group must contextualize the theme, its relevance and application in the real world as well as the objective of this project.

2. Development: In this part, the group must explain the theory used to create the equations, the steps involved in carrying out the activity, the methodology used and discuss the results obtained.

3. Conclusion: The group must conclude the work by taking up its main points, explaining the learning and the conclusions drawn about the project.

4. Bibliography: The group must indicate the sources used to work on the project such as books, web pages, videos, etc.

Students should fit in and complement the report with what they worked on in the project. The document must be clear, cohesive and coherent and the writing must be easy to understand.