Lesson Plan | Socioemotional Learning | Trigonometric Ratios

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to establish a clear and understandable foundation on trigonometric ratios, preparing students for the understanding and practical application of these concepts. Additionally, it aims to spark students' curiosity and interest, connecting mathematical content to the development of socio-emotional skills, such as self-awareness and responsible decision-making.

Main Goals

1. Recognize and name the main trigonometric ratios: sine, cosine, and tangent, in the context of a right triangle.

2. Understand the causes and consequences of trigonometric ratios for the angles of 30º, 45º, and 60º, applying them in calculations of side lengths of right triangles.

Introduction

Duration: 15 to 20 minutes

Emotional Warm-up Activity

Connecting to the Present

Guided Meditation for Focus

1. Ask students to sit comfortably in their chairs, with their feet firmly planted on the ground and their hands resting on their knees.

2. Suggest they gently close their eyes or focus their gaze on a point ahead.

3. Instruct students to breathe deeply through their nose, filling their lungs with air, and then slowly exhale through their mouth.

4. Guide them to focus on their breathing, feeling the air entering and leaving. Encourage them to notice any tension in their bodies and consciously relax those areas.

5. For 5 minutes, guide students to bring their attention back to their breath every time they notice their mind wandering.

6. Conclude the meditation by asking students to slowly open their eyes, keeping that sense of calm and focus.

Content Contextualization

Trigonometric ratios are like tools that help us solve everyday problems, even if we don’t realize it. For example, architects and engineers use them to design buildings and bridges, ensuring they are safe and functional. Just as these professionals need precision and concentration to do their work, we can also apply these skills while learning trigonometry. Developing self-awareness and self-control helps us recognize how we feel about mathematical challenges and regulate those emotions to make responsible decisions during problem-solving.

Development

Duration: 60 to 75 minutes

Theoretical Framework

Duration: 20 to 25 minutes

1. Definition of Trigonometric Ratios: Explain that trigonometric ratios are relationships between the lengths of the sides of a right triangle. The three main ratios are: sine (sin), cosine (cos), and tangent (tan).

2. Sine (sin): Define sine as the ratio between the length of the opposite side to the angle and the length of the hypotenuse. Use the formula: sin(θ) = opposite side / hypotenuse.

3. Cosine (cos): Define cosine as the ratio between the length of the adjacent side to the angle and the length of the hypotenuse. Use the formula: cos(θ) = adjacent side / hypotenuse.

4. Tangent (tan): Define tangent as the ratio between the length of the opposite side to the angle and the length of the adjacent side. Use the formula: tan(θ) = opposite side / adjacent side.

5. Notable Angles: Explain that the angles of 30º, 45º, and 60º are called notable angles and have sine, cosine, and tangent values that can be memorized to facilitate calculations.

6. Table of Trigonometric Ratios for Notable Angles: Present a table with the sine, cosine, and tangent values for 30º, 45º, and 60º. For example: 30º: sin(30º) = 1/2, cos(30º) = √3/2, tan(30º) = 1/√3 45º: sin(45º) = √2/2, cos(45º) = √2/2, tan(45º) = 1 60º: sin(60º) = √3/2, cos(60º) = 1/2, tan(60º) = √3

7. Practical Applications: Provide examples of how trigonometric ratios can be used to calculate side lengths in right triangles, such as finding the height of a building using the projected shadow.

Socioemotional Feedback Activity

Duration: 30 to 35 minutes

Exploring Right Triangles

In this activity, students will apply trigonometric ratios to solve practical problems involving right triangles. They will work in small groups to calculate the lengths of the sides of triangles with angles of 30º, 45º, and 60º, using the trigonometric ratios learned.

1. Divide the class into small groups of 3 to 4 students.

2. Provide each group with sheets of paper, a ruler, and a calculator.

3. Give each group a set of problems involving right triangles with angles of 30º, 45º, and 60º.

4. Ask students to use the trigonometric ratios to calculate the unknown side lengths of the triangles presented in the problems.

5. Encourage groups to discuss their problem-solving strategies and to check each other's results.

Group Discussion

After the activity, gather students for a group discussion. Use the RULER method to guide the discussion:

Recognize: Ask students how they felt while solving the problems. Were they confident, anxious, or frustrated? Encourage them to share their emotions.

Understand: Explore the causes of these emotions. Ask what led to feelings of confidence or anxiety. Was it the understanding of the content, group collaboration, or another factor?

Name: Help students correctly name the emotions they felt during the activity and to express those emotions appropriately.

Express: Encourage students to talk about how they expressed their emotions during the activity. Did they ask for help when confused? Did they offer support to their classmates?

Regulate: Discuss strategies for regulating emotions during challenging activities. How can they maintain calm and focus? How can they support each other during difficult times?

This discussion not only reinforces academic content but also promotes important socio-emotional skills, such as empathy, self-management, and collaboration.

Conclusion

Duration: 15 to 20 minutes

Emotional Reflection and Regulation

Suggest that students write a paragraph reflecting on the challenges faced during the trigonometry lesson. They can consider how they felt while learning new concepts and applying trigonometric ratios to practical problems. Additionally, ask them to describe the strategies they used to manage their emotions and how those strategies helped them overcome difficulties. Alternatively, lead a group discussion where students can share their experiences and listen to their peers, promoting an environment of empathy and mutual support.

Objective: The objective of this reflection is to encourage students to self-evaluate their emotional and cognitive performance during the lesson. By identifying the emotions felt and the strategies used to regulate them, students can recognize their strengths and areas for improvement. This helps them develop skills of self-awareness and self-control, essential for dealing with challenging situations both in academic contexts and in personal life.

Closure and A Look Into The Future

At the end of the lesson, ask students to set personal and academic goals related to the content learned. They can write these goals on a sheet of paper and briefly share them with the class. Goals may include regular practice of trigonometric exercises, seeking additional study resources, or applying trigonometric ratios in real-life contexts, such as school projects or everyday problems.

Possible Goal Ideas:

1. Practice trigonometric exercises at least three times a week.

2. Study notable angles and their trigonometric ratios until memorized.

3. Apply trigonometric ratios to real problems, such as measuring heights and distances.

4. Collaborate with classmates in study groups to solve trigonometry problems.

5. Seek additional resources, such as videos and online tutorials, to reinforce learning. Objective: The objective of this subsection is to strengthen students' autonomy by encouraging them to set clear and achievable goals. This promotes continuity in academic and personal development, helping students apply the knowledge gained practically and better prepare for future challenges. By setting goals, students become more responsible for their learning and development, cultivating a sense of purpose and direction.