Lesson Plan | Technical Methodology | Counting Principle

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to introduce students to the multiplicative principle of counting, essential for solving combinatorial problems. By developing practical skills such as creating tree diagrams and tables, students will be better prepared to face challenges in the job market, where the ability to organize and analyze data is highly valued.

Main Objectives

1. Understand the concept of the multiplicative principle of counting.

2. Apply the multiplicative principle to solve simple counting problems.

3. Create problems involving the combination of elements from different collections.

Side Objectives

1. Use tree diagrams to visualize possible combinations.
2. Construct tables to facilitate the counting of groupings.

Introduction

Duration: 10 to 15 minutes

The purpose of this stage is to introduce students to the multiplicative principle of counting, essential for solving combinatorial problems. By developing practical skills such as creating tree diagrams and tables, students will be better prepared to face challenges in the job market, where the ability to organize and analyze data is highly valued.

Contextualization

Imagine you need to choose an outfit to go to a party. You have 3 different t-shirts and 2 different pants. How many different clothing combinations can you form? The counting principle helps us solve this type of problem simply and efficiently. This principle is fundamental for various everyday situations, from organizing a trip to planning a menu. Today, we will learn how to use it to facilitate our decisions and solve problems practically.

Curiosities and Market Connection

The counting principle is widely used in areas such as logistics, information technology, and project management. For example, technology companies use this principle to calculate the number of possible password combinations, ensuring system security. In logistics, it is used to optimize routes and combinations for transporting goods, saving time and resources. Understanding and applying this concept can open doors to various professional opportunities in the future.

Initial Activity

To start the lesson, present students with a short video of 3 to 5 minutes on how large technology companies use the counting principle to ensure the security of their platforms. Then, ask the provocative question: 'How many phone number combinations are possible with the digits 0 to 9?' Allow students to briefly discuss their hypotheses.

Development

Duration: 40 to 45 minutes

The purpose of this stage is to ensure that students understand the multiplicative principle of counting deeply through practical and interactive activities. By applying the concept in mini challenges and solving fixation exercises, students develop essential skills for organizing and analyzing data, competencies valued in the job market.

Covered Topics

1. Concept of the Multiplicative Principle of Counting
2. Solving simple counting problems
3. Creating Tree Diagrams
4. Building Tables for Counting

Reflections on the Theme

Guide students to think about how many times in a day they need to choose between different options, such as picking an outfit, deciding on a snack, or even opting for a game. Reflect on how the counting principle can help simplify these decisions and the importance of this skill in the job market.

Mini Challenge

Ice Cream Shop Challenge

Students will simulate creating combinations of ice creams in a fictional shop, using different flavors and toppings.

Instructions

1. Divide the class into groups of 3 to 4 students.
2. Each group will receive a list with 3 ice cream flavors (chocolate, strawberry, vanilla) and 2 different toppings (sprinkles, chocolate syrup).
3. Ask each group to create all possible combinations of ice creams with toppings using tree diagrams.
4. Then, ask the groups to build a table representing all possible combinations.
5. Guide students to present their combinations to the class and discuss different ways to visualize the groupings.

Objective: Develop the skill of using tree diagrams and tables to solve counting problems, applying the multiplicative principle practically.

Duration: 30 to 35 minutes

Evaluation Exercises

1. How many combinations of outfits can be formed with 2 types of shirts (blue, green) and 3 types of pants (jeans, black, white)?
2. Create a tree diagram to combine 2 types of juices (orange, lemon) with 3 types of sides (cookie, sandwich, fruit).
3. Build a table to represent all possible combinations of 3 types of fruits (banana, apple, grape) with 2 types of drinks (water, juice).

Conclusion

Duration: 10 to 15 minutes

The purpose of this stage is to consolidate students' learning, reinforcing essential concepts and their practical applications. The discussion and reflection promote a deeper and contextualized understanding, while the summary and closing ensure that students leave the class with a clear and applied view of the counting principle.

Discussion

Promote a discussion among students about how the counting principle was used during the class. Ask what they found most challenging and what was easiest to understand. Encourage them to share examples of everyday situations where they could apply what they learned, such as organizing their school activities or in board games. Stimulate reflection on the importance of knowing how to organize and combine different elements to solve problems efficiently.

Summary

Recap the main content presented during the class: the concept of the multiplicative principle of counting, the use of tree diagrams and tables to visualize possible combinations, and the practical application of these concepts through challenges and exercises. Reinforce the importance of understanding how combinations can be organized efficiently.

Closing

Explain how the class connected theory and practice by showing concrete applications of the counting principle in different contexts, such as the security of IT systems and the optimization of logistics routes. Emphasize the relevance of the topic for everyday life and the job market, highlighting how these skills can be useful in various professions. Thank the students for their active participation and reinforce the importance of practicing what they have learned.