Objectives (5 - 7 minutes)

1. Understand the concept of factoring by difference of squares:

   • Identify when an expression is a difference of squares.
   • Apply the factoring method by difference of squares to simplify the expression.

2. Develop skills to solve problems involving factoring by difference of squares:

   • Solve exercises that involve factoring by difference of squares.
   • Apply factoring by difference of squares in practical situations.

3. Understand the importance of factoring by the difference of squares in mathematics and other disciplines:

   • Identify applications of factoring by the difference of squares in real contexts and in other disciplines.
   • Recognize the usefulness of factoring by the difference of squares to facilitate the process of solving equations and expressions.

Secondary objectives:

1. Stimulate critical thinking and problem solving:

   • Encourage students to think critically and analytically when solving exercises factoring difference of squares.
   • Encourage the search for different problem-solving strategies.

2. Promote interaction and collaboration:

   • Encourage group discussion for solving problems.
   • Encourage students to help each other in understanding the content.

Introduction (10 - 12 minutes)

1. Review of previous content:

   • The teacher begins the class by reviewing the concepts of factoring, perfect squares, and algebraic expressions.
   • It is important that students understand these basic concepts before moving on to factoring by difference of squares. (3 - 4 minutes)

2. Problem situations:

   • The teacher presents two situations that need factoring by difference of squares to be solved:

     1. "If you have a total area of 45m² and the width is 3m less than the length, how can you factor this difference of squares to find the dimensions of the rectangle?"
     2. "If you have a trinomial of the type x² - 16, how can you factor it using the difference of squares?"

   • These situations aim to arouse the students' interest and show the applicability of the content. (3 - 4 minutes)

3. Contextualization:

   • The teacher gives examples of how factoring differences of squares is used in practice, such as in solving quadratic equations and in factoring complex algebraic expressions.
   • In addition, the teacher may mention that factoring the difference of squares is an important tool in subjects such as physics and engineering. (2 - 3 minutes)

4. Gaining the students' attention:

   • The teacher can share trivia about factoring the difference of squares. For example, factoring the difference of squares is one of the oldest techniques in mathematics, dating back to the time of the Greek mathematician Euclid.
   • In addition, the teacher can present a modern application, such as the use of factoring the difference of squares in cryptography algorithms. (2 - 3 minutes)

Development (20 - 25 minutes)

1. Explanation of the theory (10 - 12 minutes)

   • The teacher begins the explanation of the theoretical content by defining factoring the difference of squares as a technique used to factor an expression that is the difference of two perfect square terms.

   • Then, the teacher explains that to factor a difference of squares, you need to identify the two terms that are perfect squares and then apply the formula (a - b)(a + b).

   • The teacher demonstrates the process of factoring the difference of squares using practical examples, step by step, ensuring that the students understand each step.

   • Example 1: x² - 9 → This is an example of factoring the difference of squares, because x² is the square of x and 9 is the square of 3. Therefore, the factored expression is (x - 3)(x + 3).

   • Example 2: 4a² - 25b² → In this example, 4a² is the square of 2a and 25b² is the square of 5b. Factoring the difference of squares results in (2a - 5b)(2a + 5b).

2. Guided practice (5 - 7 minutes)

   • The teacher provides the students with several expressions to factor, guiding them through the process.

   • Example: 16x² - 81y²

     • The teacher asks the students to identify the terms that are perfect squares (16x² and 81y²).
     • Then, the teacher guides the students to apply the factoring formula difference of squares: (a - b)(a + b).
     • The students must then factor the expression, arriving at the answer (4x - 9y)(4x + 9y).

3. Independent practice (5 - 7 minutes)

   • Now it is time for students to practice factoring the difference of squares on their own.

   • The teacher distributes a list of exercises that vary in difficulty, allowing students to work at their own pace.

   • The teacher circulates through the room, providing help as needed and checking the progress of the students.

4. Group discussion (3 - 4 minutes)

   • After the independent practice, the teacher promotes a group discussion, where the students are encouraged to share their resolution strategies.

   • The teacher may ask some students to share the expressions they factored and how they arrived at the answer.

