Lesson Plan | Active Learning | Angles: Vertically Opposite Angles

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 clearly establishing what is expected of students to learn and achieve during the lesson. By defining clear and specific objectives, students are directed to focus their studies and efforts on the fundamental skills related to vertically opposite angles. This stage also serves to align student expectations with the practical activities that will follow, ensuring effective use of classroom time.

Main Objectives:

1. Empower students to identify and name vertically opposite angles in different geometric figures.

2. Develop the ability to recognize that vertically opposite angles are congruent (equal) and to apply this property to solve mathematical problems involving the sum and equality of angles.

Side Objectives:

1. Encourage logical reasoning and the application of mathematical concepts in practical situations.

Introduction

Duration: (15 - 20 minutes)

The Introduction stage is designed to engage students through problem situations that make them revisit and apply prior knowledge about vertically opposite angles, sparking curiosity and preparing them for practical learning in the classroom. Moreover, the contextualization helps demonstrate the applicability and relevance of the topic in real and practical situations, increasing student interest and understanding.

Problem-Based Situations

1. Ask students to draw two intersecting lines and label the intersection points as A, B, C, and D. Then, ask them to determine the angles formed by AB and CD, and by BC and AD. This exercise helps visualize that vertically opposite angles are equal.

2. Propose a practical problem: 'If a mirror forms a 120° angle with a wall, what angle does the observer's image see, considering that both angles are vertically opposite?' This situation highlights the symmetry and equality of vertically opposite angles.

Contextualization

To contextualize the importance of vertically opposite angles, explain how this property is essential in various fields, such as engineering and design, where symmetry and equality of angles are crucial for ensuring balanced and aesthetically pleasing structures. Additionally, mention curiosities, such as the use of this property in mathematical theorems to prove triangle congruence, reinforcing the applicability and relevance of the topic.

Development

Duration: (65 - 75 minutes)

The Development stage is designed to allow students to practically and meaningfully apply their prior knowledge about vertically opposite angles. Through playful and contextualized activities, students explore and reinforce the concept collaboratively, developing problem-solving, measurement, and argumentation skills. This stage is essential for consolidating student understanding and stimulating critical thinking and creativity.

Activity Suggestions

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

Activity 1 - Angle Detectives

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of vertically opposite angles in practice, developing measurement and mathematical argumentation skills.

- Description: Students will be divided into groups of up to 5 and will receive a toolkit that includes a measuring tape, protractor, and paper. Each group must investigate and determine the angles formed by objects in the school environment, such as the edges of tables, the meeting of walls, and the ceiling, using the concept of vertically opposite angles.

- Instructions:

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

• Distribute the toolkits to each group.

• Guide students to choose two points on different objects, marking them with adhesive tape to consider as vertices.

• Ask them to measure and record the angles formed by these points using the protractor.

• Each group should present their findings and explain how they applied the concept of vertically opposite angles to determine the measured angles.

• Conduct a classroom discussion to compare and discuss the different measurements made by the groups.

Activity 2 - Bridge Builders

> Duration: (60 - 70 minutes)

- Objective: Utilize the concept of vertically opposite angles to create a stable and symmetrical structure, promoting practical application of mathematical concepts in engineering.

- Description: In this activity, students, organized into groups, will be tasked with designing a mini bridge made of popsicle sticks that must be symmetrical and balanced. They will need to use the concept of vertically opposite angles to ensure the symmetry and stability of the structure.

- Instructions:

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

• Provide each group with popsicle sticks, glue, and a support base.

• Explain that they need to design and construct a mini bridge that is symmetrical and can support the greatest possible weight.

• Students must use their knowledge of vertically opposite angles to guarantee the symmetry and structuring of the bridge.

• At the end, each group will present their bridge, explaining how they applied the theory of vertically opposite angles in the design of the structure.

• Conduct a load test to determine which bridge supports the most weight and discuss the results with the class.

Activity 3 - Angle Theater

> Duration: (60 - 70 minutes)

- Objective: Visualize and creatively understand the property of vertically opposite angles, promoting oral expression and collaboration among students.

- Description: Students will create and present a short play that illustrates the concept of vertically opposite angles. Each group must develop a script that includes characters that are angles, demonstrating their relationships and equalities through dialogues and movements on stage.

- Instructions:

• Organize students into groups of up to 5.

• Explain that each group must create a small script for a play involving personifications of angles.

• Students should include dialogues that illustrate the property of vertically opposite angles being equal.

• Groups must rehearse and, if possible, prepare small props for the presentation.

• Allow each group to present their play to the class, followed by a discussion about what was learned.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to allow students to articulate and reflect on what they learned during the practical activities. The group discussion helps consolidate knowledge, allowing students to express their ideas and understandings, and also learn from each other's experiences. This moment is crucial for assessing students' understanding of the topic and clarifying any remaining doubts, reinforcing the application of the concept of vertically opposite angles in varied contexts.

Group Discussion

After completing the activities, gather all students in a large circle for a group discussion. Start the conversation with a brief introduction, highlighting the importance of sharing discoveries and learnings. Suggest that each group presents a summary of the main conclusions and challenges faced during the activities. Encourage students to explain how they applied the theory of vertically opposite angles in each activity and what the most surprising results were.

Key Questions

1. What were the biggest challenges in applying the concept of vertically opposite angles in practical activities?

2. How did the symmetry and equality of the angles influence the design and stability of the structures you built?

3. Was there any situation where the theory of vertically opposite angles did not apply as expected? How did you resolve that?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion stage is to consolidate learning, linking theory and practice and highlighting the relevance of the content learned. By summarizing the main points addressed and reinforcing the applicability of the concepts in real situations, this stage helps ensure that students leave the lesson with a clear understanding and a renewed appreciation for the subject.

Summary

In this lesson, the concept of vertically opposite angles was explored and practiced through playful and practical activities. Students reviewed how to identify and measure these angles and then applied that knowledge to solve practical problems, such as constructing symmetrical structures and the theatrical representation of the property of equal angles.

Theory Connection

Today's lesson provided a clear bridge between the theory studied previously and the practice. Through experiments with measurement, construction, and dramatization, students were able to visualize and directly apply mathematical concepts, strengthening their understanding and appreciation of the importance of vertically opposite angles.

Closing

Understanding vertically opposite angles is crucial not only for academic success in mathematics but also for their applicability in various fields like engineering, design, and architecture. This lesson demonstrated how mathematics can be not only theoretical but practical and fun, increasing student engagement and comprehension.