Objectives (5 - 7 minutes)

1. Understand the concept of square and cubic roots: Students should be able to understand the concept of square and cubic roots, understanding that the square root is the number that, when multiplied by itself, results in the given number, and that the cubic root is the number that, when multiplied by itself three times, results in the given number.

2. Calculate square and cubic roots of integers and decimals: After understanding the concept, students should be able to perform calculations of square and cubic roots, both of integers and decimals, using factorization, decomposition into prime factors, and the calculator.

3. Apply the acquired knowledge in problem-solving situations: Finally, students should be able to apply the acquired knowledge in solving problem situations, which may involve determining square and cubic roots, as well as calculating measurements in practical everyday situations.

Secondary objectives:

• Stimulate critical thinking and problem-solving: In addition to developing specific math skills, the lesson also aims to stimulate critical thinking and problem-solving skills of students, encouraging them to think logically and seek efficient solutions to the challenges presented.

• Promote interaction and cooperation: The proposed lesson methodology also aims to promote interaction among students, encouraging cooperation and teamwork in solving the proposed exercises and problems.

Introduction (10 - 15 minutes)

1. Review of previous concepts: The teacher should start the lesson by reviewing previous concepts that are fundamental for understanding the lesson topic. This may include reviewing concepts such as exponentiation, factorization, and the idea that the square root of a number is the number that, when multiplied by itself, results in the given number. Additionally, the teacher can briefly introduce the idea that the cubic root is the number that, when multiplied by itself three times, results in the given number.

2. Problem situation: After the review, the teacher can propose two problem situations to spark students' interest. For example, the teacher can ask: "How can we calculate the square root of a number that is not a perfect square? And the cubic root of a number that is not a perfect cube?" Or "How can we use square and cubic roots to calculate the measurement of a side of a square or cube, if we know the total area or volume?".

3. Contextualization: The teacher should then contextualize the importance of the topic, explaining that the square and cubic roots are fundamental concepts in many areas of mathematics and other disciplines, such as physics, engineering, architecture, and economics. Additionally, the teacher can mention that square and cubic roots are also used in everyday situations, such as in calculating measurements of sides of squares or cubes, in solving geometry problems, and even in recreational activities, such as solving mathematical puzzles.

4. Introduction of the topic: Finally, the teacher should introduce the lesson topic in an engaging way. For example, the teacher can share a curiosity about the origin of the square root symbol, dating back to ancient Egypt, or can show a short video illustrating the application of square and cubic roots in practical situations. The teacher can also propose an initial challenge, such as mentally calculating the square root of 36 or the cubic root of 64.

Development (20 - 25 minutes)

1. Theory - Square and Cubic Roots (10 - 12 minutes): The teacher should present the theory of square and cubic roots clearly and objectively, using practical examples to facilitate students' understanding.

   • Definition of square and cubic roots: The teacher should explain that the square root is the number that, when multiplied by itself, results in the given number, and that the cubic root is the number that, when multiplied by itself three times, results in the given number.

   • Symbols of roots: The teacher should introduce the symbols of square and cubic roots and explain how they are used to represent the calculation operations.

   • Properties of roots: The teacher should present the properties of roots, such as the multiplication property, which states that the root of a product is equal to the product of the roots, and the division property, which states that the root of a fraction is equal to the root of the numerator divided by the root of the denominator.

2. Practice - Calculation of Roots (10 - 13 minutes): After presenting the theory, the teacher should guide students in the practice of calculating square and cubic roots.

   • Calculation of square roots: The teacher should start by teaching students how to calculate square roots. He should show how to factorize the number to be rooted and how to use the multiplication property to simplify the root. The teacher should then introduce the calculator as a tool to verify manual calculations.

   • Calculation of cubic roots: Next, the teacher should teach students how to calculate cubic roots. He should present the decomposition into prime factors as a strategy to simplify the cubic root. The teacher should then show how to perform manual calculation and how to use the calculator to verify the calculations.

