Contextualization

The radical is a segment of mathematics that deals with the inverse operation to the power, that is, the process by which the root of a number is identified. The concept of radical is frequently used in various branches of mathematics, physics, engineering and other disciplines that involve numerical calculations. There are several properties of the radical that help us to simplify and solve equations and problems involving roots.

The presence of these properties within the radical is what allows the manipulation and comprehension of the operation, which is an essential tool for various calculations and equations. Furthermore, the properties of the radical are fundamental for solving more complex problems, as they allow their reduction to simpler problems.

The radical and its properties are fundamental in all areas of mathematics and, consequently, in all exact sciences. Engineers use radical to calculate forces, moments of inertia, stresses and other variables. Physicists use it to calculate speeds, energies, frequencies and other quantities. In finance, the radical is used to calculate compound interest rates, net present value, among others. In short, understanding the radical and its properties is essential for a wide range of careers and disciplines.

The radical and its properties are also present in our daily lives. For example, it is possible to calculate the square root of a number to determine the side of a square that has a known area, or to calculate the cube root of a number to determine the side of a cube that has a known volume.

Practical Activity: Demystifying Radicals Through the "Roots Game"

Activity Objective

The objective of this activity is to increase students' understanding of the properties of the radical and its application, through the development of a didactic game to facilitate the learning process.

Project Description

Students, in groups of 3 to 5, will create a game involving the properties of the radical. This game should involve questions related to the properties of the radical and should promote collaboration and participation of all group members. The idea is that, through the game, students acquire a deeper knowledge about the radical and its properties, as well as practice teamwork and problem solving.

Required Materials

1. Paper and pens for support material.
2. Materials for creating the game board (cardboard, markers, etc.).
3. Pieces to represent the players (can be small objects, coins, etc.).
4. Computer for research and development of issues (optional).

Project Step by Step

1. Research: Initially, students should research and review the properties of the radical.

2. Game Proposal: Next, the group should outline the idea of the game. The game can be based on existing board games (such as Monopoly or Game of Life), where the objective is to solve problems using the properties of the radical. Alternatively, it can be a completely new game.

3. Game Development: After outlining the idea, students should develop the game, which includes creating the board, rules, question and answer cards, etc. The questions should address different properties of the radical and students should strive to make the game as fun and engaging as possible.

4. Gameplay and Testing: After the game is ready, students should play it several times to test its effectiveness and correct any flaws. They can even invite other groups to play and provide feedback.

5. Reporting the Project: Finally, each group must write a detailed project report, covering the following points:

   i. Introduction: Students should contextualize the theme of the radical and its properties, its relevance and application in different areas of daily and academic life, as well as the objective of the project.

   ii. Development: In this section, students should explain the theory behind the radical and its properties, describe the game in detail (how it works, rules, etc.) and present photos or illustrations of the game. In addition, they should discuss the results obtained during gameplay and whether the game was effective for understanding and practicing the properties of the radical.

   iii. Conclusion: Students should conclude the project by reviewing its main points, discussing what they learned during the project, and their perceptions about the radical and its properties after the game was completed.

   iv. Bibliography: Finally, students should indicate the sources of information they used to develop the project.

Students have one month to complete the project, and each student should expect to spend between 5 and 10 hours on its completion. The evaluation will be based on the quality and creativity of the game, the correctness and relevance of the radical questions used, the cooperation and participation in the group, as well as the quality of the written report.