Contextualization

Mathematics is a universal language that allows us to interpret and understand the world around us. One of the mathematical tools we use to do this is called a 'variable'. A variable is something that can vary, that is, its value can be changed. It is a concept of extreme importance in mathematics and sciences, and is essential for problem-solving and equations. When dealing with real-world problems, we do not always know all the values in advance, but we can assign a variable to represent an unknown value and thus solve the issue.

Variables allow us to simplify complex problems into more manageable procedures. They are used in various areas, from simple household budget calculations to more complex applications in Physics, Economics, Computing, and many other fields. They help us understand and manipulate the world around us. Therefore, understanding what a variable is, how it works, and how to use it is fundamental.

Variables are essential for understanding how the world works. Suppose you want to save money. You can represent the amount of money you have each month as a variable, and this will help you understand how your actions (spending, saving, receiving more money) affect the value of this variable. Or, if you are on a bus, the bus's position at a given moment can be represented as a variable. So, if the bus accelerates or decelerates, the bus's position changes.

For this activity, you will explore the concept of variables in a very practical and fun way. Therefore, I particularly suggest that you consult the following resources that will assist you in the proposed activity:

1. Khan Academy: What is a variable?
2. Brasil Escola: Variables
3. Só Matemática: 1st Degree Equations

Remember to study, research, and discuss these resources with your group colleagues so that everyone understands the subject well.

Practical Activity: Creating and Solving the Mystery of Variables

Objective

The objective of this activity is to build a 'mystery' that classmates will have to solve using the concept of variables. You will create a problem that requires the use of variables to find the solution.

You should work in groups of 3 to 5 people. The activity should be carried out over a week, with a workload of 2 to 4 hours, depending on the complexity of the mystery you decide to create.

Project Description

In this project, you must create a 'Mystery', that is, a problem that requires the use of variables to be solved. The mystery should be based on an everyday situation and must involve at least one variable. The goal is to have classmates solve the mystery using the variable concept, applying the concepts learned during the class.

Necessary Materials

• Paper and pen for the initial sketch.
• Computer or tablet for the final writing and presentation.

Step by Step

1. Concept Discussion: Before starting, all group members must understand the concept of variables. Discuss as a group, watch the suggested videos, and clarify all doubts.

2. Scenario Choice: Think of an everyday situation that involves variables. It can be a trip to the store, a journey, a game, etc.

3. Creating the Mystery: Based on the chosen scenario, create a mystery that needs to be solved. Remember that the mystery needs to involve at least one variable.

4. Mystery Resolution: Write, step by step, how to solve the mystery using the concept of variables. This will be the 'key' to solving the mystery.

5. Writing: Write a clear and concise document explaining the mystery and how to solve it.

6. Mystery Presentation: Present the mystery to the class and see if they can solve it.

Project Deliverables

At the end of the project, you must deliver:

1. The Mystery: A detailed description of the mystery and how to solve it using variables.

2. Report: A written document that includes the following topics:

   • Introduction: Contextualizing the theme of variables, their relevance, real-world application, and explaining the project's objective.
   • Development: Explaining the theory behind variables, the activity in detail, the methodology used, and presenting and discussing the creation and resolution of the mystery.
   • Conclusions: Summarizing the main points, explaining the learnings obtained, and drawing conclusions about the project.
   • Bibliography: Indicating the sources they relied on to work on the project such as books, web pages, videos, etc.

Remember, the idea is that the 'Mystery of Variables' is not only an interesting activity but also an effective way to learn about the concept of variables and how to use these mathematical tools to solve problems.