   • Calculation of roots of decimal numbers: Finally, the teacher should teach students how to calculate roots of decimal numbers. He should explain that the process is the same as for integers, but that it is necessary to add zeros at the end of the number before factorizing it.

3. Application - Problem Situations (5 - 10 minutes): After the practice, the teacher should propose some problem situations for students to apply the acquired knowledge. The situations may involve determining square and cubic roots, as well as calculating measurements in practical everyday situations. The teacher should guide students in solving the problems, clarifying doubts and providing feedback.

   • Examples of problem situations: For example, the teacher may propose that students calculate the square and cubic root of some numbers, determine the measurement of a side of a square or cube, if they know the total area or volume, or solve a geometry problem involving root calculations.

Return (8 - 10 minutes)

1. Group discussion (3 - 4 minutes): The teacher should promote a group discussion about the solutions found by students for the proposed problem situations. During the discussion, the teacher should encourage students to explain how they arrived at their answers, to share the strategies they used, and to discuss the validity of the solutions found.

2. Connection with theory (2 - 3 minutes): The teacher should then make the connection between the solutions found by students and the theory presented. He should highlight how the properties of roots, factorization, and decomposition into prime factors were used by students to simplify the calculations and to solve the proposed problem situations. The teacher should also reinforce the importance of understanding the theory to be able to correctly apply it in practical situations.

3. Individual reflection (1 - 2 minutes): After the group discussion, the teacher should propose that students make a brief individual reflection on what they learned in the lesson. The teacher can ask questions like: "What was the most important concept you learned today?" and "What questions have not been answered yet?". The goal of this step is to have students internalize the acquired knowledge and identify possible gaps in their understanding, which can be addressed in future lessons.

4. Teacher's feedback (2 - 3 minutes): Finally, the teacher should provide feedback to students about the lesson. He should praise students' efforts, highlight the positive aspects of their participation, and point out possible areas for improvement. Additionally, the teacher should answer questions and doubts that arose during the lesson, clarify concepts that have not been fully understood yet, and reinforce the most important points of the lesson.

5. Preparation for the next lesson: The teacher should then introduce the topic of the next lesson and propose some additional reading or study material, if necessary. The teacher can also suggest some practice exercises for students to do at home, in order to consolidate the acquired knowledge and prepare for the next lesson.

Conclusion (5 - 7 minutes)

1. Summary of contents (2 - 3 minutes): The teacher should start the Conclusion by recalling the main points covered during the lesson. This includes the concept of square and cubic roots, the definition of the symbols representing these operations, the properties of roots, the strategies for calculating roots (factorization, decomposition into prime factors, and use of the calculator), and the application of this knowledge in solving problem situations. The teacher should reinforce the importance of each of these topics and how they relate to each other.

2. Connection between theory, practice, and applications (1 - 2 minutes): Next, the teacher should emphasize how the lesson was able to connect the theory, practice, and applications of root calculation. The teacher should highlight that theory provides the necessary foundations for practice, which, in turn, allows students to solve real problem situations. Additionally, the teacher should mention how square and cubic roots are applied in various areas of knowledge and everyday life.

3. Extra materials (1 - 2 minutes): The teacher should then suggest some extra materials for students who wish to deepen their knowledge on the subject. This may include books, websites, videos, and apps that offer additional explanations and exercises on root calculation. The teacher should encourage students to explore these materials and use them to review the content seen in class and to prepare for future lessons.

4. Importance of the subject (1 minute): Finally, the teacher should reinforce the importance of the subject for students' education. He should explain that calculating square and cubic roots is an essential skill not only for mathematics but also for various other areas of knowledge and life. The teacher should encourage students to continue practicing and applying the acquired knowledge in everyday situations. He should also highlight the importance of critical thinking and problem-solving, skills that were stimulated during the lesson and that are fundamental for students' academic and professional success.