Lesson Plan | Active Learning | 3D Geometric Solids

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 - 7 minutes)

The objectives stage is crucial for establishing a clear foundation of what is expected to be achieved by the end of the lesson. By defining the main objectives, the focus of students and the teacher can be directed towards the central aspects of the content, ensuring that all involved are aligned with the learning goals. Thus, subsequent activities can be effectively directed to achieve the desired results.

Main Objectives:

1. Empower students to identify and count the number of vertices, faces, and edges of 3D figures, such as pyramids and prisms, reinforcing the concept that a cube has 8 vertices.

2. Develop spatial visualization skills and logical reasoning by manipulating and analyzing different geometric solids.

Side Objectives:

1. Encourage collaboration and teamwork through practical classroom activities requiring the application of mathematical knowledge.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students with the content they studied previously, using problem situations that reinforce the practical use of concepts related to geometric solids. Additionally, the contextualization aims to show the importance and presence of these concepts in the real world, increasing interest and relevance of the learning for the students.

Problem-Based Situations

1. Imagine you are an architect and need to design a pyramid to serve as the ceiling of a small exhibition room. How many vertices will this pyramid have? And how many faces and edges?

2. Suppose you are a civil engineer tasked with designing a prism for a new building. If this prism has a rectangular base, how many vertices, faces, and edges will it have, knowing that the base has 4 vertices, 4 faces, and 4 edges?

Contextualization

Geometric solids are present in many aspects of our daily lives, from the packaging we use to the shapes of the buildings around us. For example, knowledge about pyramids and prisms is crucial for architects and designers, who need to understand how different shapes can be used structurally and aesthetically in constructions. Furthermore, the history of geometric solids dates back to ancient civilizations like the Egyptians and Greeks, who used these shapes in their architecture and mathematical calculations, demonstrating the relevance and permanence of these concepts over the centuries.

Development

Duration: (75 - 85 minutes)

The Development stage is designed to allow students to apply the studied concepts about geometric solids in a practical and playful way. By working in groups, they not only solidify their theoretical understanding but also develop collaboration, communication, and critical thinking skills. The proposed activities aim to engage students in active and meaningful learning, where the manipulation of materials and the resolution of practical problems reinforce the understanding of the content.

Activity Suggestions

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

Activity 1 - Solid Builders

> Duration: (60 - 70 minutes)

- Objective: Apply theoretical knowledge of geometric solids in practice, developing teamwork skills and precision in construction.

- Description: In this activity, students will be challenged to build models of different geometric solids using materials such as popsicle sticks and modeling clay.

- Instructions:

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

• Distribute the necessary materials, including popsicle sticks, modeling clay, and small labels for identification.

• Each group chooses a geometric solid (pyramid, prism, cylinder, cone) to build.

• Students must first draw a plan for how they will construct the solid, considering the number of faces, vertices, and edges.

• Using the popsicle sticks as edges and the modeling clay for the vertices, they will construct the solid.

• Finally, they label each vertex, face, and edge for easy identification.

Activity 2 - Geometric Detectives

> Duration: (60 - 70 minutes)

- Objective: Develop deduction skills and practical application of mathematical knowledge, as well as promote effective communication of the solutions found.

- Description: Students will take on the role of detectives and will have to solve a 'mystery' involving identifying and counting the elements of three-dimensional geometric figures.

- Instructions:

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

• Give each group a 'clue' that describes a geometric solid (such as the number of faces, vertices, or edges and a partial description).

• Students must use prior knowledge to identify which solid the clue refers to.

• Once identified, they must build a model of the solid using available materials.

• Each group presents the solid built and explains how they arrived at the solution to the mystery.

• Score each group based on the accuracy of the construction and the ability to explain the reasoning used.

Activity 3 - Olympics of Solids

> Duration: (60 - 70 minutes)

- Objective: Foster creativity and self-expression of students, while reinforcing knowledge about geometric solids in a fun and competitive manner.

- Description: Transform the classroom into a competition field where each group must design and explain a geometric solid creatively and accurately.

- Instructions:

• Divide the class into groups and distribute cards containing the specifications of a random geometric solid.

• Each group must draw a plan of the solid and think of a creative way to present and explain the solid to the rest of the class.

• Groups have a limited time to assemble the solid using recyclable materials and other available resources.

• After assembly, each group presents to the class, explaining the characteristics of the solid, such as the number of vertices, faces, and edges.

• The class votes on the most creative and accurate presentation.

Feedback

Duration: (10 - 15 minutes)

The purpose of this feedback stage is to allow students to reflect on what they have learned and articulate their understanding, reinforcing the connection between theory and practice. Group discussion helps consolidate knowledge, as students have the opportunity to hear different perspectives and approaches from their peers, as well as to receive immediate feedback from the teacher. This exchange of ideas promotes deeper and more collaborative learning, ensuring that the learning objectives are met.

Group Discussion

To start the group discussion, the teacher should ask each group to share the discoveries and challenges faced during the activities. Encourage students to discuss how the theory studied earlier helped them in practice and what new things they learned while building the solids. It can also be requested that each group presents a summary of the main characteristics and interesting facts about the solid they built, reinforcing the importance of knowing how to identify and count elements in geometric solids.

Key Questions

1. What were the main challenges in trying to identify and count the elements of geometric solids during the activities?

2. How did the practical application of theoretical concepts help clarify doubts or deepen your understanding of geometric solids?

3. Was there any unexpected discovery or something you would have liked to do differently in building the solids?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage is essential for consolidating learning, allowing students to revisit and reinforce the knowledge acquired during the lesson. Additionally, it serves to highlight the applicability of the concepts studied in real and theoretical situations, reinforcing the importance of studying mathematics in students' academic and professional development. This final reflection helps close the learning cycle, ensuring that students leave the lesson with a clear understanding and a renewed appreciation for the topic.

Summary

In the final stage, the teacher should summarize the main points addressed, reiterating the importance of understanding and counting the elements of geometric solids, such as vertices, faces, and edges. The properties of the solids constructed, such as pyramids, prisms, cones, and cylinders, should be recapitulated, and how these figures are essential in many practical applications, ranging from architecture to the design of everyday objects.

Theory Connection

It is crucial to point out how today's lesson connected theory with practice, demonstrating to students how theoretical knowledge of mathematics applies in real and practical situations. The activities of building models and detective games allowed students to see and directly manipulate the concepts studied, facilitating understanding and retention of content.

Closing

Finally, emphasize the ongoing relevance of geometric solids in various professions and everyday situations, highlighting how understanding these concepts can help students in future careers and in solving practical problems. Encourage students to maintain interest in geometry, exploring more about the subject and applying it to other fields of knowledge.