Lesson Plan | Active Learning | Prisms and Pyramids: Layouts and Characteristics

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 stage of defining objectives is crucial to direct the focus of the lesson and ensure that both the teacher and the students have a clear understanding of what is expected to be achieved by the end of the session. By establishing clear and specific objectives, students can better direct their learning efforts, while the teacher can adjust the content and activities to ensure that the objectives are effectively met.

Main Objectives:

1. Enable students to recognize and identify the unfoldings of prisms and pyramids, highlighting their differences and similarities.

2. Develop the ability to count and identify the number of edges and faces in prisms and pyramids, promoting a more detailed understanding of the characteristics of these geometric figures.

Side Objectives:

1. Encourage spatial reasoning and the students' ability to visualize through the manipulation of physical models and flat figures.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students and connect previously studied content with everyday situations and curiosities, facilitating understanding and interest in the topic. Problem-based questions encourage students to think critically about what they have learned, while contextualization helps them perceive the importance and presence of geometric figures in the real world. This moment also lays the groundwork for the practical activities that will follow, where students will apply knowledge in real or simulated situations.

Problem-Based Situations

1. Imagine you are a very famous architect and have been tasked with designing a new pyramid for a historic city. What type of pyramid would you choose and why?

2. Think of a gift box that you need to assemble. If this box were a pyramid, what would the unfolding of the necessary paper look like to construct it? And if it were a prism, how would the unfolding be different?

Contextualization

Prisms and pyramids are common geometric figures in our daily lives, even if we do not always recognize them immediately. For example, many buildings have bases that can be considered prisms, such as water tanks and rectangular buildings. Pyramids, in addition to having been used as tombs in ancient Egypt, appear in many modern architectural forms, such as the Louvre in Paris. This practical application shows how the study of these shapes is relevant and can be useful for professions such as architecture and engineering.

Development

Duration: (70 - 75 minutes)

The Development stage is designed to allow students to practically and interactively apply the theoretical knowledge about prisms and pyramids acquired previously. Through the proposed activities, students will have the opportunity to physically manipulate the geometric figures, reinforcing their understanding of their unfoldings and characteristics. Additionally, group activities encourage collaboration and communication, essential for effective learning.

Activity Suggestions

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

Activity 1 - Building and Decorating Pyramids and Prisms

> Duration: (60 - 70 minutes)

- Objective: Reinforce knowledge about the characteristics and unfolding of prisms and pyramids, as well as stimulate creativity and teamwork.

- Description: In this activity, students will be divided into groups of up to 5 people and will receive pre-cut cardboard kits representing the faces of prisms and pyramids. The task will be to assemble and decorate these figures, creating three-dimensional pyramids and prisms. Each group must assemble a prism and a pyramid, identifying the faces, edges, and vertices, and then decorate them with drawings or collages.

- Instructions:

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

• Distribute the cardboard kits containing the faces of prisms and pyramids.

• Guide the students to assemble a pyramid and a prism, identifying and counting the faces, edges, and vertices.

• Allow the students to decorate their figures as they wish, using pens, colored pencils, collages, etc.

• Ask each group to present their pyramid and prism, explaining the geometric characteristics and the decoration process.

Activity 2 - The Unfolding Challenge

> Duration: (60 - 70 minutes)

- Objective: Enhance understanding of the structure and unfolding of prisms and pyramids, as well as develop technical drawing skills and teamwork.

- Description: Students, in groups, will receive different models of prisms and pyramids already assembled and should, based on these models, create unfoldings on paper. Each group will choose one of the provided models, dismantle it, observe it, and draw the unfolding, trying to maintain the proportions and identifying each face.

- Instructions:

• Form groups of up to 5 students and distribute assembled models of prisms and pyramids.

• Each group chooses a model and carefully dismantles it to observe the faces.

• Using graph paper, students draw the unfolding of the dismantled model.

• Students must correctly count and identify the faces, edges, and vertices in the unfolding.

• At the end, each group presents their unfolding and explains the dismantling and unfolding process.

Activity 3 - Geometric Escape Room

> Duration: (60 - 70 minutes)

- Objective: Develop problem-solving skills and practical application of geometric knowledge in a playful and dynamic way.

- Description: Transform the classroom into an 'escape room' where students must solve puzzles and riddles related to prisms and pyramids to 'escape'. Each station in the escape room will present a different challenge, such as quickly assembling a pyramid's unfolding, counting the number of edges in a prism, among others.

- Instructions:

• Prepare the room with challenge stations that include puzzles and activities related to prisms and pyramids.

• Divide the class into groups and instruct them to start at any desired station.

• Each completed station will provide a clue for the next station until all challenges are completed.

• Students must write down the answers and solutions for each challenge.

• The first group to complete all challenges 'escapes' and wins a small prize.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate the practical and theoretical learning acquired throughout the lesson, allowing students to verbalize and share their understanding. The group discussion helps reinforce knowledge, identify areas that may need revision, and promote students' confidence in using the new geometric skills. This collective feedback also serves for the teacher to assess students' understanding and adjust future activities according to the identified needs.

Group Discussion

At the end of the practical activities, gather all students for a group discussion. Start the conversation by asking each group to share their findings and challenges faced during the construction and unfolding of the prisms and pyramids. Encourage students to discuss the differences between the models and foldings, and how creativity influenced the process. This is a moment for reflection and exchange of ideas, where students can learn from each other and expand their collective understanding.

Key Questions

1. What were the main differences you noticed when assembling a pyramid and a prism, both in terms of structure and unfolding?

2. How did the decoration of the figures help to better understand the geometric characteristics of each of them?

3. Was there any concept about prisms and pyramids that you found most challenging? How did you manage to overcome it?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion stage is to ensure that students have a clear and consolidated understanding of the topics covered during the lesson. By recapping the key points, the teacher reinforces learning and helps students better organize the acquired knowledge. Furthermore, by highlighting the connection between theory and practice and the applicability of the studied concepts, students are able to perceive the importance and utility of mathematics in their daily lives, motivating a continuous interest in the subject.

Summary

In the conclusion of the lesson, the teacher should recap the main concepts addressed about prisms and pyramids, highlighting the differences between these geometric figures, the unfoldings, and the number of faces, edges, and vertices of each. It is essential that students have clarity on these aspects since they were explored in practical activities that consolidated the learning.

Theory Connection

Today's lesson demonstrated the importance of connecting theory with practice. By engaging in activities such as building prisms and pyramids, as well as unfolding these figures, students were able to visualize and directly apply the concepts previously studied. This practical interaction reinforced theoretical understanding, showing how mathematics can be applied in real and imaginative situations.

Closing

Finally, it is crucial to highlight the relevance of prisms and pyramids in everyday life. These geometric figures are present in many structures, from gift boxes to large buildings, and understanding their properties and unfoldings allows students to appreciate mathematics in action. This knowledge not only enriches academic understanding but also prepares students to recognize and utilize mathematical concepts in various practical situations.