Contextualization

The theme of this project, "Square and Cube Root 2", may seem complex at first glance, but it is a fundamental and exciting part of the mathematics discipline. To understand square and cube roots, we first need to talk about exponentiation, which is the process of multiplying a number by itself a certain number of times. For example, 2 raised to the power of 3, denoted as 2^3, is 2 multiplied by 2, multiplied by 2 again, resulting in 8.

Now, the opposite of exponentiation is root. So, when we have the number 8 and want to find out which number, multiplied by itself three times, resulted in 8, we are looking for the cube root of 8. Similarly, if we want to find out which number multiplied by itself resulted in 4, we are looking for the square root of 4. This is the main concept we will work on in this project.

Understanding the calculation of square and cube roots is a significant milestone in mathematics, as it is the basis of many other concepts and applications. This includes everything from solving quadratic equations to understanding the laws of motion in physics.

Now you might be wondering, "But why are square and cube roots important in real life?" Well, believe it or not, they are everywhere! If we want to calculate the area of a square, we need the square root. If we want to calculate the volume of a cube, we need the cube root. Moreover, in many other fields such as engineering, computing, and economics, we use square and cube roots to solve complex problems.

To delve deeper into the subject and enrich your knowledge of square and cube roots, we recommend the following sources, which are reliable and in Portuguese:

• Khan Academy: On this site, you will find a series of videos presenting the concepts of roots and powers, as well as practical exercises. (https://pt.khanacademy.org/math)
• Só Matemática: This site offers a section dedicated to explaining the concepts of square and cube roots in a simple and easy-to-understand way. (https://www.somatematica.com.br/fundam/radiciacao.php)
• Youtube: Channels like Matemática Rio with Prof. Rafael Procopio and Ferretto Matemática present very rich and didactic content on the subject.

With the knowledge accumulated from these sources and the activities proposed in this project, you will be ready to master the subject!

Practical Activity

Activity Title: "Roots in Practice: Squares and Cubes in Action"

Project Objective

Enhance the understanding of square and cube root concepts by putting them into playful and participatory practices. Students will work in groups of 3 to 5 to develop an interdisciplinary activity involving Mathematics and Art. The project is expected to take at least twelve hours per student to complete, given the complexity and scope of the topics and concepts involved.

Detailed Project Description

This interdisciplinary project is based on creating a "roots city" on a large paper poster. Each group will be responsible for designing and building their own city, using concepts of square and cube roots to determine the areas and volumes of various buildings and structures.

Required Materials

• Large paper for the poster
• Pencils, colored pens
• Ruler, protractor, compass
• Calculator
• Cardboard, scissors, construction glue for building the structures
• Internet access and bibliographic resources for research

Detailed Step-by-Step

1. Study of Concepts: Each group should start by studying and deeply understanding the concepts of square and cube roots and their relationship with exponentiation.

2. City Planning: After understanding the concepts, each group will move on to the city planning phase. Here, they should decide which structures to include in their city (e.g., schools, hospitals, parks, etc.) and use the concepts of square and cube roots to determine the areas and volumes of these structures.

3. City Construction: In this stage, students will draw and build the city on the poster, remembering to include all the calculations they used when planning the city.

4. Preparation of the Report: While building the city, students should also work on a report documenting the entire process. The report should include the following topics: Introduction, Development, Conclusions, and Bibliography used.

   • Introduction: They should contextualize the theme, its relevance and real-world application, as well as the objective of this project.

   • Development: They should explain the theory behind the central theme(s) of the project, describe the activity in detail, indicate the methodology used, and finally present and discuss the results obtained.

   • Conclusions: They should conclude the work by summarizing its main points, explaining the learnings obtained, and drawing conclusions about the project.

   • Bibliography: They should indicate the sources they relied on to work on the project such as books, web pages, videos, etc.

5. Final Presentation: The groups will present their "roots cities", highlighting the mathematics behind their projects and discussing the lessons learned in the process.

Each group should remember that, although this project focuses on understanding and applying square and cube roots, it is also about teamwork, time management, communication, and creative thinking. Therefore, each group member should be engaged and contribute significantly to the project.

The final deliverables will be the city model, the report documenting the entire process, and the final presentation. These will be used to assess students' understanding of the topic, their ability to work in a team, and to apply mathematics to real-world problems.