Objectives (5 - 7 minutes)

1. Understanding of the first-degree function: Students should be able to understand the concept of a first-degree function, its general form, and how it relates to the graph and table. This includes identifying the coefficients a and b in the first-degree function y = ax + b.

2. Relationship between graph and table: Students should learn the connection between the graph of a first-degree function and its corresponding value table. They should be able to identify how the points on the graph align with the values in the table.

3. Graph construction from the table: Students should be able to construct the graph of a first-degree function given its value table. This includes the ability to identify and plot the corresponding points on the graph.

Secondary Objectives:

• Application of knowledge in everyday situations: Students should be encouraged to apply the acquired knowledge in solving practical problems of daily life, reinforcing the relevance of the content learned.
• Development of logical-mathematical thinking: The study of first-degree functions and their graphical representation contributes to the development of students' logical-mathematical thinking, an essential skill for the study of mathematics and other disciplines.

Introduction (10 - 15 minutes)

1. Review of Previous Content: The teacher should start the lesson by briefly reviewing the concepts of first-degree equation and data representation in a table. This is crucial for students to adequately understand the topics to be covered in the lesson. Additionally, the review will serve to spark students' interest and curiosity about the new content.

2. Problem Situation 1: The teacher should propose the following problem situation: 'Imagine you are in a bike race and you record the distance traveled every minute. If we plot a graph with time on the x-axis and distance on the y-axis, what would be the shape of this graph? And if time does not start at zero, but at one minute? And if the distance traveled is not the same every minute, but increases every minute?'

3. Problem Situation 2: Next, the teacher should propose another problem situation: 'Suppose you are selling lemonade at your stand, and every hour you record the number of lemonades sold. If we plot a graph with time on the x-axis and the number of lemonades on the y-axis, what would be the shape of this graph? And if time does not start at zero, but at one hour? And if the number of lemonades sold is not the same every hour, but increases every hour?'

4. Contextualization: The teacher should explain that these problem situations are examples of how the first-degree function, the graph, and the table can be used to represent and analyze everyday situations. This helps to show the importance and applicability of the content to be studied.

5. Introduction to the Topic: Finally, the teacher should introduce the topic of the lesson in an engaging way, mentioning that students will learn to construct graphs of first-degree functions from tables, and vice versa. Additionally, the teacher can pique students' curiosity by mentioning that these skills are important not only for mathematics but also for other areas such as physics, economics, and engineering.

Development (20 - 25 minutes)

1. Practical Activity 1 - The Bike Race: The teacher should provide each group of students with a table containing the times (in minutes) and the distances (in meters) traveled during the Bike Race. The students should then plot the corresponding graph for this first-degree function. The teacher should move around the classroom to monitor the groups' progress and provide guidance if necessary.

   • Step 1: The teacher should divide the class into groups of up to 5 students and distribute the tables and graph paper.
   • Step 2: Students should discuss in their groups how to organize the data from the table on the graph. They should remember that time is represented on the x-axis and distance on the y-axis.
   • Step 3: Students should mark the graph points corresponding to the values in the table and then draw the line passing through these points.
   • Step 4: The teacher should select some groups to present their graphs to the class, discussing the similarities and differences between them.
   • Step 5: The teacher should reinforce the idea that the line drawn on the graph is the representation of the first-degree function.

2. Practical Activity 2 - The Lemonade Stand: The teacher should provide each group of students with a new table containing the times (in hours) and the number of lemonades sold at the Lemonade Stand. The students should then plot the corresponding graph for this first-degree function. Similar to the previous activity, the teacher should move around the classroom to monitor the groups' progress and provide guidance if necessary.

   • Steps 1 to 4: The steps for carrying out this activity are the same as Activity 1.
   • Step 5: The teacher should again select some groups to present their graphs to the class, discussing the similarities and differences between them.

