Lesson Plan | Active Learning | Proportion

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 to directing both students' and teachers' focus on the essential competencies that will be developed during the class. By clearly establishing what is expected to be achieved, students can better prepare and engage with the content they have already studied at home, ensuring an effective and meaningful application in the classroom. This stage also serves to align expectations and ensure that everyone involved has a common understanding of the desired learning outcomes.

Main Objectives:

1. Empower students to solve practical problems involving the application of rules of proportionality, such as calculating the amount spent and the volume of fuel purchased.

2. Develop the ability to recognize and verify when two or more quantities are proportional, using methods of comparison and logical reasoning.

Side Objectives:

1. Encourage collaboration and dialogue among students during problem-solving, fostering an active and participatory learning environment.
2. Promote critical thinking and the application of mathematical knowledge in everyday situations, reinforcing the relevance of mathematics in developing analytical and practical skills.

Introduction

Duration: (15 - 20 minutes)

The introduction stage is designed to engage students with the content they have studied previously, using problem situations to activate prior knowledge and contextualize the importance of the theme in daily life. The problem situations serve to get students thinking about how to apply the concepts of proportionality in various contexts, while contextualization seeks to show the practical relevance of studying proportion, thereby increasing students' interest and motivation.

Problem-Based Situations

1. Imagine you are organizing a birthday party and need to buy balloons. The store sells packages of balloons, where each package contains 20 balloons and costs R$ 5. If you need 100 balloons for the party, how much would you pay?

2. A car travels 240 km with 20 liters of fuel. If the price of gasoline is R$ 4.00 per liter, how much would it cost to fill the 60-liter tank of this car?

Contextualization

Proportionality is one of the most commonly used mathematical tools in everyday life, whether in simple situations like adjusting cooking recipes or in more complex calculations like fuel consumption on trips. Understanding how quantities relate proportionally is essential not only for the study of mathematics but also for solving practical problems and making informed decisions in everyday life. For example, by understanding proportionality, we can save money by calculating the best product deals per kilogram in a supermarket or plan our trip more efficiently by optimizing the fuel used.

Development

Duration: (70 - 75 minutes)

The development section is designed for students to practically and contextually apply the concepts of proportionality they studied previously. Through group activities, they will have the opportunity to solve real and challenging problems, promoting critical thinking and collaboration. This moment is crucial to solidifying learning, allowing students to see mathematics as a useful and applicable tool in everyday situations.

Activity Suggestions

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

Activity 1 - The Great Balloon Race

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of proportionality to calculate quantities in a practical party situation, developing logical reasoning and mathematical skills.

- Description: Students will be divided into groups of up to 5 people. Each group will be tasked with organizing a balloon race where they must calculate how many balloons each participant can fill with a helium gas bottle, considering the time and gas available.

- Instructions:

• Divide the class into groups of up to 5 students.

• Each group will receive a helium gas bottle and a timer.

• The students must measure the time needed to fill one balloon and calculate how many balloons they can fill in 5 minutes.

• Based on this, they must calculate how many balloons a helium gas bottle will allow them to fill at a 30-minute party, assuming each balloon takes the same time to fill.

• Present the calculations and discuss the strategies used with the class.

Activity 2 - The Fuel Challenge

> Duration: (60 - 70 minutes)

- Objective: Use proportionality to optimize fuel consumption on a trip, integrating knowledge of geography and mathematics.

- Description: In this activity, students will plan a bike trip in groups using maps and calculating the fuel cost needed for the journey, considering price and distance. The goal is to reach the destination spending the least possible.

- Instructions:

• Organize students into groups of up to 5.

• Distribute maps and information about the terrain (including elevations) and fuel prices at different stations.

• Students must plan the route that minimizes fuel consumption, considering that each liter of fuel travels a different distance depending on the terrain.

• Calculate the total fuel cost for the trip and present the route and calculations to the class.

• Discuss the different strategies used by the groups.

Activity 3 - Mathematical Party: Proportional Decoration

> Duration: (60 - 70 minutes)

- Objective: Apply concepts of proportionality and area calculations in a practical and creative context, encouraging collaboration and precision in calculations.

- Description: Students will plan the decoration of a party, calculating the amount of materials needed for the decoration to be proportional to the size of the environment. This includes calculations for balloons, ribbons, and other decorative elements.

- Instructions:

• Divide the students into groups of up to 5 people.

• Provide measurements of the party environment and recommended proportions for decoration.

• Students must calculate how many balloons, ribbons, and other elements are needed to decorate the space proportionally.

• Present the decoration plan and calculations to the class, discussing each group's choices.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate learning, allowing students to articulate and reflect on what they learned and how they applied proportionality in practical activities. Group discussion helps develop communication and argumentation skills, in addition to providing an opportunity for students to evaluate their own understanding and that of their peers. This collective reflection is essential to ensure that mathematical concepts are understood and internalized effectively.

Group Discussion

Start the group discussion with a brief introduction, recalling the objectives of the lesson and encouraging students to share their experiences and discoveries. Ask each group to present a summary of what was discussed and the solutions found in the practical activities. Emphasize the importance of explaining the reasoning behind the calculations and how they applied proportionality in the different proposed situations. Encourage students to question and comment on their peers' presentations, promoting constructive and critical dialogue.

Key Questions

1. What were the biggest challenges in applying the concept of proportionality in the practical activities?

2. How can proportionality help in everyday situations beyond those we explored today?

3. Was there any situation where proportionality did not apply as expected? How did you deal with that?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage serves to consolidate learning, allowing students to connect practical activities with the theoretical concepts studied, and understand the applicability and importance of the topic of proportionality in their lives. This final reflection helps reinforce learning, ensuring that students can not only solve mathematical problems but also recognize and apply mathematics in everyday contexts.

Summary

To conclude, the teacher should summarize the main points covered during the lesson, recalling the definitions of proportionality and the ways it applies in everyday life. Highlight the solutions found in practical activities, such as calculating party costs, optimizing fuel consumption, and planning proportional decoration, reinforcing the importance and versatility of the concept.

Theory Connection

During the lesson, the connection between the theory studied at home and the innovative practices in class was clearly established. The problem situations and practical activities were designed to apply the concepts of proportionality tangibly, showing students how mathematics can be used to solve real and everyday problems. This approach not only facilitates understanding but also highlights the relevance of mathematical learning in the real world.

Closing

Finally, it is essential to highlight the importance of proportionality in everyday life. From calculating discounts on purchases to planning trips, understanding and applying proportionality helps make informed and efficient decisions. These skills are valuable not only in mathematics but also in various other areas of life, reinforcing the idea that mathematics is a powerful and indispensable tool.