Lesson Plan | Socioemotional Learning | Perfect Squares

Objectives

Duration: 10 - 15 minutes

The purpose of this stage is to provide students with a clear and detailed view of what they will be able to achieve by the end of the lesson, aligning mathematical skills with socio-emotional development. By understanding the objectives, students can direct their attention and efforts, as well as develop self-awareness and self-control by monitoring their own progress.

Main Goals

1. Describe and identify the concept of perfect squares.

2. Apply the notable product of perfect squares in solving mathematical exercises.

3. Recognize and differentiate numbers that are perfect squares from numbers that are not.

Introduction

Duration: (15 - 20 minutes)

Emotional Warm-up Activity

Mindful Breathing for Focus

The proposed activity is a Mindfulness practice focused on breathing. The practice of Mindfulness helps students to be present in the moment, increasing concentration and focus, which are essential for learning complex content like perfect squares. This activity also aids in self-awareness and self-control, allowing students to recognize their emotions and internal states, and learn to regulate them.

1. Preparation of the Environment: Ask students to sit comfortably in their chairs, with their feet flat on the ground and their hands resting on their knees.

2. Closing the Eyes: Instruct students to gently close their eyes or, if they prefer, to maintain a soft gaze at a fixed point on the ground.

3. Start of Breathing: Guide them to begin breathing deeply through their nose, filling their lungs and then slowly releasing the air through their mouth.

4. Counting Breaths: Ask them to mentally count each breath from 1 to 5, then start again from 1.

5. Attention to Breathing: Encourage students to focus on the sensation of air entering and leaving their bodies, paying attention to the sensations in their nose, throat, and lungs.

6. Recognition of Thoughts: If thoughts arise, instruct them to acknowledge them without judgment and gently return their focus to their breathing.

7. Duration of the Practice: Continue this practice for 5 to 10 minutes.

8. Finalization: Request that students gradually move their fingers and toes, slowly open their eyes, and return their attention to the classroom environment.

Content Contextualization

Perfect squares are present in various aspects of our lives, from the geometry of our environments to art and music. For example, when we think of a square or a soccer field, we visualize square shapes that have equal sides, and often, these areas are perfect squares. Additionally, in music, beats can be organized in patterns that resemble the structure of perfect squares, bringing harmony and balance.

Understanding perfect squares is not just a mathematical skill but also a way to appreciate the beauty and symmetry that surround us. By recognizing these shapes in everyday life, students can develop greater social and aesthetic awareness, perceiving how mathematics and art are interlinked and how this affects their emotions and the way they interact with the world.

Development

Duration: (60 - 75 minutes)

Theoretical Framework

Duration: (20 - 25 minutes)

1. Definition of Perfect Squares: A number is a perfect square if it can be expressed as the square of an integer. For example, 1, 4, 9, 16, 25 are all perfect squares because they can be written as 1², 2², 3², 4², and 5², respectively.

2. Identification of Perfect Squares: Teach students to recognize perfect squares by observing if a number can be factored as the product of an integer by itself. For example, to check if 49 is a perfect square, note that 49 = 7 x 7, hence 49 is a perfect square.

3. Notable Product of Perfect Squares: Explain the notable product (a + b)² = a² + 2ab + b², and how it applies in expanding algebraic expressions. Show examples such as (x + 3)² which expands to x² + 6x + 9.

4. Practical Example: Demonstrate with practical examples: (a) Check if 64 is a perfect square. (Answer: Yes, 64 = 8 x 8). (b) Expand the expression (2x + 5)². (Answer: 4x² + 20x + 25).

5. Analogies: To facilitate understanding, use the analogy of a square plaza where, if we know the measurement of one side, we can easily calculate the area (side²). Similarly, if we know the area, we can find the measurement of the side (square root of the area).

Socioemotional Feedback Activity

Duration: (35 - 45 minutes)

Identification and Expansion of Perfect Squares

In this activity, students will work in pairs to solve problems about perfect squares and expand algebraic expressions using the notable product of perfect squares. The activity promotes social skills and social awareness, as students will learn to collaborate and recognize different perspectives.

1. Pair Formation: Divide students into pairs.

2. Distribution of Problems: Give each pair a list of problems involving perfect squares and expressions to expand.

3. Joint Resolution: Students must work together to solve the problems, discussing their strategies and checking the answers.

4. Pair Exchange: After solving some of the problems, students switch partners and discuss the solutions obtained, promoting the exchange of ideas and collaboration.

5. Review of Answers: Gather the class and review the answers together, clarifying doubts and reinforcing the concepts learned.

Group Discussion

After the activity, lead a group discussion using the RULER method:

Recognize: Ask students how they felt working in pairs and recognize the emotions involved in collaboration and problem-solving. Understand: Explore the causes of the emotions by asking why they felt that way. Was it the difficulty of the problem? The interaction with the partner? Label: Help students correctly label emotions such as frustration, joy, anxiety, etc. Express: Encourage students to express their emotions appropriately and share their experiences with the class, fostering a supportive environment. Regulate: Discuss strategies for regulating emotions during collaborative and challenging activities, such as breathing techniques, taking breaks, and open communication with the partner.

Conclusion

Duration: (20 - 25 minutes)

Emotional Reflection and Regulation

To conclude the lesson, ask students to reflect on the challenges faced during the lesson and how they managed their emotions. This reflection can be conducted in two ways: (1) Individual Writing: Distribute a piece of paper and ask each student to write a paragraph about the challenges faced and the emotions felt, as well as the strategies they used to cope with those emotions. (2) Group Discussion: Form small groups and instruct students to discuss the aforementioned points. After the discussion, each group can share their conclusions with the class.

Objective: The goal of this activity is to encourage students to perform a self-assessment and regulate their emotions. Through this reflection, students can identify effective strategies for dealing with challenging situations, promoting self-awareness and self-control. Additionally, the activity strengthens social awareness by allowing students to share and learn from each other's experiences.

Closure and A Look Into The Future

To close the lesson, suggest that students set personal and academic goals related to the content learned. Explain that the goals should be specific, measurable, achievable, relevant, and time-bound (SMART). For example, an academic goal could be 'to practice solving five perfect square problems per week,' while a personal goal could be 'to participate more actively in group activities.' Ask students to write their goals down and, if possible, share them with a classmate so they can support each other in achieving these goals.

Possible Goal Ideas:

1. Practice solving five perfect square problems per week.

2. Collaborate more actively in group activities.

3. Review the concepts of perfect squares before tests.

4. Research applications of perfect squares in other subjects.

5. Help a classmate who has difficulty with the content. Objective: The objective of this subsection is to strengthen students' autonomy and the practical application of learning. By setting personal and academic goals, students are encouraged to continue developing both academically and personally. This practice helps create a sense of responsibility and commitment to their own learning, as well as promoting the continuity of the socio-emotional skills worked on during the lesson.