3. Discussion and Sharing of Experiences: After the conclusion of the practical activities, the teacher should facilitate a classroom discussion where each group shares their experiences in constructing the graphs. This discussion will allow students to see different approaches to the same problem and reinforce the understanding of the concept of first-degree function. Additionally, the teacher should encourage students to make connections between the activities carried out and the problem situations proposed in the Introduction of the lesson.

4. Final Reflection: To conclude the Development stage, the teacher should propose that students reflect for a minute on what they have learned. The teacher can ask questions like: 'What was the most important concept learned today?' and 'What questions have not been answered yet?'. Students can share their reflections with the class if they wish. This will help consolidate learning and identify any areas that may require review or additional clarification.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes): The teacher should facilitate a group discussion with all students to share the solutions or conclusions of their activities. Each group should have up to 3 minutes to present their constructed graphs and tables and explain how they arrived at these representations. During the presentations, the teacher should encourage students to ask each other questions and provide comments or observations on the solutions presented, thus promoting interaction and exchange of ideas among students.

2. Connection with Theory (2 - 3 minutes): After the presentations, the teacher should summarize the main ideas presented by the groups, connecting them with the theory presented at the beginning of the lesson. For example, the teacher can highlight how the points in the table relate to the points on the graph, and how the line drawn on the graph represents the first-degree function. Additionally, the teacher should reinforce the importance of understanding and applying these concepts, not only for mathematics but also for other areas of knowledge and everyday life.

3. Learning Verification (2 - 3 minutes): The teacher should propose that students reflect for a minute on what they have learned in the lesson. Then, the teacher should ask some questions to verify the students' understanding. These questions may include, for example: 'How did you construct the graph from the table?' and 'What is the relationship between the table, the graph, and the first-degree function?'. Students should orally respond to the questions, and the teacher should provide immediate feedback, correcting any misunderstandings and reinforcing the correct concepts.

4. Final Reflection (1 minute): To conclude the lesson, the teacher should propose that students reflect for a minute on what they have learned. The teacher can ask questions like: 'What was the most important concept learned today?' and 'What questions have not been answered yet?'. Students can share their reflections with the class if they wish. This will help consolidate learning and identify any areas that may require review or additional clarification.

5. Teacher Feedback (1 minute): Finally, the teacher should provide overall feedback on the lesson, highlighting the main achievements of the students and identifying any areas that may need review or additional practice. The teacher should also emphasize the importance of the subject studied and how it relates to other topics in mathematics and the real world.

Conclusion (5 - 7 minutes)

1. Summary of Contents (2 - 3 minutes): The teacher should start the Conclusion by summarizing the main points covered during the lesson. This includes the definition of a first-degree function, the identification of its coefficients a and b, the relationship between the graph and the table, and the construction of the graph from the table. The teacher should reinforce these concepts, reminding students of their practical applications and how they contribute to the development of logical-mathematical thinking.

2. Connection with Practice (1 - 2 minutes): Next, the teacher should connect the presented theory with the practical activities carried out. The teacher should remind students that during the activities, they applied theoretical concepts to construct graphs from tables, and vice versa. This will help reinforce the idea that mathematics is not just a set of abstract rules and formulas but a powerful tool for solving everyday problems.

3. Additional Materials (1 minute): The teacher should suggest additional study materials for students who wish to deepen their knowledge of first-degree functions, graphs, and tables. This may include math books, educational websites, instructional videos, and math learning apps. The teacher should encourage students to explore these materials on their own, reinforcing the importance of autonomy and initiative in the learning process.

4. Relevance of the Subject (1 - 2 minutes): To conclude, the teacher should emphasize the importance of the subject studied for everyday life and other areas of knowledge. For example, the teacher can mention that the ability to construct and interpret graphs of first-degree functions is crucial for understanding and solving problems in various areas such as physics, economics, engineering, and social sciences. Additionally, the teacher should emphasize that the development of logical-mathematical thinking, promoted by the study of mathematics, is a valuable skill that can be applied in many aspects of life.