Objectives (5 - 10 minutes)

1. Understanding First-Degree Equations: Students should be able to understand the concept of first-degree equations and their importance in solving mathematical problems. They should be able to identify a first-degree equation and differentiate it from other types of equations.

2. Solving First-Degree Equations Problems: Students should be able to solve practical problems involving first-degree equations. They should learn how to translate problems into equations and solve these equations using the properties of equality.

3. Application in Everyday Situations: Students should be able to apply the knowledge acquired in solving first-degree equations problems in real-life everyday situations. This will help strengthen the relevance of the topic and motivate learning.

Secondary Objectives:

• Development of Critical and Analytical Thinking Skills: Solving mathematical problems, in general, helps develop critical and analytical thinking skills. The focus in this lesson will be on applying these skills to solve first-degree equations problems.

• Strengthening Basic Math Skills: Understanding and solving first-degree equations require mastering basic math concepts, such as basic operations, properties of equality, and simplification of expressions. This lesson will help reinforce these skills.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher should start the lesson by briefly reviewing the concepts of basic operations (addition, subtraction, multiplication, and division), as well as the idea of equality. This is essential for students to understand and solve first-degree equations. The teacher can ask quick questions or solve some review problems on the board to reinforce these concepts.

2. Problem Situations: To spark students' interest and demonstrate the applicability of the subject, the teacher can propose two problem situations:

   a. "The math teacher bought 20 pens and 15 pencils for her classroom, spending a total of $25.00. Each pen cost the same amount and each pencil cost the same amount. How much did each pen and each pencil cost?"

   b. "John is three times older than Mary. The sum of their ages is 40. What is the age of each one?"

3. Contextualization: The teacher should then explain that these problems are examples of real-life situations that can be solved using first-degree equations. He/she can mention that the ability to solve these types of problems is useful in various areas, such as engineering, finance, sciences, among others.

4. Introduction to the Topic: The teacher should introduce the topic of first-degree equations, explaining that they are mathematical expressions that contain only one variable raised to an exponent of 1, and that the solution is the value of the variable that makes the equality true.

5. Curiosities and Applications: To make the Introduction more interesting, the teacher can share some curiosities or applications of the subject:

   a. Curiosity 1: "Did you know that linear equations, which are a special type of first-degree equation, are used to model many natural and societal phenomena? For example, Hooke's Law, which describes the force needed to stretch a spring, is a linear equation."

   b. Curiosity 2: "Did you know that linear equations were used by the ancient Egyptians to solve practical problems, such as calculating the amount of grain needed to make an offering to a god?"

   c. Application: "First-degree equations are very useful in everyday situations, such as solving proportionality problems, dividing expenses, calculating time and distance, among others. Learning how to solve them will help you solve many everyday situations more efficiently."

Development (20 - 25 minutes)

1. Activity 1 - Equations Game (10 - 15 minutes):

   a. Preparation: The teacher should divide the class into groups of 4 to 5 students. Then, he/she will distribute to each group a set of cards, each containing a first-degree equation and a related problem, as in the following examples:

    - "x + 3 = 7" (Problem: John had x candies and received 3 more. How many candies does he have now, knowing that the total is 7?)
    - "2x - 5 = 7" (Problem: Twice a number minus 5 equals 7. What is the number?)
    - "3(x - 2) = 9" (Problem: The triple of the difference between a number and 2 is equal to 9. What is the number?)
   

   b. Execution: The teacher will explain the rules of the game: each group must solve the equations and problems within a set time. Then, they should exchange their cards with another group, which will check if the answer is correct. Next, the initial group will receive cards from another group to check. The game continues until all cards have been used.

   c. Feedback and Discussion: After the game, the teacher will lead a group discussion, questioning students about the strategies used to solve the equations and problems, the difficulties encountered, the similarities and differences between the equations, etc.

2. Activity 2 - Creation of Problem Situations (10 - 15 minutes):

   a. Preparation: The teacher, still with the groups formed, will ask each group to create two different problem situations involving first-degree equations. These problems should be written on paper, along with the corresponding equation.

   b. Execution: Each group will present their problem situations to the class. The other groups will have a set time to solve the equation and the problem.

   c. Feedback and Discussion: After each presentation, the teacher will lead a discussion, asking students about the strategies used to solve the equations and problems, the difficulties encountered, the similarities and differences between the presented equations, etc.

   d. Evaluation: The teacher will assess the students' participation and performance during the activities, as well as their ability to create and solve problem situations involving first-degree equations.

