Lesson Plan | Active Learning | Negative Numbers

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The Objectives stage is crucial for establishing a clear roadmap of what is expected to be achieved during the lesson. By defining specific objectives, the teacher guides both their own preparation and that of the students, ensuring that the focus is on the fundamental points for understanding negative numbers. This section also serves to align expectations and ensure that everyone involved is aware of the desired learning outcomes.

Main Objectives:

1. Clearly differentiate between negative and positive numbers, applying this distinction in practical and theoretical contexts.

2. Perform the four basic operations (addition, subtraction, multiplication, and division) with negative numbers, using varied examples to consolidate understanding.

3. Solve everyday and mathematical problems involving negative numbers, such as balance calculations, debts, and temperatures below zero, to apply theoretical knowledge in practice.

Side Objectives:

1. Develop logical and critical reasoning skills through the manipulation of negative numbers in different contexts.
2. Encourage collaboration among students in solving practical and mathematical problems, promoting the exchange of ideas and strategies.

Introduction

Duration: (15 - 20 minutes)

The Introduction phase serves to engage students and review concepts learned at home. By presenting problem situations, the teacher stimulates the practical application of negative numbers, laying the groundwork for a deeper understanding. The contextualization with real examples and curiosities seeks to show the relevance of negative numbers in daily life, increasing students' interest and motivation for the topic.

Problem-Based Situations

1. Imagine that a thermometer registers -5°C and, after a few hours, the temperature drops another 3 degrees. What would be the final recorded temperature? Ask students to apply the operation of subtraction with negative numbers to solve this problem.

2. Consider that a soccer player has a goal balance of -2 in one season, and in the next season, he scores 5 goals. How can we represent this change, and what would his new goal balance be? Ask students to use the addition of negative numbers to solve this situation.

Contextualization

Negative numbers are like the secret heroes of mathematics, always present to solve situations that positive numbers cannot. For example, they are essential for representing values of temperature below zero or for tallying debts. Additionally, curiosities such as the use of negative numbers in music (to adjust frequencies) and in finance (to represent losses) can spark students' interest. Exploring these real and curious situations helps relate the concept to the world around, making learning more meaningful.

Development

Duration: (65 - 75 minutes)

The Development stage is designed to allow students to apply the concepts of negative numbers practically and engagingly, through activities that simulate real situations and playful challenges. This approach not only reinforces theoretical learning but also promotes collaboration, logical reasoning, and problem-solving skills. The activities are planned to be interactive and contextualized, ensuring meaningful and lasting learning.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - The Quest for the Lost Treasure

> Duration: (60 - 70 minutes)

- Objective: Apply knowledge of negative numbers in a playful and collaborative context, developing mathematical reasoning and teamwork skills.

- Description: Students are divided into teams of up to 5 people, each representing a crew of pirates in search of buried treasure. The treasure map is in a mathematical code involving operations with negative numbers. Each team receives a part of the map, which contains clues that must be solved to discover the exact location of the treasure, represented by negative numerical coordinates.

- Instructions:

• Divide the classroom into groups of no more than 5 students.

• Distribute parts of the 'treasure map' to each team, which contain mathematical problems involving negative numbers.

• Each team must solve the problems to decipher the clues leading to the next location on the map (each correct answer indicates the next part of the map).

• Students must use the four basic operations with negative numbers to solve the clues.

• The first team to decipher all the clues and reach the treasure, represented by an 'X' on a giant map in the classroom, is the winner.

Activity 2 - The Mystery of the Missing Balance

> Duration: (60 - 70 minutes)

- Objective: Utilize concepts of negative numbers to solve a practical accounting problem, promoting analytical and problem-solving skills.

- Description: In this activity, students act as financial detectives tasked with solving a case of missing funds. They receive bank statements that show transactions with negative numbers and must reconcile the accounts to find the correct final balance. The challenge is that the statements are partially erased, and some transactions are coded.

- Instructions:

• Organize the students into groups of up to 5 members.

• Provide each group with a set of partially erased bank statements and a code table to decipher the transactions.

• Students must use operations with negative numbers to correct the statement, recording each operation performed.

• After correcting it, students must present the final balance found and justify their operations.

• The group that finds the correct balance in the shortest time and with the most accurate justifications will be the winner.

Activity 3 - The Expedition to the North Pole

> Duration: (60 - 70 minutes)

- Objective: Apply concepts of negative numbers in a realistic scientific scenario, developing calculation and forecasting skills.

- Description: Students participate in a simulation of an expedition to the North Pole, where they must calculate the temperature throughout the day, considering negative numerical variations. Each group acts as a team of scientists who collect temperature data at determined intervals and must predict the future temperature based on these collections.

- Instructions:

• Divide the class into groups of up to 5 students, with each representing a team of scientists.

• Distribute cards with temperature data at time intervals to each team, including negative temperatures.

• Students must use addition, subtraction, and data interpretation to calculate the current temperature and predict the future one.

• Each group presents its predictions, and the work is discussed in class, comparing the strategies and results of the different groups.

• The group with the predictions closest to reality, demonstrating good use of negative numbers, is considered the most successful.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate learning, allowing students to reflect on their experiences and articulate the knowledge acquired. The group discussion helps internalize the discussed concepts and also promotes communication and argumentation skills. This moment also serves for the teacher to assess students' understanding and clarify any remaining doubts, ensuring that everyone has a solid comprehension of negative numbers.

Group Discussion

Start the group discussion by reminding students of the activities carried out, asking how they felt applying the concepts of negative numbers in such varied contexts. Encourage each group to share the challenges faced and the strategies used to overcome them. Highlight the importance of each team member and how collaboration was fundamental to the success of the tasks. Also, ask if there were any surprises or discoveries that changed their perspective on negative numbers.

Key Questions

1. What were the main challenges when working with negative numbers, and how did you overcome them?

2. How did the application of negative numbers in different contexts help to consolidate your understanding of the concept?

3. Was there a situation where the understanding of negative numbers changed your way of approaching the problem?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage is to ensure that all students have a clear and consolidated understanding of the discussed concepts, as well as to understand the importance and practical applicability of negative numbers. The conclusion serves as a bridge between theoretical and practical learning, reiterating the benefits of understanding and applying negative numbers in various situations. This moment of reflection also helps reinforce learning and student motivation.

Summary

To conclude, the teacher should summarize the main concepts covered during the lesson, reinforcing understanding of negative numbers and their operations. It is essential to recapitulate the differences between addition, subtraction, multiplication, and division with negative numbers, presenting practical examples as used in the activities. This moment serves to consolidate the knowledge acquired and ensure that all students have understood the fundamental concepts.

Theory Connection

Throughout the lesson, the connection between the theory of negative numbers and their practical application was constantly reinforced. Activities like 'The Quest for the Lost Treasure' and 'The Mystery of the Missing Balance' allowed students to visualize and experience the relevance of negative numbers in real and playful contexts. This not only facilitates understanding of mathematical concepts but also demonstrates the importance of understanding theory and practice together.

Closing

Finally, the teacher should highlight the importance of negative numbers in daily life, such as in accounting, weather forecasting, and other everyday situations. This understanding helps form a solid foundation for mathematical and critical reasoning, essential for the academic and professional development of students. Concluding with this reflection reinforces the relevance of what has been learned and motivates students to apply their knowledge in their lives.