Contextualization

Square and cubic roots are fundamental in arithmetic and mathematics, being concepts that help understand how numbers can be decomposed and reconfigured. These concepts are the basis for many mathematical equations, including geometric shapes and problem resolutions in physics.

In the square root, we are looking for a number that, when multiplied by itself, results in the number under the root. In the cubic root, we are looking for a number that, if multiplied by itself and then by the same number again, results in the number under the root. The symbols used to indicate square and cubic roots are √ and ∛ respectively.

Have you ever wondered why we need to know about square and cubic roots? Well, they have a wide range of applications in various areas of knowledge. For example, in physics, speed is often calculated by the square root of the distance traveled in a certain time. In engineering, geometry, and architecture, square and cubic roots are used to calculate areas, volumes, and distances.

For this activity, we recommend the following resources:

1. Khan Academy: a free online resource that provides step-by-step video tutorials on mathematics, sciences, and many other disciplines. Visit the section on 'Square Root and Cubic Root' - Khan Academy

2. Só Matemática: an excellent website with detailed theoretical explanations about the concepts and a large collection of solved exercises. Check out the section on 'Roots' - Só Matemática

3. YouTube: Explanatory videos about square and cubic roots. For example, the channel 'Matemática Rio with Prof. Rafael Procopio' has several well-explained videos on the subject - Matemática Rio

4. Book 'Mathematics in School'. This book also explains these concepts very clearly.

Practical Activity: 'The Discovery of Roots - The Game'

Project Objective:

Students will build a board game where they will have to calculate square and cubic roots to advance. The goal is that, at the end of the project, students will be able to calculate and recognize square and cubic roots, as well as understand their importance in mathematics.

Project Description:

Within the groups, students will create a board game. In each square of the game, there will be an operation involving a square or cubic root to be solved. If solved correctly, the player has the right to advance the number of squares corresponding to the obtained value. But be careful! Some squares have traps and can make the player go back in the game!

Necessary Materials:

• Cardboard or cardboard for the base of the game.
• Colored pencils or markers to illustrate the game.
• Small objects to be used as pawns.
• Paper, pencil, and eraser for notes and calculations during the game.

Step-by-Step for Carrying Out the Activity:

1. Divide into groups of 3 to 5 people and elect a leader for the group.
2. Draw a board on the cardboard or cardboard. It can be in the format you prefer, as long as it has at least 20 squares.
3. In each square, write an equation involving square or cubic roots to be solved.
4. The equations should be elaborated in such a way that their results are integer numbers from 1 to 5.
5. Define some squares as 'trap squares'. When a player lands on this square, they must go back the indicated number of squares.
6. Test the game among the group members to make sure everything is working correctly.
7. After finishing the game, prepare an oral explanation to present to the class, commenting on the difficulties and easiness encountered during the game construction.
8. Each group must present their game to the class, explaining the construction method and the rules. After the presentations, the groups will exchange their games with each other and play the game created by the other group.

Project Delivery:

In addition to the physical game, each group must submit a written report containing:

1. Introduction: Here, the group must explain the relevance and application of square and cubic roots in mathematics and the real world, as well as point out the objective of this project.

2. Development: In this section, the group must describe the theory behind square and cubic roots, the detailed description of the game, how the creation process was, the challenges faced and how they were overcome, the results of the game test, and the results of the rounds played by the other groups.

3. Conclusion: In this part, the group must summarize the main points of the work, comment on the learnings acquired, and the conclusions drawn about the project.

4. Bibliography: Indicate the sources that were used for the project elaboration.

The report must be submitted in digital format, within one week after the project completion.