Objectives (5 - 7 minutes)

1. Understand the concept of the area of a square: The teacher should explain to the students the concept of area and how it applies to the square. It should be emphasized that the area is the measure of how much surface the square covers.

2. Calculate the area of a square: The teacher should teach the students the formula to calculate the area of a square. It should be explained that the area of the square is the side of the square squared. For example, if the side of the square is 5 cm, then the area of the square is 5 x 5 = 25 cm².

3. Solve practical problems involving the area of a square: The teacher should guide the students to solve practical problems that involve calculating the area of a square. This will help students apply the concept and formula in a practical way and understand how the area of a square is used in the real world.

   • Secondary objective: Develop critical thinking and problem-solving skills. By solving practical problems, students will have the opportunity to enhance their critical thinking and problem-solving skills, which are valuable skills in many areas of life.

The teacher should present these Objectives at the beginning of the lesson so that students know what to expect and what they should learn. Additionally, the teacher should check if the students have any questions about these Objectives and clarify them if there are any.

Introduction (10 - 12 minutes)

1. Review of previous content: The teacher should start the lesson by briefly recalling the concepts of a square, sides of a square, and exponentiation. These are fundamental concepts that students need to understand before learning about the area of a square.

2. Problem situations:

   • Situation 1: The teacher can present an image of a soccer field, which is generally a square, and ask the students how they could calculate the area of this field. This situation will help students understand the relevance of calculating the area and how it applies in real-world situations.

   • Situation 2: The teacher can present an image of a rectangular plot and ask the students if they know how to calculate the area of this plot. This will help introduce the concept of area, as the rectangular plot can be divided into smaller squares, making it easier to calculate the area.

3. Contextualization: The teacher can explain that calculating the area of a square is a very useful skill in many professions and everyday situations. For example, architects need to calculate the area of plots to design buildings, farmers need to calculate the area of their fields to determine the amount of seeds to be planted, and so on.

4. Gaining students' attention:

   • Curiosity 1: The teacher can explain that the formula to calculate the area of a square, which is side squared, is one of the simplest and most important formulas in mathematics. He can ask the students if they know what "squared" means and how it affects the calculation of the area.

   • Curiosity 2: The teacher can share that the concept of area was developed by the ancient Egyptians and Greeks, who needed to calculate the area of their lands for taxation purposes. He can ask the students if they can imagine how the ancient Egyptians and Greeks could have calculated the area of a square without the formula we have today.

At the end of the Introduction, students should be engaged and ready to learn more about the area of a square. The teacher can then move on to the next stage, which is the explanation of the lesson content.

Development (20 - 25 minutes)

1. Theory: The teacher should start presenting the theory about the area of a square. He should explain that the area is a two-dimensional measure that expresses the amount of surface a flat object occupies.

   • Definition of area: The teacher should explain that the area is a measure and should be expressed in square units, such as cm², m², or km². He can draw a parallel with the idea of volume, which is the three-dimensional measure that expresses the space an object occupies, and which is expressed in cubic units, such as cm³, m³, or km³.

   • Properties of area: The teacher should explain that the area of a square is always a non-negative number, as we cannot have a negative or zero area in the real world. Additionally, the area of a square always increases when the side of the square increases, which makes sense because if we increase the side of a square, we are increasing the surface it occupies.

2. Formula for the area of a square: The teacher should present the formula to calculate the area of a square. He should explain that the formula is simple and straightforward: the area of a square is the side of the square squared.

   • Derivation of the formula: The teacher can explain how the formula is derived. He can draw a square and divide the square into small smaller squares, each with a side of the original square. Then, he can explain that the area of the original square is equal to the sum of the areas of all the small squares. Since all the small squares have the same area, the area of the original square is equal to the number of small squares (i.e., the side of the square) squared.

3. Practical examples: After explaining the theory, the teacher should present some practical examples to illustrate the calculation of the area of a square. He can start with simple examples, where the side of the square is an integer, and then move on to more complex examples, where the side of the square is a decimal number or a fraction.

   • Example 1: The teacher can ask the students to calculate the area of a square with a side of 3 cm. He should explain step by step how to do the calculation, and the students should follow along and do the calculation in their notes.

