Lesson Plan | Socioemotional Learning | Second Degree Function: Graph and Table

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to introduce students to the topic of the lesson, highlighting the essential skills they will develop throughout the activity. This introduction is crucial for establishing a clear and defined starting point, allowing students to understand the specific objectives and importance of the content to be addressed. In addition, this stage aims to engage students from the beginning, providing an overview that will facilitate the connection between theory and practice, as well as the application of socio-emotional competencies in the context of mathematical learning.

Main Goals

1. Understand that it is possible to represent a quadratic function in graphs and tables.

2. Differentiate the representation in the form of graphs and in the form of tables.

3. Sketch a graph of a quadratic function.

Introduction

Duration: (15 - 20 minutes)

Emotional Warm-up Activity

Deep Breathing for Focus

The chosen emotional warm-up activity is 'Deep Breathing'. This practice involves a series of controlled, deep breaths that help calm the mind, promote focus, and increase students' attention. Deep breathing is a simple and effective technique that can be used to reduce stress and anxiety, providing a calmer and more concentrated learning environment.

1. Preparing the Environment: Ask students to sit comfortably in their chairs, with their backs straight and feet firmly planted on the floor. Request that they close their eyes if they feel comfortable doing so.

2. Starting the Breathing: Explain to the students that they will inhale deeply through their nose for 4 seconds, hold the air in their lungs for 4 seconds, and then exhale slowly through their mouth for 6 seconds.

3. Breathing Guidance: Guide the students through the first breaths: 'Inhale deeply through your nose... one, two, three, four. Hold your breath... one, two, three, four. Now, exhale slowly through your mouth... one, two, three, four, five, six.'

4. Repetition: Repeat this cycle of deep breathing for about 2 to 3 minutes, encouraging students to focus on the rhythm of their breathing.

5. Finalization: Gradually ask students to return to their normal breathing rhythm and, when ready, slowly open their eyes. Allow a few moments for them to adjust before proceeding with the lesson.

Content Contextualization

The quadratic function is a mathematical concept that we encounter in various situations in our daily lives, such as in physics, economics, and even engineering. Understanding how to represent it graphically and in tables is essential for interpreting data and solving problems effectively. For example, when analyzing the trajectory of an object thrown into the air, the path can be described by a parabola, which is the graph of a quadratic function. Developing the ability to recognize and interpret these graphs not only enhances mathematical knowledge but also contributes to responsible decision-making, as it allows for a better understanding of the information around us. Furthermore, working with graphs and tables of quadratic functions can be an opportunity for students to practice self-control and patience, as it requires attention to detail and precision. It is a way to develop social skills, such as collaboration and communication, while working in groups to solve problems, and social awareness, by understanding how these functions can be applied in practical contexts that impact society.

Development

Duration: (60 - 75 minutes)

Theoretical Framework

Duration: (20 - 25 minutes)

1. Concept of Quadratic Function: Explain that a quadratic function is a polynomial function of degree 2, which can be expressed in the general form f(x) = ax² + bx + c, where a, b, and c are constants and 'a' must be different from zero.

2. Graph of the Quadratic Function: Detail that the graph of a quadratic function is a parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. Point out that the vertex of the parabola is the maximum or minimum point of the function, and can be found using the formulas -b/2a for the x-coordinate of the vertex and substituting this x into the function to find the y-coordinate.

3. Roots of the Quadratic Function: Indicate that the roots (or zeros) of the function are the values of x for which f(x) = 0. Explain that these roots can be found by solving the equation ax² + bx + c = 0, using Bhaskara's formula: x = (-b ± √(b²-4ac)) / 2a.

4. Value Table: Show how to construct a value table for the quadratic function. Choose values of x and calculate the corresponding values of f(x). Use this table to plot the graph of the function.

5. Practical Example: Give a concrete example, such as f(x) = 2x² - 4x + 1. Construct the value table for x varying from -1 to 3, calculate f(x) for each value of x, and draw the corresponding graph of the parabola.

Socioemotional Feedback Activity

Duration: (30 - 35 minutes)

Construction and Interpretation of Graphs and Tables

In this activity, students will work in groups to build value tables and sketch graphs of quadratic functions. Afterwards, they will interpret the graphs and compare the results with other groups.

1. Group Division: Divide the class into groups of 3 to 4 students.

2. Function Distribution: Provide each group with a different quadratic function to work on. For example, f(x) = x² + 2x - 3, f(x) = -x² + 4x - 2, etc.

3. Table Construction: Each group must construct a value table for the given function, choosing values of x and calculating the corresponding f(x).

4. Graph Sketching: Using the value table, each group must sketch the function's graph on graph paper.

5. Interpretation and Discussion: After finalizing the graph, groups should interpret the main points (vertex, roots, concavity) and discuss how these characteristics are reflected in the context of the function.

6. Group Comparison: Ask the groups to present their graphs and tables to the class. Compare the different graphs and discussions, highlighting similarities and differences.

Group Discussion

After the activity, gather the students for a group discussion using the RULER method. Recognize: Ask students to identify how they felt during the activity. Understand: Encourage them to reflect on the causes of these emotions and how they influenced their group work. Name: Help students to accurately name these emotions. Express: Provide a safe space for students to express their emotions and experiences, both positive and negative. Regulate: Discuss strategies that could be used to regulate emotions during future activities, such as breathing techniques or reflective pauses. Through this discussion, students can develop greater self-awareness and emotional skills, which are essential for effective collaboration and learning.

Conclusion

Duration: (15 - 20 minutes)

Emotional Reflection and Regulation

For reflection and emotional regulation, suggest to students that they write a brief paragraph or participate in a group discussion about the challenges faced during the lesson. Ask them to reflect on how they managed their emotions during moments of frustration or success and what strategies they used to maintain focus and collaboration. Encourage them to share their experiences and consider how they could apply these strategies in future situations.

Objective: The objective of this subsection is to encourage students to self-evaluate their emotional responses and develop emotional regulation skills. By reflecting on the challenges faced and the strategies used, students can identify effective ways to deal with challenging situations, promoting more mindful and balanced learning.

Closure and A Look Into The Future

For the closing, ask students to set personal and academic goals related to the lesson content. Explain the importance of setting clear and achievable objectives to continue developing their skills in mathematics and emotional intelligence. Encourage them to consider how they can apply what they learned in future contexts, both in school and in everyday life.

Possible Goal Ideas:

1. Understand and apply the graphical and tabular representation of quadratic functions in mathematical problems.

2. Develop the ability to identify and interpret the main elements of a parabola, such as vertex, roots, and concavity.

3. Practice effective collaboration and communication in group activities, sharing responsibilities and respecting peers' opinions.

4. Use emotional regulation strategies, such as deep breathing, to maintain focus and calm in challenging situations.

5. Reflect on learning and constantly seek ways to enhance both academic knowledge and socio-emotional skills. Objective: The objective of this subsection is to strengthen students' autonomy and promote the practical application of learning, encouraging them to set clear goals for continuous development. By defining personal and academic objectives, students can direct their efforts more effectively, ensuring steady progress in their mathematical and emotional skills.