Objectives (5 - 7 minutes)

1. Understand the concept of absolute value and modulus:

   • Identify the absolute value of a real number as the distance from that number to zero on a number line.
   • Understand that the modulus is a generalization of absolute value for any set that has a norm function.

2. Apply the property of absolute value in equations and inequalities:

   • Solve equations and inequalities involving absolute value, using the definition of modulus.

3. Develop critical thinking skills and problem-solving abilities:

   • Use absolute value and modulus to solve real-world problems, applying the concept of distance.

Secondary Objectives:

1. Foster active participation of students in the class, encouraging discussion and questioning on the topic.
2. Stimulate research and autonomous study, by indicating support materials for the prior study of the content.
3. Promote interdisciplinarity, relating mathematical content to other areas of knowledge.

Introduction (10 - 15 minutes)

1. Review of Previous Content:

   • The teacher starts the class by quickly reviewing the concepts of real numbers, number line, and basic operations (addition, subtraction, multiplication, and division). This review is essential to ensure that students have the necessary foundation to understand the new content. (3 - 5 minutes)

2. Problem-Solving Scenarios:

   • The teacher presents two problem-solving scenarios that arouse the interest and curiosity of students towards the new content. For example:
     • 'Imagine you are in a city and want to know the distance to the sea, but you don't have a GPS. How could you use mathematics to solve this problem?'
     • 'If you have a bank account with a negative balance, what does that mean in mathematical terms? How would you represent this situation on the number line?' (3 - 5 minutes)

3. Contextualization:

   • The teacher explains that absolute value and modulus are fundamental concepts in mathematics and have various practical applications. For example:
     • In physics, modulus is used to represent the intensity of vector quantities, such as force and velocity.
     • In economics, absolute value is used to represent the difference between two prices or rates.
     • In geography, absolute value is used to represent latitude and longitude, which are coordinates describing the location of a point on Earth. (2 - 3 minutes)

4. Topic Introduction:

   • The teacher introduces the concept of absolute value and modulus, explaining that they represent the distance between a number and zero on the number line. He also mentions that the modulus is a generalization of absolute value, which can be used in any set that has a norm function. (2 - 3 minutes)

This Introduction stage is crucial to capture students' attention, clarify the importance of the content, and establish a solid conceptual foundation for the Development of the rest of the class.

Development (20 - 25 minutes)

1. Activity 'The Modulus Game':

   • The teacher divides the class into groups of 3 to 5 students and gives each group a set of numbered cards and a 'ruler' (which can be the classroom ruler or a measuring tape).
   • Each card has a real number, both positive and negative.
   • The goal of the game is to order the cards from the smallest to the largest absolute value, using only the ruler to measure the distance from zero to the number on the card.
   • The group that can correctly order all the cards in the shortest time possible is the winner.
   • The teacher circulates around the room, guiding the groups and clarifying doubts.
   • This activity aims to reinforce the concept of absolute value as the distance from a number to zero, in a playful and interactive way. Additionally, it promotes teamwork and critical thinking in problem-solving. (10 - 12 minutes)

2. Activity 'Solving Inequalities':

   • After the conclusion of the game, the teacher proposes a challenge: each group must create a sequence of inequalities involving the absolute value of the numbers on the cards and solve them.
   • The group that creates the most complex set of inequalities (but still solvable) and solves it correctly is the winner.
   • The teacher reinforces the idea that absolute value transforms inequalities into equations, which facilitates the resolution.
   • This activity aims to apply the concept of absolute value in solving inequalities, in a practical and contextualized way. Additionally, it stimulates the creativity and logical reasoning of students. (8 - 10 minutes)

3. Activity 'Real-World Problems':

   • Finally, the teacher suggests that each group think of a real-world problem that can be solved using absolute value.
   • The groups must present the problem and the solution to the class, explaining step by step how they arrived at that solution.
   • The teacher provides feedback on the groups' solutions, encouraging discussion and reflection.
   • This activity aims to promote the application of the concept of absolute value in real situations, encouraging reflection on the usefulness of mathematics in everyday life. (5 - 7 minutes)

These activities promote active learning and knowledge construction, as students are challenged to solve problems, discuss ideas, and apply mathematical concepts in a practical and contextualized way. Additionally, they encourage collaboration and communication among students, essential skills for life in society.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes):

   • The teacher asks each group to share the solutions or ideas they developed during the activities. Each group will have a maximum of 3 minutes to present.
   • During the presentations, the teacher should encourage active participation from the class, asking questions that promote reflection and deepening the understanding of the concept of absolute value and modulus.
   • The teacher should also take this opportunity to correct any conceptual misunderstandings that may have arisen during the activities.

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

   • After the presentations, the teacher gives a brief recap of the activities, highlighting the main concepts and skills that were worked on.
   • The teacher should also connect practice with theory, reinforcing how the activities carried out illustrate the application of absolute value and modulus in solving real-world problems.
   • Additionally, the teacher can link the theoretical contents presented in the Introduction, reinforcing the definition of absolute value and modulus and their importance in mathematics and other areas of knowledge.

3. Final Reflection (2 - 3 minutes):

   • To conclude the class, the teacher proposes that students reflect briefly on what they have learned. He can ask questions like:
     1. 'What was the most important concept you learned today?'
     2. 'What questions have not been answered yet?'
   • The teacher should give a minute for students to think and then ask some of them to share their answers with the class.
   • This final reflection serves to consolidate learning, identify possible gaps in students' understanding, and stimulate curiosity and interest in the topic.

The Return is a crucial stage of the lesson plan, as it allows the teacher to assess students' progress, correct conceptual misunderstandings, and reinforce the main points of the content. Additionally, it promotes reflection and metacognition, essential skills for effective learning.

Conclusion (5 - 7 minutes)

1. Content Summary (2 - 3 minutes):

   • The teacher summarizes the main points covered during the class, reinforcing the concept of absolute value as the distance from a number to zero on the number line and the modulus as a generalization of absolute value for any set that has a norm function.
   • He also highlights the applications of absolute value and modulus, such as in solving real-world problems involving the idea of distance.
   • The teacher can use the number line and examples of equations and inequalities with absolute value to illustrate these concepts.

2. Theory-Practice Connection (1 - 2 minutes):

   • The teacher reinforces how the activities carried out during the class connected theory with practice, allowing students to understand the concepts of absolute value and modulus in a concrete and applied way.
   • He emphasizes the importance of understanding theoretical concepts to solve practical problems and how problem-solving can help consolidate theoretical knowledge.

3. Supplementary Materials (1 minute):

   • The teacher suggests some complementary study materials for students who wish to deepen their knowledge of absolute value and modulus.
   • These materials may include explanatory videos, online exercises, interactive math websites, and textbooks.
   • For example, the teacher may recommend using Khan Academy, a website that offers a wide variety of free educational resources, including video lessons on absolute value and modulus.

4. Subject Importance (1 - 2 minutes):

   • To conclude the class, the teacher emphasizes the importance of absolute value and modulus in everyday life and in other disciplines.
   • He may mention again examples of applications of absolute value and modulus in areas such as physics, economics, and geography.
   • The teacher can also highlight that the ability to understand and work with absolute value and modulus is a valuable skill, not only for mathematics but also for critical thinking and general problem-solving.

The Conclusion is an essential stage to consolidate learning, reinforce key points of the content, promote the connection between theory and practice, and stimulate curiosity and interest of students in the topic. Additionally, by suggesting complementary study materials and highlighting the applications of the content, the teacher demonstrates to students that learning is not limited to class time but is a continuous process that can be explored in various ways.