   • Example 2: The teacher can ask the students to calculate the area of a square with a side of 5.5 cm. This example will help students understand how to calculate the area when the side of the square is a decimal number.

4. Problem-solving: After presenting the theory and practical examples, the teacher should guide the students to solve practical problems that involve calculating the area of a square. The problems can vary in difficulty, from simple problems that involve direct calculation of the area to more complex problems that involve using the area to solve other mathematical problems.

At the end of the Development, students should have a clear understanding of the concept of the area of a square, the formula to calculate the area of a square, and how to apply this knowledge to solve practical problems. The teacher can then move on to the next stage, which is independent practice.

Feedback (8 - 10 minutes)

1. Review of concepts: The teacher should start this stage by recapping the key concepts learned during the lesson. He should remind the students about the concept of area, the formula to calculate the area of a square, and how this formula is derived. He should also reinforce the idea that the area of a square is always a non-negative number and that it increases when the side of the square increases.

2. Connection between theory and practice: The teacher should then explain how the theory connects with practice, recalling the practical examples presented during the lesson. He should show how the formula is applied to calculate the area of a square, and how this skill can be useful in real-life situations, such as calculating the area of a plot, a soccer field, or any surface that is approximately a square.

3. Individual reflection: The teacher should ask the students to take a minute to think about what they learned during the lesson. They should reflect on what were the most important concepts learned, what difficulties they encountered, and how they could apply what they learned in other situations.

4. Sharing reflections: After the minute of reflection, the teacher can ask some students to share their reflections with the class. This can be done voluntarily, so as not to embarrass the shyer students. The students can talk about what they found most interesting in the lesson, what they found most difficult, and how they think they could use what they learned in their lives or in other contexts.

5. Teacher feedback: The teacher should listen carefully to the students' reflections and offer constructive feedback. He should praise the positive points, such as effort, participation, and understanding of the concepts, and should also offer suggestions for improvement, if necessary. He should reinforce that practice is essential for learning mathematics, and should encourage students to continue practicing at home.

6. Lesson closure: Finally, the teacher should close the lesson in a positive way, reinforcing the importance of the subject studied and thanking everyone for their participation and effort. He should remind the students to study the content at home and to bring any questions to the next lesson.

At the end of this stage, students should have a clear understanding of what they learned during the lesson, how the theory connects with practice, and how they can continue learning and practicing the subject at home. The teacher can then move on to the next stage, which is the Conclusion of the lesson.

Conclusion (5 - 7 minutes)

1. Summary of content: The teacher should start the Conclusion by making a brief summary of the content covered during the lesson. He should recap the concept of area, the formula to calculate the area of a square, and how this formula is derived. He should also remind the students about the importance of understanding and correctly applying the formula for the area of a square.

2. Connection between theory, practice, and applications: Next, the teacher should reinforce how the lesson connected theory, practice, and applications. He should remind the students about the practical examples presented during the lesson and how they helped illustrate the application of the formula for the area of a square. The teacher should also reinforce the importance of calculating the area of a square in various professions and everyday situations.

3. Extra materials: The teacher can suggest some extra materials for students who want to deepen their knowledge about the area of a square. He can recommend math books, educational websites, YouTube videos, and math learning apps. The teacher should remind the students that self-study is an essential part of the learning process, and that they should make the most of these additional resources.

4. Importance of the subject: Finally, the teacher should emphasize the importance of the subject presented for the students' daily lives. He can cite examples of everyday situations where calculating the area of a square can be useful, such as calculating the area of a plot, a room, a soccer field, and so on. The teacher should reinforce that mathematics is a powerful tool that can help us understand and solve real-world problems.

5. Lesson closure: The teacher should close the lesson by reinforcing the importance of study and practice for learning mathematics. He should thank everyone for their participation and effort, and remind the students to study the content at home and bring any questions to the next lesson.

At the end of the lesson, students should have a clear understanding of the concept of the area of a square, how to calculate the area of a square, and how to apply this knowledge to solve practical problems. They should also be aware of the importance of self-study and how they can continue learning and practicing the subject at home.