Lesson Plan | Active Learning | Congruent Figures

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 establish a clear foundation of what is expected to be achieved with the class. In this context, the focus is to ensure that students can not only identify congruent figures but also apply this knowledge in practical situations, such as the superposition of figures on grids. This skill is fundamental for the development of spatial perception and the logical-mathematical reasoning ability of students.

Main Objectives:

1. Train students to recognize and identify identical figures when placed over quadrilateral or triangular grids.

2. Develop spatial visualization skills and comparison of geometric figures in different contexts.

Side Objectives:

1. Encourage teamwork and communication among students during practical activities.

Introduction

Duration: (15 - 20 minutes)

The purpose of the introduction stage is to engage students with the topic of the lesson through problem situations that encourage the use of prior knowledge and curiosity. Additionally, it seeks to contextualize the importance of studying congruent figures in everyday life, showing the relevance of the topic in practical and real applications. This helps to increase student motivation and understanding of the usefulness of what they learned outside the school environment.

Problem-Based Situations

1. Imagine you have a puzzle with pieces of different shapes, but you don't know if they are identical or not. How would you decide if two pieces are the same just by looking at them?

2. Have you ever noticed patterns in carpets or tiles that repeat? How can you use these patterns to find congruent figures?

Contextualization

The idea of congruent figures is not just an abstract mathematical concept, but something we encounter in our daily lives, especially in design and art. For example, the tiles of a floor may all be of the same size and shape, which implies they are congruent figures that fit perfectly. Furthermore, the study of congruent figures helps to develop important skills, such as detailed observation and the ability to predict how different shapes behave in relation to one another.

Development

Duration: (65 - 75 minutes)

The Development stage is designed for students to practically and collaboratively apply the concepts of congruent figures they studied previously. The proposed activities aim to strengthen students' understanding through direct manipulation of figures, fostering critical thinking, problem-solving, and teamwork. By choosing just one of the activities, the teacher can adapt the content to meet the specific learning needs of the class, ensuring a more personalized and effective approach.

Activity Suggestions

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

Activity 1 - Congruent Figure Detectives

> Duration: (60 - 70 minutes)

- Objective: Develop the ability to recognize and identify congruent figures through the practice of superposition and measurement.

- Description: Students will be divided into groups of up to 5 and will become mathematical detectives. Each group will receive a set of cards with geometric figures drawn, some identical and others not. They should use rulers and protractors to superimpose the cards and determine which figures are congruent and which are not.

- Instructions:

• Form groups of up to 5 students.

• Distribute a set of cards with geometric figures to each group.

• Explain that some figures are identical and others are not.

• Students should use rulers and protractors to superimpose the cards and determine congruence.

• Each group should write down in a notebook the figures that are congruent.

• At the end, each group presents their findings to the class.

Activity 2 - Congruent Mosaic Builders

> Duration: (60 - 70 minutes)

- Objective: Encourage creativity and understanding of congruence in artistic and practical contexts.

- Description: In this activity, students will use cut-out geometric shapes from paper to create a mosaic. They should organize the shapes so that they are congruent, forming symmetrical and aesthetically pleasing patterns.

- Instructions:

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

• Provide each group with different cut-out geometric shapes from paper.

• Students should organize the shapes on a large paper, trying to create congruent and symmetrical patterns.

• Discuss with the students what makes the patterns congruent.

• Each group presents its mosaic and explains the choice of patterns used.

Activity 3 - Congruent Figures Olympics

> Duration: (60 - 70 minutes)

- Objective: Deepen students' knowledge of congruent figures and their properties in a playful and challenging way.

- Description: Students will participate in a competition where they must identify congruent figures in a series of visual and practical challenges. Each challenge will progressively become more complex, involving rotation and reflection of figures.

- Instructions:

• Organize the room into challenge stations, each with a set of visual and practical tasks.

• Students, in groups, should rotate between the stations, completing the challenges at each one.

• The first to correctly complete all challenges earns extra points.

• Make sure each station has a supervisor to clarify doubts.

Feedback

Duration: (15 - 20 minutes)

The purpose of this stage is to allow students to articulate and consolidate what they have learned, as well as to reflect on the learning process and the applicability of the concepts of congruent figures. Group discussions help develop communication and argumentation skills, while sharing experiences promotes a deeper and collective understanding of the topic.

Group Discussion

To initiate the group discussion, the teacher should gather all students in a circle and ask each group to share their experiences and key learnings from the activities conducted. Start by asking: 'What did you discover about congruent figures that you didn't know before the activities?' and encourage each group to present at least one discovery or challenge overcome. Use this moment for students to express their ideas and listen to their peers, promoting a collaborative and reflective learning environment.

Key Questions

1. What were the biggest challenges when trying to identify congruent figures in the activities?

2. How can the ability to identify congruent figures be useful in everyday situations?

3. Was there any surprise or new discovery during the activities that changed your understanding of congruent figures?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate the knowledge gained by students, ensuring that they can link the practical activities conducted with the theoretical concepts of congruent figures. Furthermore, it emphasizes the relevance of mathematical studies for practical applications, encouraging students to see mathematics as a useful and necessary tool in various everyday situations.

Summary

In this final stage, the teacher should summarize the main points addressed about congruent figures, highlighting the properties and identification methods, such as superposition on grids and pattern observation. It is essential to recap what was learned to reinforce students' memory and ensure the assimilation of concepts.

Theory Connection

During the lesson, the connection between theory and practice was evidenced through practical activities, such as the puzzles of figures and the mosaics, which allowed students to directly apply theoretical knowledge. This approach not only reinforced the understanding of mathematical concepts but also demonstrated the relevance of congruent figures in real and everyday situations, such as in art and design.

Closing

Finally, it is important to highlight the importance of studying congruent figures in daily life. The ability to identify and manipulate congruent figures is essential in various areas, from engineering to interior decoration, highlighting how mathematical learning can be applied practically and usefully. This closing helps students realize the value of what they learned and its applicability in the real world.