Contextualization

Introduction

Radication is a mathematical operation inverse to potentiation. Imagine you have a number and want to know which number multiplied by itself will result in this one. This is radication. In the universe of real numbers, the operation of radication is a mathematical operation that aims to find a root of a number or expression.

There are three main types of roots that we will study in this project: square roots, cubic roots, and roots of higher indices. Square roots involve finding the number that, multiplied by itself, results in the number under the root, while cubic roots involve finding the number that, multiplied by itself twice, results in the number under the root. The roots of higher indices follow the same idea.

It is important to understand that not all numbers have exact roots in the set of real numbers. In such cases, we can approximate the root using numerical methods.

Relevance

Radication is commonly used in several disciplines, going from physics to engineering, economics, statistics, geometry, and others, and they are the basis for the comprehension of more complex mathematical topics. Besides that, the ability to calculate exact and approximate roots is an essential competence for many careers based on mathematics and science.

In addition to the theoretical aspect and the direct applications in different areas of knowledge, the study of radication can help develop skills such as logical thinking, problem-solving, and abstract thinking.

Practical Activity

Title: The Marvelous Root Journey

Project Goal:

This project seeks to develop students' understanding of the concept of radication, its applications, and its role in mathematics through engaging and collaborative hands-on activities. Teams of 3 to 5 students will explore the calculation of square roots, cubic roots, and roots of higher indices, the transformation of a root into a power, as well as the approximation of inexact roots.

Project Description:

Students will be tasked with creating a "Roots Board Game". Similar to games like Monopoly, the objective of this game is to go around the board as fast as possible. However, instead of rolling dice, players will advance by solving radication problems.

The game board should be divided into three sections: the first for square roots, the second for cubic roots, and the third for roots of higher indices. Each section must have at least 10 squares representing different radication problems that must be solved by the players to advance.

The squares will alternate between questions of calculating exact roots and approximating inexact roots. In addition, there should be some "challenge" squares, where players need to transform the root into a power.

Materials Required:

• Cardstock or cardboard for the game board
• Colored markers
• Game pieces (could be simply colored stones)
• Tape
• Deck of cards with radication problems (teams can create this using index cards or cardstock)

Steps:

1. Students should divide the cardboard into three equal sections, representing the square roots, cubic roots, and roots of higher indices, respectively.
2. Then, they should divide each section into squares, where each square represents a radication problem.
3. Students should then write the problems on the squares, alternating between exact and inexact roots. The "challenge" squares should be identified with a different color.
4. After the board is finished, students should create a deck of cards with the corresponding problems and their solutions.
5. To play the game, students will draw a card from the deck and solve the problem. If they get it right, they move forward a number of spaces equal to the index of the root in the problem. The answer should always be validated by the rest of the group.

Project Deliverable:

In addition to the physical creation of the game, students must deliver a report detailing the game's design and development process, the rules, and how the activity helped deepen their understanding of radication.

The report must be structured as follows:

1. Introduction: Should include a summary of the main ideas of radication, the relevance and justification for the project.
2. Development: Should detail the process of creating the game, the rules, the difficulties encountered, and how they were resolved. Here, students should make explicit the methodology used, as well as present and discuss the results.
3. Conclusion: Students should summarize their learnings, both in relation to radication and to the socio-emotional skills acquired, such as time management, creative thinking, problem-solving and proactivity.
4. Bibliography: Here, all the references used in the project should be inserted, whether books, videos, websites, among others.