Lesson Plan | Active Learning | Triangles and Their Classifications

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 essential for directing the focus of students and the teacher towards the specific goals of the lesson. By clearly establishing what is expected to be achieved, this section lays the groundwork for more effective and targeted learning. The formulated objectives aim to consolidate students' prior knowledge about triangles and expand their understanding, allowing them to apply mathematical concepts in practical and classification situations.

Main Objectives:

1. Empower students to recognize and name different types of triangles based on their side and angle properties.

2. Develop skills for classifying triangles according to the measurements of their sides and angles, promoting logical-mathematical reasoning.

Side Objectives:

1. Encourage active participation of students in identifying and describing triangles during practical activities.

Introduction

Duration: (15 - 20 minutes)

The introduction serves to engage students and bridge the gap between prior theoretical knowledge and its practical application. By presenting problem situations, it stimulates reflection and review of the concepts studied at home, preparing students for more interactive activities in class. The contextualization, in turn, broadens students' perception of the importance of triangles in the real world, increasing interest and motivation for learning the subject.

Problem-Based Situations

1. Imagine you are drawing a map for an adventure game. You need to draw a bridge connecting two points, but you don't know what angle it needs to be for safety. How would you use knowledge about triangles and their angles to decide the slope of the bridge?

2. Think of a situation where you need to cut a cake into equal pieces and want to use only one cut. How can you use the property of triangles to ensure the pieces will be equal?

Contextualization

Triangles are one of the most fundamental and versatile geometric shapes and are present in countless everyday situations. From bridge construction, where stability is ensured through the study of triangles, to games, where maze and puzzle designs utilize mathematical properties to create interesting challenges. Furthermore, the study of triangles dates back to ancient times, with cultures such as the Egyptian and Greek exploring their properties in architecture and astronomy, making the topic even more fascinating and relevant.

Development

Duration: (70 - 75 minutes)

The development stage is designed to allow students to practically and interactively apply the knowledge acquired about triangles and their classifications. Through playful and contextualized activities, students have the opportunity to solidify their theoretical understanding, develop problem-solving skills, and strengthen group collaboration. This section is crucial for transforming passive knowledge into active and meaningful learning.

Activity Suggestions

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

Activity 1 - Culinary Triangle

> Duration: (60 - 70 minutes)

- Objective: Apply geometry concepts to divide a shape into equal parts and practice planning and execution skills in a group.

- Description: In this activity, students will apply their knowledge of triangles to cut a sandwich in a way that it is divided into equal and visually appealing parts. Using a large square sandwich, they must plan and execute diagonal cuts to create identical triangles.

- Instructions:

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

• Give each group a large square sandwich and a kitchen knife.

• Ask them to plan how to cut the sandwich into the maximum number of identical triangles using only diagonal cuts.

• Students should discuss in groups the best strategy and sketch a plan on paper before executing it.

• Each group makes cuts on the sandwich following their drawn plan.

• After execution, students must count the number of triangles obtained and check if they are all identical.

• Groups present their planning process and results to the class.

Activity 2 - The Great Triangular Treasure Hunt

> Duration: (60 - 70 minutes)

- Objective: Review and deepen knowledge about the classification of triangles, promoting collaboration and quick reasoning.

- Description: Students will participate in a treasure hunt in the classroom where they must identify and classify hidden triangles. Triangles of different sizes, types, and orientations will be spread throughout the room, and each group will receive cards with characteristics to find and classify the triangles.

- Instructions:

• Prepare several paper triangles of different types (equilateral, isosceles, scalene) and sizes in advance.

• Hide the triangles around the classroom, some in easily accessible locations and others in more challenging spots.

• Distribute cards to each group with characteristics they must find in the triangles, such as 'a triangle with all sides equal' or 'a triangle with an acute angle.'

• Groups must use the cards and prior knowledge to find and classify the hidden triangles.

• The first team to find and correctly classify all the triangles wins a small prize.

Activity 3 - Bridge Builders

> Duration: (60 - 70 minutes)

- Objective: Apply engineering and geometry concepts to build a stable structure, promoting teamwork and creativity.

- Description: Students, divided into groups, must design and build a popsicle stick bridge that can support the weight of a small box. The challenge is to use knowledge about triangles to ensure the stability and strength of the bridge.

- Instructions:

• Provide each group with popsicle sticks, glue, and a small box that will serve as 'load' for the bridge.

• Explain that the bridge must be able to support the box without collapsing.

• Students must plan the shape of the bridge, which should include strategic use of triangles to reinforce the structure.

• After planning, groups build their bridges, applying glue to the junction points of the sticks.

• Test each bridge by gradually placing the box until it gives way or remains stable.

• Groups discuss what worked and what could be improved in their designs.

Feedback

Duration: (10 - 15 minutes)

The purpose of this feedback stage is to consolidate students' practical learning, allowing them to reflect on the activities carried out and articulate theoretical knowledge with their experiences. Through group discussion, students have the opportunity to verbalize what they learned and listen to different perspectives, which can deepen their understanding and clarify possible doubts. This reflection process is crucial for active learning and long-term knowledge retention.

Group Discussion

To initiate the group discussion, the teacher should ask each group to share their experiences and learnings from the activities carried out. One can start with a general recap, asking what each group discovered about the different types of triangles and how they were applied in practical activities. Then, the teacher can guide the discussion for each group to explain the challenges encountered and how they overcame them, promoting the exchange of ideas and strategies among students.

Key Questions

1. What were the main challenges in classifying and identifying the triangles during the activities? How did you overcome them?

2. How does the practical application of triangle concepts help to better understand the theory studied?

3. Was there any surprise or interesting discovery during the activities that changed your understanding of triangles?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage aims to reinforce and synthesize the knowledge acquired, ensuring that students have a clear and consolidated understanding of the topics discussed. Furthermore, it serves to highlight the importance and relevance of triangles in the real world, encouraging students to perceive mathematics as a practical and applicable tool in various situations. This final section also helps prepare students for possible future applications of the concepts learned.

Summary

In this final phase of the lesson, it is crucial to summarize the main points covered about triangles and their classifications, reinforcing the identification and differentiation between triangles by their sides and angles. By recapping the types of triangles (equilateral, isosceles, scalene) and the classifications by angles (acute, right, obtuse), students consolidate the knowledge acquired and ensure a clear understanding of the concepts.

Theory Connection

Today’s lesson was outlined to connect theory and practice in an integrated manner. Activities such as 'Culinary Triangle', 'The Great Triangular Treasure Hunt', and 'Bridge Builders' were designed for students to directly apply the concepts studied about triangles in real and fun situations, thus ensuring that the theory was not only understood but also experienced and applied in practical contexts.

Closing

The importance of triangles goes beyond the mathematical context, extending to various areas of knowledge and practical applications in daily life. Understanding the properties of triangles is fundamental in fields such as architecture, engineering, and design, where stability and precise proportions are essential. This knowledge is also applicable in everyday tasks, such as equitably dividing areas or objects.