Lesson Plan | Active Learning | Hexagon Area

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 the direction of the class and ensuring that students clearly understand what is expected of them by the end of the session. By setting clear and specific goals, students can focus their learning efforts on the competencies necessary to calculate the area of the hexagon and apply this knowledge in practical situations. This section also serves to motivate students by showing them the relevance and applicability of the topic in various everyday and professional situations.

Main Objectives:

1. Enable students to calculate the area of regular and irregular hexagons using specific formulas and practical methods.

2. Develop skills to apply area calculation in real contexts such as environment design and solving architectural problems.

Side Objectives:

1. Encourage logical reasoning and critical analysis when manipulating different geometric shapes and proposing solutions to complex problems.

Introduction

Duration: (20 - 25 minutes)

The introduction stage aims to engage students and help them connect their prior knowledge with new applications and situations. By presenting problem-based scenarios from real or playful contexts, students are challenged to think about how to apply the concept of the hexagon's area practically and contextually. The contextualization with real examples and curiosities helps expand students' perception of the importance and ubiquity of the hexagon, preparing them for a more meaningful and motivating learning experience.

Problem-Based Situations

1. Imagine you are an architect and need to design a house with a hexagonal room. How would you determine the area of this room to plan the distribution of furniture and circulation of people?

2. In a board game, the land where players build their cities is made up of hexagonal tiles. Each tile has a different area, but they are all regular. How could you quickly calculate the area of each tile to decide where to build?

Contextualization

The hexagon is a common shape in many aspects of design and nature. For example, honeycombs are hexagonal because this shape allows the space to be efficiently filled with the least amount of wax, maximizing storage capacity and minimizing material use. Furthermore, the hexagon is widely used in architecture and engineering due to its ability to form regular patterns and its visual appeal. Knowing how to calculate the area of a hexagon is a useful and practical skill that can be applied in many real-life contexts.

Development

Duration: (65 - 75 minutes)

The development section is designed to allow students to apply the concepts studied at home about the area of the hexagon in a practical and meaningful way. By working in groups, they not only deepen their mathematical understanding but also develop collaboration and communication skills. Each proposed activity aims to simulate real or playful situations that require the use of area calculation, ensuring that students can transfer their learning to diverse and complex contexts. This practical approach aims to strengthen knowledge retention and the applicability of the studied theme.

Activity Suggestions

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

Activity 1 - Hexagon Festival

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of the hexagon's area in a practical and creative context, developing teamwork and presentation skills.

- Description: Students will be divided into groups, and each group will receive a 'magic box' containing various materials such as poster boards, scissors, measuring tapes, and colored pens. The challenge will be to create a booth for a fictional festival, where all booths must have hexagonal bases. Each group must decide the size of the base hexagon, calculate the available area, and design the layout of items such as banners, tables, and chairs, which will be drawn and arranged on the poster board.

- Instructions:

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

• Distribute the 'magic boxes' to each group.

• Ask each group to decide on the size of the base hexagon they will use.

• Instruct students to calculate the area of the chosen base hexagon.

• Guide the groups to draw the booth layout, including the arrangement of decorative and informative items.

• After completing the drawings, each group will present their booth to the class, explaining the area calculation process and the design chosen.

Activity 2 - Hexagon Hunt in School

> Duration: (60 - 70 minutes)

- Objective: Practice area calculation in real-world situations, promote critical observation and the application of mathematical concepts in practical contexts.

- Description: In this activity, students will explore the school in search of objects or shapes that can be approximated by hexagons. After data collection, each group must calculate the area of at least three of these 'hexagonal shapes' using specific formulas. The found objects can range from windows to frames on the wall, which should be measured and their hexagons inscribed for area calculation.

- Instructions:

• Organize students into groups of up to 5 members.

• Explain the task: find objects in the school that can be approximated by hexagons and calculate their areas.

• Provide students with measuring tapes and instructions on how to measure and inscribe hexagons.

• Each group must present at least three objects found with their respective area calculations.

• Discuss the different approaches and results in a collective feedback session.

Activity 3 - Hexagon on Stage

> Duration: (60 - 70 minutes)

- Objective: Develop area calculation skills in design and decoration situations, promote creativity and teamwork.

- Description: Students will plan the decoration of a school party, where every detail, from the stage to the tables and decorations, must follow the hexagonal theme. The challenge is to calculate the areas of different hexagonal decorative elements to optimize space and harmonize the design. This will involve not only area calculation but also creativity in arranging the elements.

- Instructions:

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

• Explain the theme of the party and present the various elements that must be decorated in hexagonal shape.

• Help students calculate the areas of the various hexagonal elements.

• Allow students to use materials such as paper, glue, and scissors to create models of the decorative elements.

• Each group will present their project, explaining their design choices and the calculations made.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate learning, allowing students to articulate what they have learned and how they applied the knowledge in different contexts. Group discussion helps identify areas of confusion or misunderstanding, allowing the teacher to clarify doubts and reinforce concepts. Additionally, this exchange of experiences promotes communication skills and collaborative learning, essential for the academic and personal development of students.

Group Discussion

After completing the group activities, gather all students for a collective discussion. Start the discussion with a brief review of the hexagon's area concepts, asking students what they learned and what challenges they encountered. Encourage each group to share their findings and the methods used to calculate the areas, highlighting the differences between each group's approaches. This is a moment for reflection and idea exchange, where students can learn from each other and see the practical applications of mathematical knowledge.

Key Questions

1. What were the main challenges in calculating the area of hexagons in the different proposed situations?

2. How did changing the size of the base hexagon affect the total area of the booths or decorative elements?

3. Were there any surprises in the calculations or any situation where prior knowledge about the areas of other figures helped in solving the problem?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage is to ensure that students have a clear and consolidated understanding of the content covered during the lesson. The review helps fix the concepts, while the discussion about the interaction between theory and practice and real applications motivates students and highlights the relevance of what they learned. This moment also serves to clarify any remaining doubts and reinforce the importance of the theme beyond the academic environment.

Summary

In conclusion, let's revisit the concept of the area of the hexagon. Students were able to explore both the formula for calculating the area of a regular hexagon, A = (3√3)/2 * L², and its application in practical contexts, such as creating booths for a fictional festival and decorating a party. This concept was solidified through the analysis of diverse problem situations, where students had to adapt area calculations to hexagonal shapes in different scales and contexts.

Theory Connection

The lesson provided a clear bridge between theory and practice, where students could apply the theoretical knowledge acquired about polygon areas in real and playful situations. The group activities allowed the exploration of mathematical concepts in a practical and fun way, while class discussions helped connect these experiences with the theory previously studied at home, reinforcing the understanding and applicability of mathematical content.

Closing

Understanding and being able to calculate the area of the hexagon is crucial not only for academic success but also for practical applications in areas such as architecture, design, and engineering. Furthermore, strong mathematical skills, such as those exercised in this lesson, are essential for developing logical reasoning and problem-solving abilities in various areas of life.