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

Objective

Duration: (10 - 15 minutes)

This introduction aims to familiarise students with the lesson topic, emphasising key skills they will develop during the activity. Setting a clear starting point helps students grasp the specific objectives and the relevance of the material. Moreover, this phase is designed to engage students right from the start, offering an overview that links theory with practical application, while fostering emotional and social skills within the context of mathematical learning.

Objective Utama

1. Recognise that quadratic functions can be represented using graphs and tables.

2. Distinguish between graphical and tabular representations.

3. Sketch a graph of a quadratic function.

Introduction

Duration: (15 - 20 minutes)

Emotional Warmup Activity

Deep Breathing for Focus

The emotional warm-up activity chosen is 'Deep Breathing'. This involves a series of controlled, deep breaths to help calm the mind, enhance focus, and boost attention. Deep breathing is a straightforward and effective technique to reduce stress and anxiety, creating a more serene learning environment.

1. Prepare the Environment: Ask students to sit comfortably, with back straight and feet flat on the floor. Encourage them to close their eyes if they feel comfortable doing so.

2. Start Breathing: Explain that they will inhale deeply through their nose for 4 seconds, hold their breath for 4 seconds, and exhale slowly through their mouth for 6 seconds.

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

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

5. End: Gradually allow students to revert to their normal breathing pattern and, when ready, slowly open their eyes. Give them a moment to adjust before continuing with the lesson.

Content Contextualization

Quadratic functions are mathematical concepts we encounter in everyday life, such as in physics, economics, and engineering. Being able to represent these functions graphically and in tables is crucial for data interpretation and problem-solving. For instance, when examining the path of an object thrown in the air, its trajectory can be depicted by a parabola, the graph of a quadratic function. Developing the skill to recognise and interpret these graphs not only enriches mathematical understanding but also aids in responsible decision-making, as it offers better insight into the information around us. Furthermore, working with graphs and tables fosters self-control and patience, requiring attention to detail and precision. This approach also enriches social skills like collaboration and communication as students work in groups to solve problems, along with social awareness through understanding how these functions apply to real-life contexts that affect society.

Development

Duration: (60 - 75 minutes)

Theory Guide

Duration: (20 - 25 minutes)

1. Understanding Quadratic Functions: Explain that a quadratic function is a polynomial of degree 2, expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and 'a' cannot be zero.

2. Graphing Quadratic Functions: Describe that the graph of a quadratic function is a parabola. If 'a' is positive, the parabola opens upwards, and if 'a' is negative, it opens downwards. Indicate that the vertex of the parabola represents the function’s maximum or minimum point, which can be found using the formula -b/2a for the x-coordinate and substituting that x into the function to derive the y-coordinate.

3. Finding Roots: Clarify that the roots of the function (or zeros) are values of x for which f(x) = 0. These roots can be calculated by solving the equation ax² + bx + c = 0, typically using the quadratic formula: x = (-b ± √(b²-4ac)) / 2a.

4. Constructing a Value Table: Show how to create a table of values for the quadratic function by selecting values of x and calculating corresponding f(x). Use this table to plot the graph.

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

Activity with Socioemotional Feedback

Duration: (30 - 35 minutes)

Constructing and Analysing Graphs and Tables

In this activity, students will collaborate in groups to create value tables and sketch graphs of given quadratic functions. They will then analyse the graphs and compare results with their peers.

1. Group Formation: Split the class into groups of 3 to 4 students.

2. Assign Functions: Provide each group with a distinct quadratic function to explore, such as f(x) = x² + 2x - 3 or f(x) = -x² + 4x - 2.

3. Build the Table: Each group should generate a table of values for their assigned function, choosing x-values and computing corresponding f(x).

4. Sketch the Graph: Using their table of values, each group must draw the graph of their function on graph paper.

5. Analysis and Discussion: Upon completing the graph, groups should interpret key features (vertex, roots, concavity) and discuss how these elements relate to the function’s context.

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

Discussion and Group Feedback

Following the activities, bring students together for a group reflection using the RULER method. Recognise: Invite students to express how they felt during the activity. Understand: Encourage them to consider what caused those feelings and how they impacted their teamwork. Name: Assist students in identifying and labelling their emotions accurately. Express: Create a safe space for students to share their emotional experiences, both positive and negative. Regulate: Discuss techniques to manage emotions in future activities, such as deep breathing or taking reflection breaks. This discussion supports greater self-awareness and emotional skills, which are vital for effective collaboration and learning.

Conclusion

Duration: (15 - 20 minutes)

Reflection and Emotional Regulation

To conclude, suggest that students write a short paragraph or engage in a group discussion about challenges they encountered during the lesson. Prompt them to think about how they managed their emotions in times of frustration or success and what strategies were effective in maintaining focus and cooperation. Encourage sharing of experiences and considering how they might apply these techniques in the future.

Objective: The aim of this section is to help students evaluate their emotional responses and build emotional regulation skills. By reflecting on challenges and the strategies that worked, students can discover effective ways to handle tough situations, promoting a more intentional and balanced approach to learning.

Glimpse into the Future

To wrap things up, invite students to set personal and academic goals linked to the lesson's content. Clarify the importance of having clear and attainable goals to further enhance their skills in both mathematics and emotional intelligence. Urge them to contemplate how they can utilise what they've learned in school and everyday life.

Penetapan Objective:

1. Grasp and apply graphical and tabular representations of quadratic functions in mathematical challenges.

2. Cultivate the ability to identify and interpret key aspects of a parabola, such as the vertex, roots, and concavity.

3. Engage in effective collaboration and communication during group tasks, respecting peer perspectives and sharing responsibilities.

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

5. Reflect on their learning journey and actively seek opportunities to enhance both academic insights and emotional competencies. Objective: The purpose of this segment is to bolster students’ independence and encourage practical application of their learning, guiding them to establish clear goals for ongoing growth. By setting personal and academic objectives, students can direct their efforts efficiently, ensuring steady advancement in both mathematical understanding and emotional proficiency.