Objectives (5 - 7 minutes)

1. Understand the concept of prime numbers and their importance in mathematics.
2. Identify and differentiate prime numbers from composite numbers.
3. Practice identifying prime and composite numbers through exercises and problem-solving situations.

Secondary Objectives:

1. Develop critical thinking and logical-mathematical skills in identifying prime and composite numbers.
2. Encourage active student participation through practical activities and group discussions.
3. Reinforce prior knowledge about factors and multiples, which are fundamental concepts for understanding prime and composite numbers.

Introduction (10 - 12 minutes)

1. Review of previous concepts: The teacher starts the lesson by reviewing the concepts of factors and multiples, which are essential for understanding prime and composite numbers. This review can be done through questions and answers with the students, encouraging their active participation. (3 - 4 minutes)

2. Problem-solving situation 1: The teacher presents the following situation: 'Imagine you have a box with 12 balls and need to organize them in rows with the same number of balls in each row. How many different ways can you do this?' This situation is presented so that students realize the importance of understanding the concepts of factors and multiples, which are directly related to prime and composite numbers. (3 - 4 minutes)

3. Contextualization: The teacher explains that prime and composite numbers are widely used in mathematics and in various other areas, such as data encryption, game theory, economics, among others. Therefore, understanding these concepts is fundamental for the development of logical-mathematical skills and for the practical application of knowledge. (2 - 3 minutes)

4. Curiosities: The teacher presents two curiosities to spark the students' interest:

   • Curiosity 1: 'Did you know that the Greek mathematician Euclid proved over 2000 years ago that there are infinite prime numbers? This problem, known as 'The Infinitude of Prime Numbers,' is one of the oldest in mathematics and still does not have a simple solution.'

   • Curiosity 2: 'How about this: Have you heard of Mersenne prime numbers? They are prime numbers that can be written in the form 2^n - 1, where n is a natural number. Despite appearing as a simple formula, only 51 Mersenne prime numbers have been discovered to this day!'

The teacher concludes the Introduction, emphasizing the importance of the lesson and reinforcing that, despite being complex concepts, they will be addressed gradually and didactically so that all students can understand them. (1 - 2 minutes)

Development (20 - 25 minutes)

1. Activity 1: 'Discovering Prime Numbers' (10 - 12 minutes)

   • The teacher divides the class into groups of 3 to 4 students and gives each group a sheet of sulfite paper and a set of colored pens.
   • Next, the teacher proposes the following activity: 'Each group must create a 'Number Tree' with all numbers from 1 to 50. Prime numbers should be represented by colored circles and composite numbers by white squares. The groups should use different colors to represent Mersenne prime numbers and the other prime numbers. In addition, each group must write next to each composite number its factorization into prime factors.'
   • The students begin the activity. They should work together, discussing which numbers are prime and which are composite. They should also try to factorize composite numbers into prime factors. The teacher circulates around the room, guiding the students and clarifying doubts.
   • At the end of the activity, each group presents their 'Number Tree' to the class, explaining their choices and reasoning. The teacher takes this opportunity to make comments, reinforce concepts, and correct possible errors.

2. Activity 2: 'The Numbers Game' (10 - 12 minutes)

   • The teacher introduces the game to the class: 'In this game, each group will receive a card with different numbers. The goal is to identify, among the numbers on the card, which are prime and which are composite. You have 5 minutes to complete this task. At the end of the time, the group that has correctly identified the highest number of primes and composites will be the winner!'
   • The teacher distributes the cards and the students begin to play. During the game, the teacher circulates around the room, observing the groups' performance and assisting when necessary.
   • At the end of the game, the teacher leads a brief discussion about the strategies used by the groups to identify prime and composite numbers. The teacher also takes the opportunity to reinforce concepts, correct possible errors, and clarify doubts.

3. Activity 3: 'Mersenne Prime Numbers Challenge' (5 - 6 minutes)

   • The teacher proposes a final challenge to the class: 'Whoever can identify the highest number of Mersenne Prime Numbers in their group's 'Number Tree' will earn an extra point in the bimonthly average!'
   • The students, motivated by the challenge, return to their 'Number Trees' and begin searching for Mersenne Prime Numbers. The teacher circulates around the room, encouraging the students and clarifying doubts.
   • At the end of the time, the teacher checks the 'Number Trees' and announces the winning group. The teacher takes this opportunity to make comments about Mersenne Prime Numbers, their importance in mathematics, and the difficulties they pose for mathematicians.