3. Activity 3 - Application in Everyday Situations (5 - 10 minutes):

   a. Preparation: The teacher, still with the groups formed, will hand out to each group a set of cards containing everyday situations that can be solved with first-degree equations, as in the following examples:

    - "Maria spent $30.00 to buy 5 boxes of pencils and 2 pens. Each box of pencils cost the same amount and each pen cost the same amount. How much did each box of pencils and each pen cost?"
    - "Carlos is twice as old as his brother. The sum of their ages is 40. What is the age of each one?"
   

   b. Execution: Each group must choose one of the cards and solve the problem situation, translating it into a first-degree equation and solving it.

   c. Feedback and Discussion: After the activity, the teacher will lead a group discussion, questioning students about the application of what they learned in solving everyday situations, the difficulties encountered, etc.

   d. Evaluation: The teacher will assess the students' ability to apply what they learned in solving everyday situations, as well as their participation and performance during the activity.

Return (10 - 15 minutes)

1. Group Discussion (5 - 7 minutes):

   a. Sharing Solutions: The teacher should ask each group to share their solutions or conclusions from the activities carried out. This may include the first-degree equations they created, the strategies they used to solve them, and the difficulties they encountered. The teacher should encourage students to explain their reasoning and justify their answers.

   b. Teacher's Feedback: After each group shares, the teacher should provide feedback, praising strengths, correcting errors, and clarifying misunderstood concepts. The teacher can also highlight effective strategies that students used and encourage them to apply them in other situations.

   c. Group Discussion: The teacher should then lead a group discussion, connecting the solutions from different groups, identifying patterns, and highlighting key ideas or strategies. For example, the teacher may ask: "How many of you used the same strategy to solve this problem?" or "How did you approach this challenge differently?"

2. Learning Verification (3 - 5 minutes):

   a. Verification Questions: The teacher should ask questions to verify if the lesson Objectives were achieved. This may include questions about the concept of first-degree equations, solving problems involving these equations, and applying these skills in everyday situations.

   b. Quick Assessment: The teacher should assess the students' answers, identifying any gaps in their understanding and planning future interventions, if necessary.

3. Final Reflection (2 - 3 minutes):

   a. Reflection Questions: The teacher should ask questions for students to reflect on what they have learned. This may include questions like: "What was the most important concept you learned today?" or "What questions have not been answered yet?"

   b. Students' Responses: The teacher should listen to students' responses, valuing their perspectives and helping them make connections between what they learned and the world around them.

4. Closure (1 minute):

   a. Recap: The teacher should recap the main points of the lesson, emphasizing key concepts, effective strategies, and practical applications.

   b. Next Steps: The teacher should inform students about what to expect in the next lesson and what tasks or extra studies can help them deepen their understanding of the subject.

   c. Final Encouragement: The teacher should encourage students to continue practicing and exploring the topic outside the classroom, reminding them that mathematics, like any other skill, improves with practice and persistence.

Conclusion (5 - 7 minutes)

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

   a. Key Concepts: The teacher should summarize the main concepts covered in the lesson, reminding students about what first-degree equations are, how to solve them, and how to apply these skills in solving everyday problems.

   b. Review of Strategies and Methods: The teacher should review the strategies and methods discussed during the lesson, highlighting those that students found most useful or effective.

   c. Connections between Theory and Practice: The teacher should emphasize how the lesson connected theory, practice, and application, and how this is essential for a deep understanding of the topic.

2. Extra Materials (1 - 2 minutes):

   a. Reading Recommendations: The teacher should suggest additional readings for students who wish to deepen their knowledge of first-degree equations. This may include references from textbooks, websites, online videos, among others.

   b. Practice Activities: The teacher can also suggest additional practice activities, such as problems to solve, math games, among others, that students can do at home to strengthen their skills.

3. Connection with Everyday Life (1 - 2 minutes):

   a. Practical Application: The teacher should reinforce the practical application of what was learned, reminding students how the ability to solve first-degree equations can be useful in various everyday situations, such as solving financial problems, time and distance calculations, and many others.

   b. Importance of Mathematics: The teacher should highlight the importance of mathematics in daily life, showing that the ability to solve mathematical problems is not only useful for school but also for life.

4. Closure (1 minute):

   a. Thanking and Encouraging: The teacher should thank the students for their participation and effort during the lesson, and encourage them to continue studying and practicing what they have learned.

   b. Subject Importance: To conclude, the teacher can remind the importance of the subject and how mastering first-degree equations can facilitate problem-solving in different areas of knowledge.