Objectives (5 - 7 minutes)

1. Understanding the concept of perfect squares: Students should be able to understand and define what a perfect square is, recognizing that it is the result of multiplying a number by itself.

2. Identification of perfect squares: Students should be able to identify if a number is a perfect square, using verification methods efficiently and accurately.

3. Application of concepts in practical problems: Students should be able to apply the concept of perfect squares in everyday situations and mathematical problems, demonstrating the relevance and usefulness of the topic.

Secondary Objectives

1. Development of critical thinking: By working with the identification of perfect squares, students will develop their critical thinking skills, as they will have to analyze and evaluate different verification methods.

2. Promoting group interaction: Through group discussion activities and problem-solving, students will be encouraged to collaborate and interact with each other, promoting cooperative learning.

Introduction (10 - 12 minutes)

1. Review of previous concepts: The teacher should start the lesson by reminding students about the concept of square numbers and the multiplication operation. This review is essential for students to better understand the concept of perfect squares. (2 - 3 minutes)

2. Problem situations: Next, the teacher can present two problem situations to instigate students' curiosity and introduce the topic. For example:

   • Situation 1: 'Imagine you have a square made up of 25 blocks. How many blocks are there on each side of the square?'

   • Situation 2: 'If you have a square made up of a number x of blocks, how can we know the value of x just by looking at the square?' (3 - 4 minutes)

3. Contextualization of the importance of the subject: After presenting the problem situations, the teacher should explain that the concept of perfect squares is widely used in various areas, such as engineering, architecture, computer science, and even in games and puzzles. For example, in cryptography, an important field of computer science, the concept of perfect squares is used to create security algorithms. (2 - 3 minutes)

4. Engaging introduction to the topic: To make the introduction to the topic more interesting, the teacher can share two curiosities:

   • Curiosity 1: 'Did you know that the concept of perfect squares has a long history, dating back to the Babylonian civilization, which lived over 4,000 years ago? They already knew and used perfect squares in their constructions and calculations.'

   • Curiosity 2: 'Perfect squares are also present in various famous works of art and architecture. For example, in the famous Chartres Cathedral in France, architects used a series of perfect squares in their proportions and design.' (2 - 3 minutes)

Development (20 - 25 minutes)

1. Activity 'Building Perfect Squares' (10 - 12 minutes):

   • Materials needed: For this activity, grid paper, colored pencils, and a ruler will be necessary.

   • Activity description: Students will be divided into groups of up to 5 members. Each group will receive grid paper and colored pencils. They should draw a perfect square on the grid paper, starting from the number 1 and going up to a number determined by the teacher (for example, 10). In the end, each group must present their perfect square and explain how they know it is a perfect square.

   • Activity objective: This activity aims to allow students to visualize and better understand the concept of perfect squares. By drawing the squares, they will also be practicing multiplication.

2. Activity 'Hunt for Perfect Squares' (10 - 12 minutes):

   • Materials needed: For this activity, cards with numbers (ranging from 1 to 100), markers, and a list of perfect squares up to 100 will be necessary.

   • Activity description: Students will continue in their groups. Each group will receive a set of cards with numbers. They must identify which of these numbers are perfect squares, marking them with a marker. The group that correctly identifies the most perfect squares wins the activity.

   • Activity objective: This activity aims to develop students' ability to identify perfect squares quickly and efficiently. Additionally, healthy competition among groups can increase student engagement and motivation.

3. Activity 'Applying Perfect Squares' (5 - 10 minutes):

   • Materials needed: For this activity, mathematical problems involving the concept of perfect squares will be necessary.

   • Activity description: Each group will receive a list of mathematical problems to solve. These problems may include things like calculating the square root of a perfect square, finding the next perfect square number in a sequence, etc. Students should work together to solve the problems, applying what they have learned about perfect squares.

   • Activity objective: This activity aims to help students see how the concept of perfect squares can be applied in practical situations and reinforce their understanding of the concept.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes):

   • The teacher should ask each group to share their solutions or conclusions from the activities carried out. Each group will have a maximum of 3 minutes to present.
   • During the presentations, the teacher should encourage the participation of all students and ask questions to ensure that the concepts are being understood.
   • The teacher should also take this opportunity to highlight the strengths of each presentation and correct any errors or misunderstandings that may have arisen.

2. Connection with Theory (2 - 3 minutes):

   • After all presentations, the teacher should quickly review the theoretical concepts covered in the lesson, emphasizing the importance of perfect squares and how they are calculated.
   • The teacher should then connect the theory with the practical activities, explaining how the exercises performed help to apply and deepen the understanding of perfect squares.

3. Individual Reflection (2 - 3 minutes):

   • To conclude the lesson, the teacher should propose that students engage in a brief individual reflection. They should think for a minute about the following questions:

     1. What was the most important concept learned today?
     2. What questions have not been answered yet?

   • After this reflection time, the teacher can ask some students to share their answers with the class. This can help identify any gaps in students' understanding and provide valuable feedback for future lessons.

4. Feedback and Closure (1 minute):

   • Finally, the teacher should thank all students for their participation and encourage them to continue practicing what they have learned.
   • The teacher should also reinforce that they are available to address any future doubts and that learning is a continuous process that requires practice and effort.
   • The teacher may also request feedback from students about the lesson, asking what they liked the most and what they would like to see more of in future classes.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes):

   • The teacher should recap the main contents covered during the lesson. This includes the concept of perfect squares, methods of identification, and practical applications.
   • It is important for the teacher to summarize this information clearly and concisely, emphasizing the most important points and recalling key concepts.

2. Connection between Theory, Practice, and Applications (1 - 2 minutes):

   • The teacher should explain how the lesson connected the theory of perfect squares with practice, through the activities of building and identifying perfect squares, and with real-world applications, through the proposed mathematical problems.
   • The importance of understanding the theoretical concept to be able to apply it in practical situations and understand its relevance in the real world should be emphasized.

3. Additional Materials (1 - 2 minutes):

   • The teacher should suggest additional study materials for students who wish to deepen their knowledge of perfect squares. This may include math books, educational websites, explanatory videos, among others.
   • It is important for the teacher to provide a variety of resources so that students can choose those that best suit their learning style.

4. Relevance of the Subject (1 minute):

   • Finally, the teacher should summarize the importance of the concept of perfect squares in everyday life, reinforcing that it is used in various areas, from architecture and engineering to computer science and cryptography.
   • The teacher may also suggest to students to pay attention to identify situations where knowledge about perfect squares can be applied, such as in puzzles, games, construction projects, among others.