Lesson Plan | Socioemotional Learning | Statistics: Median

Objectives

Duration: 10 to 15 minutes

The purpose of this stage is to introduce students to the concept of median, providing a solid foundation for them to understand and calculate this statistical measure. Understanding the role of the median as a measure of central tendency is fundamental for the development of students' mathematical skills and for practical application in everyday situations. Additionally, this stage prepares students for subsequent activities, where they will be encouraged to explore their emotions and socio-emotional skills while solving mathematical problems.

Main Goals

1. Understand the concept of median and its importance as a measure of central tendency.

2. Learn to calculate the median of a set of ordered data in ascending or descending order.

3. Recognize the practical application of the median in everyday contexts and other disciplines.

Introduction

Duration: 15 to 20 minutes

Emotional Warm-up Activity

✨ Mindfulness of Conscious Breathing ✨

This emotional warm-up activity is a mindfulness practice focused on promoting students' focus, presence, and concentration. Through conscious breathing and mindfulness, students will be encouraged to connect with the present moment, calming their minds and preparing emotionally for the class. Mindfulness helps reduce stress and anxiety, promoting a more receptive and positive learning environment.

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

2. Instruct them to close their eyes if they feel comfortable, or to focus on a fixed point on the floor.

3. Guide students to start paying attention to their breathing, feeling the air entering and exiting through their noses.

4. Ask them to breathe deeply, inhaling through the nose for four seconds, holding the breath for four seconds, and exhaling slowly through the mouth for six seconds.

5. Repeat this deep breathing cycle for approximately three minutes.

6. During the practice, encourage students to focus on the sensation of air coming in and out, noticing any thoughts or distractions that arise and gently bringing their attention back to their breathing.

7. After three minutes, ask students to slowly open their eyes or lift their gaze, bringing their attention back to the classroom.

Content Contextualization

The median is a statistical measure that helps us understand data sets better, especially when there are extreme or outlier values that may distort other measures like the mean. Just as the median helps us find a central point in a set of numbers, we can use our socio-emotional skills to find balance and centrality in our lives. By recognizing and understanding our emotions, we can name them, express them appropriately, and regulate them efficiently, just as we do with data when calculating the median.

Imagine a situation where you are organizing a party with your friends and need to decide which music to play. Some friends like rock, others like pop, and some prefer classical music. Instead of choosing a song that only pleases a part of the group, you can find a solution that satisfies most, like a song that everyone moderately enjoys. Similarly, the median helps us find a central value that well represents a dataset without being influenced by extremes.

Development

Duration: 60 to 75 minutes

Theoretical Framework

Duration: 20 to 25 minutes

1. Introduction to the Median:

2. Explain that the median is a measure of central tendency that represents the middle value of an ordered data set.

3. Emphasize that, unlike the mean, the median is not influenced by extreme values.

4. Provide the formal definition: 'The median of a dataset is the value that separates the upper half from the lower half of the data.'

5. Steps to Calculate the Median:

6. Order the data in ascending or descending order.

7. If the number of elements (n) is odd, the median is the middle value.

8. If the number of elements (n) is even, the median is the average of the two middle values.

9. Practical Examples:

10. Example 1: For the dataset [1, 2, 5], the median is 2, as it is the middle value.

11. Example 2: For the dataset [1, 2, 3, 4, 5, 6], the median is (3 + 4) / 2 = 3.5.

12. Analogies to Facilitate Understanding:

13. Compare the median to the idea of finding a balance point on a seesaw, where there is no tilt to either side.

14. Use the analogy of organizing students in line by height and finding the student who is exactly in the middle of the line.

15. Practical Applications of the Median:

16. Discuss how the median is used in various fields, such as economics (to measure median income), health (to measure median values of certain indicators), and in everyday life (such as finding the median in school assessments).

17. Explain that the median is useful for understanding data distribution without being distorted by outliers.

Socioemotional Feedback Activity

Duration: 30 to 35 minutes

 Finding the Median in Data Sets 

In this activity, students will calculate the median of different datasets and reflect on the importance of this measure in real situations. The activity will be conducted collaboratively, encouraging communication and idea exchange among students.

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

2. Distribute different datasets to each group. For example: [3, 1, 4, 1, 5, 9], [2, 7, 1, 8, 2, 8], [5, 3, 2, 6, 4, 7].

3. Ask the groups to order the data and calculate the median of each set.

4. After calculating the median, each group should discuss and note the possible applications of the median in the context of the provided data.

5. Encourage students to reflect on how the median can be a fair representation of data, comparing with the mean if necessary.

6. At the end, each group should present their findings and reflections to the class.

Group Discussion

After completing the activity, start a group discussion using the RULER method. Ask students to recognize and name the emotions they felt during the activity, such as frustration, satisfaction, or excitement. Understand the causes of these emotions, such as challenges in ordering the data or the satisfaction of correctly finding the median.

Encourage students to express their emotions appropriately, discussing how they felt while working in a group and solving the proposed problems. Finally, help them to regulate their emotions by suggesting strategies to deal with frustrations and anxieties, such as asking for help from peers or the teacher, and celebrating achievements as a group.

Conclusion

Duration: 15 to 20 minutes

Emotional Reflection and Regulation

Suggest that students write a paragraph or participate in a group discussion about the challenges faced in class when calculating the median and how they managed their emotions during the process. Encourage them to reflect on the moments they felt frustrated, satisfied, or collaborative, and think about the strategies they used to overcome obstacles. The reflection may include questions like: 'What was the biggest challenge in calculating the median?' 'How did you feel when collaborating with your group?' 'What strategies were effective for maintaining calm and concentration?'

Objective: The objective of this subsection is to encourage self-assessment and emotional regulation, helping students identify effective strategies to deal with challenging situations. This promotes self-knowledge and self-control, which are essential for developing socio-emotional competencies, as well as strengthening students' ability to face future challenges with resilience and confidence.

Closure and A Look Into The Future

Explain to students the importance of setting personal and academic goals to continue advancing both in statistics learning and in socio-emotional development. Ask each student to write a specific goal related to the lesson content, such as 'Calculating the median of more complex datasets' or 'Applying the concept of median in everyday situations.' Then, ask each of them to set a personal goal, like 'Improving my group work skills' or 'Practicing emotional regulation in stressful situations.'

Possible Goal Ideas:

1. Understand and calculate the median of different datasets.

2. Apply the concept of median to real-life problems.

3. Develop group work and collaboration skills.

4. Practice emotional regulation strategies in academic and personal contexts. Objective: The objective of this subsection is to strengthen students' autonomy and the practical application of learning, encouraging them to continue developing their academic and personal competencies. Establishing clear goals helps students maintain focus and motivation, promoting continuous growth and the ability to face future challenges with confidence and resilience.