   • This discussion helps to reinforce the understanding of the content and allows students to learn from each other.

5. Reinforcement of the importance of the content (1 - 2 minutes)

   • Finally, the teacher reinforces the importance of factoring the difference of squares, reminding students that this technique is useful in several areas of mathematics and other disciplines.

   • The teacher can provide additional examples of how factoring the difference of squares is used in practice, helping to illustrate the relevance of the content.

Feedback (8 - 10 minutes)

1. Group discussion (3 - 4 minutes):

   • The teacher promotes a group discussion, where students are encouraged to share their solutions to the problems proposed during the class.
   • The teacher may ask some students to explain how they arrived at the answer to a specific exercise, promoting the exchange of ideas and learning among students.
   • The teacher must guide the discussion, ensuring that all aspects of the content have been understood, and clarify any doubts that may arise.

2. Connecting content with practice (2 - 3 minutes):

   • The teacher reinforces the applicability of the content, making connections with real situations and/or other disciplines.
   • For example, the teacher can show how the factoring of the difference of squares is used in calculations of areas and volumes, in solving physics problems, in cryptography algorithms, among others.
   • The teacher can also ask students to think about other situations where factoring the difference of squares could be useful, promoting critical thinking and the application of content.

3. Individual reflection (2 - 3 minutes):

   • The teacher proposes that students reflect for a minute on what they learned during class.

   • Then, the teacher asks the students the following questions:

     1. What was the most important concept you learned today?
     2. What questions do you still have about factoring the difference of squares?

   • Students can write down their answers in a notebook or share them with the class, according to the dynamics of the class.

4. Feedback and clarification of doubts (1 - 2 minutes):

   • The teacher collects feedback from students about the class, asking if they found the content difficult or confusing, and if they felt that their doubts were clarified.
   • The teacher also takes advantage of this moment to clarify any doubts that may still exist and to reinforce the most important concepts of the class.

5. Closure of the class (1 minute):

   • The teacher makes a brief summary of the main points covered in the class and thanks the students for their participation and effort.
   • The teacher may also suggest additional study materials to students, such as books, websites, videos, etc., so that they can deepen their understanding of factoring the difference of squares.

This Feedback is important to evaluate the effectiveness of the class, ensure that all students have understood the content, and clarify any doubts that may have arisen. Furthermore, individual reflection and group discussion allow students to consolidate their learning and develop critical thinking and problem-solving skills.

Conclusion (5 - 7 minutes)

1. Recap of the content (2 - 3 minutes):

   • The teacher reviews the main points covered during the class, reinforcing the concept of factoring the difference of squares and how to apply it in the resolution of expressions.
   • The teacher highlights the importance of identifying which terms are perfect squares and the formula (a - b)(a + b) for factoring a difference of squares.
   • The teacher may also briefly review the practical examples that were used to demonstrate the factoring of the difference of squares.

2. Connection between theory, practice and applications (1 - 2 minutes):

   • The teacher reinforces how the class connected the theory of factoring the difference of squares with practice, through the exercises carried out, and with applications, showing how this technique is useful in several areas, such as mathematics, physics, engineering, among others.
   • The teacher can emphasize that factoring the difference of squares is not just a mathematical tool, but also a useful skill for solving everyday problems and in other disciplines.

3. Extra materials for study (1 minute):

   • The teacher suggests additional study materials so that the students can deepen their understanding of factoring the difference of squares.
   • These materials may include math books, educational websites with interactive exercises, explanatory videos, among others.
   • The teacher can also indicate specific sections of these materials that are relevant to the content of the class.

4. Importance of the content for everyday life (1 - 2 minutes):

   • Finally, the teacher emphasizes the importance of factoring the difference of squares for everyday life, explaining that this technique can be used to solve a variety of practical problems.
   • The teacher can give concrete examples of how factoring the difference of squares can be applied in everyday situations, such as in calculating areas and volumes, in solving physics problems, among others.
   • The teacher concludes the class by reinforcing that factoring the difference of squares is a powerful and versatile tool that students must master in order to succeed in their mathematics studies and in their lives.