Contextualization

Theoretical Introduction

Mathematics is a universal language, and like any language, it has its own rules and vocabulary. Throughout the study of mathematics, we encounter terms such as 'variable' and 'unknown'. The concept and understanding of these terms are fundamental to solving many mathematical problems.

In this sense, a variable is a value that can change or vary, depending on the conditions of the problem. In summary, the variable is a value that is not fixed and is usually represented by a letter of the alphabet. For example, in a rectangle area formula A = l * w, 'l' and 'w' (length and width, respectively) are variables that indicate the dimensions of the rectangle.

On the other hand, an unknown is a variable whose value we do not know and want to discover. Frequently, we find unknowns in equations, where they are represented by letters of the alphabet, usually 'x', 'y', 'z'. For example, in the equation 2x = 10, 'x' is the unknown we want to find.

Contextualization of the Theme

The reason why we should learn about variables and unknowns is not limited to solving mathematical problems. Understanding the concept of variable and unknown can help us understand how the world works. Both concepts are used in various disciplines beyond mathematics, such as physics, chemistry, economics, computer programming, among others.

For example, in physics, we use variables to represent velocity, time, force, etc., and solve equations to find unknown values (unknowns). In economics, we use variables to represent production cost, selling price, profit, etc., and solve equations to maximize profit or minimize cost.

Practical Activity: 'Unraveling Mysteries with Variables and Unknowns'

Project Objective

The objective of the project is to apply the concepts of variable and unknown in an investigative activity, using logic and mathematics to solve challenging questions. This project makes the connection between Mathematics and Computer Science, the two disciplines involved.

It will be a group activity, with 3 to 5 students, and the estimated duration of the project is 15 hours.

Detailed Project Description

The groups will create a 'Mystery', a complex problem that will involve multiple variables and unknowns, in order to challenge other groups to solve them. The mystery can be a riddle, a puzzle, a logic problem, etc. Each group must also develop an algorithm in pseudocode that solves this mystery.

After creating the mystery and the pseudocode, the groups will exchange their mysteries and try to solve them, using logic, pseudocode, and the concepts of variables and unknowns.

Necessary Materials

1. Notebook or paper for notes and problem sketching.
2. Computer or mobile device with internet access for research.
3. Pencils, colored pens, post-its to assist in planning and solving the mystery.

Detailed Step-by-Step for the Activity

1. Formation of work groups.
2. Review of the concepts of variable, unknown, and pseudocode.
3. Creation of the 'Mystery': a problem involving variables and unknowns that will be given to other groups to solve.
4. Writing and reviewing the created mystery, ensuring clarity and applicability of the concepts of variables and unknowns.
5. Development of the pseudocode that solves the mystery.
6. Testing and refining the pseudocode.
7. Exchange of mysteries between groups.
8. Solving the received mysteries, using the pseudocode and the studied concepts.
9. Presentation of the results and discussion in the classroom.

Project Deliverables

After the practical activity, each group must deliver a report containing:

1. Introduction: Contextualization of the theme, its relevance and application in the real world, as well as the project's objective.
2. Development: Detailed explanation of the elaborated mystery, identifying the variables and unknowns involved and the relationship between them. Presentation of the developed pseudocode and the logic behind its construction. Description of the process of solving the received mystery, highlighting the use of the concepts of variables and unknowns.
3. Conclusions: Reflection on the learnings acquired in the project execution, revisiting the main points discussed, and sharing insights or conclusions drawn about the project.
4. Bibliography: Indication of the sources that supported the project elaboration and report writing.

The interdisciplinarity of the project and teamwork are essential for its success. Seek to collaborate and learn from your colleagues. Remember, the goal is to unravel the mystery and, in the process, better understand the concepts of variables and unknowns.