Return (8 - 10 minutes)

1. Group Discussion (3 - 4 minutes)

   • The teacher gathers all students and initiates a group discussion. First, each group is asked to share the solutions or conclusions they reached during the activities.
   • Each group will have a maximum of 2 minutes to share their findings. The teacher must ensure that all groups have the opportunity to speak and that the time is respected.
   • While the groups present, the teacher should ask probing questions to stimulate the students' reflection and to ensure that everyone understood the concepts discussed.

2. Connection to Theory (2 - 3 minutes)

   • After all presentations, the teacher should summarize the main ideas and concepts discussed, linking them to the theory presented at the beginning of the lesson.
   • For example, the teacher can highlight the importance of factors and multiples in identifying prime and composite numbers, and how the practical activity of creating the 'Number Tree' helped visualize these concepts.
   • The teacher can also reinforce the relevance of Mersenne Prime Numbers, mentioning again the curiosity that despite appearing as a simple formula, only 51 Mersenne prime numbers have been discovered to this day.

3. Individual Reflection (2 - 3 minutes)

   • To conclude the lesson, the teacher proposes that students reflect for a minute on the following questions:
     1. 'What was the most important concept you learned today?'
     2. 'What questions have not been answered yet?'
   • After the minute of reflection, the teacher asks students to share their answers. This is an opportunity for the teacher to assess students' understanding of the concepts covered and for students to express their doubts or difficulties.
   • The teacher should note the main doubts or difficulties identified to be addressed in future lessons.

4. Feedback and Closure (1 minute)

   • The teacher thanks everyone for their participation and reinforces the importance of continuous study and practice for understanding prime and composite numbers.
   • The teacher also informs students that the identified doubts will be addressed in future lessons and that they can approach him at any time to clarify doubts or seek help.

This Return moment is essential to consolidate learning, identify possible gaps in understanding, and encourage reflection and self-assessment among students. Additionally, it promotes interaction and the exchange of ideas among students, contributing to the development of social skills and the collective construction of knowledge.

Conclusion (5 - 7 minutes)

1. Summary of Activities (2 - 3 minutes)

   • The teacher begins the Conclusion by summarizing the activities carried out throughout the lesson, recalling the importance of each one for understanding the concepts of prime and composite numbers.
   • The 'Discovering Prime Numbers' activity is highlighted, which allowed students to visualize and identify these numbers within a set.
   • Additionally, the 'Numbers Game' is mentioned, which provided students with the opportunity to apply what they learned in a playful and fun way.
   • Finally, the challenge of 'Mersenne Prime Numbers' was highlighted as an opportunity to deepen knowledge and work on critical and logical-mathematical thinking.

2. Connection between Theory and Practice (1 - 2 minutes)

   • The teacher reinforces how the lesson connected theory, through the review of factors and multiples concepts, with practice, through the activities carried out.
   • It is explained that theory was applied in a practical and contextualized manner, which facilitated students' understanding of the concepts.
   • Additionally, it is emphasized that the activities provided students with the opportunity to develop critical thinking and logical-mathematical skills.

3. Supplementary Materials (1 - 2 minutes)

   • The teacher suggests some supplementary materials for students who wish to deepen their knowledge of prime and composite numbers. Suggestions include:
     • Educational videos available on YouTube, which explain the concept and importance of prime and composite numbers in a didactic and fun way.
     • Websites and math game apps that offer interactive activities for practice and deepening of knowledge.
   • The teacher emphasizes that autonomous study is an excellent way to consolidate learning and develop autonomy and responsibility for studies.

4. Importance of Prime and Composite Numbers (1 minute)

   • To conclude, the teacher reinforces the importance of prime and composite numbers, explaining that they are fundamental in mathematics and in various other areas, such as data encryption, game theory, economics, among others.
   • The teacher emphasizes that, in addition to their practical application, the study of prime and composite numbers contributes to the development of logical-mathematical skills, problem-solving ability, and critical thinking.

The Conclusion is an important moment to reinforce the concepts learned, connect theory to practice, and motivate students to continue studying and exploring the topic. Additionally, by suggesting supplementary materials and highlighting the importance of prime and composite numbers, the teacher contributes to the formation of more curious, autonomous, and mathematically interested students.