Objectives (5 - 7 minutes)

• Main Objective: Introduce students to the concept of combination and how it is applied in mathematics. The teacher should ensure that students understand the difference between permutation and combination, and how the order of elements is crucial in a permutation but not in a combination.

• Secondary Objective: Develop students' ability to solve combination problems, including the application of the Fundamental Counting Principle. Students should be able to apply this knowledge in a variety of contexts and scenarios.

• Secondary Objective: Foster students' logical and critical thinking skills, encouraging them to analyze combination problems from different perspectives and find effective and efficient solutions.

Detailed Objectives:

• Explain what a combination is and how it differs from permutation.
• Apply the Fundamental Counting Principle in combination problems.
• Solve combination problems in different contexts and scenarios.
• Develop logical and critical thinking skills when addressing combination problems.

Introduction (10 - 15 minutes)

• Review of Previous Concepts: The teacher can start the lesson by briefly reviewing the concepts of factorial and permutation, as they are fundamental concepts to understand combination. The teacher can ask students questions to verify if they remember these concepts and how they are applied. For example, the teacher can ask: "What is a factorial?" and "How would you calculate the number of possible permutations of a list of 5 items?"

• Problem Situations: The teacher can present two problem situations to capture students' attention and demonstrate the relevance of the topic. For example, the teacher can ask: "If you have a box with 10 numbered balls from 1 to 10 and need to choose 3 balls without replacement, how many possible combinations exist?" and "If you have a group of 5 friends and need to choose 2 to form a team, how many possible team combinations can be formed?"

• Contextualization: The teacher can explain that combination is an important concept in various areas such as statistics, probability, computer science, and even in games and puzzles. For example, the teacher can mention that combination is used to calculate the probability of winning the lottery or a card game, or to solve puzzles like the Rubik's Cube.

• Introduction of the Topic: The teacher can introduce the topic of combination in an interesting and engaging way. For example, the teacher can tell the story of how the French mathematician Blaise Pascal (1623-1662) contributed to the development of the field of combination while working on a gambling problem with his friend Pierre de Fermat. Or the teacher can show a short video of a magician performing a trick involving the combination of cards or objects.

• Capturing Students' Attention: To capture students' attention, the teacher can share some curiosities or practical applications of combination. For example, the teacher can mention that combination is used to solve popular puzzles like Sudoku and the Rubik's Cube. Or the teacher can tell the story of how combination was used to decipher secret codes during World War II, a field of study known as cryptography.

Development (20 - 25 minutes)

• Activity 1: Building a Team (10 - 12 minutes)

  • Description: In this activity, students will be divided into groups of 3. Each group will receive a list of 10 celebrity names and the task of choosing 3 names to form their "Star Team".

  • Step by Step:

    1. The teacher distributes the lists of celebrity names to each group.
    2. Students discuss among themselves and choose 3 names for their team, without considering the order of the names.
    3. Students record the name of their "Star Team".
    4. The teacher circulates around the room, observing and assisting the groups as needed.
    5. When all groups finish, the teacher requests each group to share the name of their "Star Team" and the names of the chosen celebrities.

  • Objective: This activity aims to help students understand the concept of combination and the application of the Fundamental Counting Principle in a practical scenario. Students will be combining elements (celebrity names) without considering the order, which is an example of combination.

• Activity 2: Sudoku Contest (10 - 12 minutes)

  • Description: In this activity, students will continue working in their groups. Each group will receive a partially filled Sudoku board and the task of filling the empty spaces with numbers from 1 to 9, so that each number appears only once in each row, column, and 3x3 block.

  • Step by Step:

    1. The teacher distributes the Sudoku boards and explains the rules of the game.
    2. Students start solving the Sudoku in their groups, combining the available numbers in a way that does not violate the rules of the game.
    3. The teacher circulates around the room, observing and assisting the groups as needed.
    4. When a group believes they have completed the Sudoku, they call the teacher to check.
    5. The first group to correctly complete the Sudoku is the winner of the contest.

  • Objective: This activity aims to reinforce students' understanding of the concept of combination and the application of the Fundamental Counting Principle. Students will be combining the Sudoku numbers in a way that does not violate the rules of the game, which is an example of combination.

• Activity 3: Mathematical Puzzle (5 - 8 minutes)

  • Description: In this activity, each group will receive a mathematical puzzle. The goal is to solve the puzzle by combining the pieces correctly.

  • Step by Step:

    1. The teacher distributes the puzzles to each group.
    2. Students start solving the puzzle in their groups, combining the pieces in a way that they fit together correctly.
    3. The teacher circulates around the room, observing and assisting the groups as needed.
    4. The first group to correctly complete the puzzle is the winner of the activity.

  • Objective: This activity aims to consolidate students' understanding of the concept of combination and the application of the Fundamental Counting Principle. Students will be combining the puzzle pieces in a way that they fit together correctly, which is an example of combination.