Lesson Plan | Active Learning | Statistics: Median

Assumptions: This Active Lesson Plan assumes: a 100-minute class, prior student study with both the Book and the start of Project development, and that only one activity (among the three suggested) will be chosen to be conducted during the class, as each activity is designed to take up a significant portion of the available time.

Objectives

Duration: (5 - 10 minutes)

The objectives stage is crucial for clearly establishing what is expected for students to learn and master by the end of the lesson. By outlining clear and specific objectives, the teacher guides both the teaching and learning process, ensuring that students focus on the most important aspects of the topic. This section also serves to align student expectations with the planned activities, maximizing classroom time efficiency and content absorption.

Main Objectives:

1. Empower students to understand the concept of median and its importance as a measure of central tendency.

2. Enable students to calculate the median in data sets, reinforcing theoretical learning with practical calculations and problem-solving.

Side Objectives:

1. Develop logical reasoning and critical analysis skills by exploring different data sets in search of the median.
2. Encourage collaboration and communication among students during practical activities, promoting mutual learning.

Introduction

Duration: (15 - 20 minutes)

The purpose of the introduction is to engage students with the topic of the median through problem situations that may occur in their daily lives, stimulating the practical application of prior knowledge. Furthermore, by contextualizing the importance of the median in real-life scenarios, students can see the relevance of the concept and how it applies outside the academic environment, thus increasing interest and motivation to learn.

Problem-Based Situations

1. Imagine a classroom of 30 students who took a math test. The scores ranged from 0 to 10. To calculate the cutoff score, the school decided to use the median. If the scores are 5, 6, 2, 7, 3, 8, 1, 5, 9, 4, what would the cutoff score be?

2. A technology company is analyzing the ages of users of its new application. They collected data from 20 users, and the ages were: 21, 18, 24, 17, 30, 35, 20, 19, 29, 22, 20, 26, 28, 27, 23, 21, 20, 31, 24, 25. What is the median age of the users?

Contextualization

The median is one of the most commonly used measures of central tendency in everyday situations and in science. For example, in a hospital, the median waiting time for patients to receive care can be crucial in determining service efficiency. Additionally, in market studies, the median household income of a certain group of consumers can directly influence companies' marketing strategies. Understanding and being able to calculate the median is essential for making informed decisions in various contexts.

Development

Duration: (70 - 75 minutes)

The development stage is designed to allow students to practically and playfully apply the median concept they studied earlier. Through activities simulating real situations or requiring problem-solving, students can solidify their understanding of the topic and develop logical reasoning, collaboration, and calculation skills. This active and engaging approach aims to maximize knowledge retention and deepen students' understanding of the median as a measure of central tendency.

Activity Suggestions

It is recommended to carry out only one of the suggested activities

Activity 1 - The Median Fair

> Duration: (60 - 70 minutes)

- Objective: Understand and apply the concept of median in a practical context, developing calculation and data visualization skills.

- Description: Students will participate in a playful activity simulating the organization of a fair where various products are sold in different quantities and prices. Each group receives a list of products, their respective quantities sold, and unit prices. The challenge is to find the median price of the products. Subsequently, students must create a simple bar graph to visualize the distribution of prices and quantities.

- Instructions:

• Divide the class into groups of up to 5 students.

• Distribute the lists with products and quantities sold, and unit prices.

• Guide students to calculate the median price of each product.

• Ask them to build a bar graph representing the distribution of prices and quantities.

• Each group presents its graph and explains how they arrived at the median price.

Activity 2 - The Mystery of the Missing Median

> Duration: (60 - 70 minutes)

- Objective: Develop problem-solving and median calculation skills, promoting logical reasoning and collaboration among students.

- Description: In this problem-solving activity, students are detectives who need to discover the value of the median to solve a mystery. They receive a series of numbers representing a password that opens a safe. The median is part of the password but has been replaced by a question mark. Students must use their skills to deduce and calculate the correct median and discover what is inside the safe.

- Instructions:

• Form groups of up to 5 students.

• Give each group a letter containing the series of numbers with the question mark indicating the median.

• Students must calculate the missing median to discover the safe's password.

• After calculating, students must test the password on the 'safe' to see if they can open it.

• Each group presents how they deduced the median.

Activity 3 - The Median Championship

> Duration: (60 - 70 minutes)

- Objective: Foster the skill of quickly and accurately calculating the median, as well as promoting healthy competition and teamwork.

- Description: Students will participate in a median calculation tournament. Each team will receive different data sets with varying quantities of numbers. They will compete to calculate the median most quickly and accurately. The teacher will project the measurement results and a scoreboard for everyone to track each team's performance.

- Instructions:

• Divide the class into groups of up to 5 students.

• Give each group a series of data sets to calculate the median.

• Start a timer and ask the groups to calculate the medians as quickly as possible.

• Each time a group finishes, they signal, and the teacher checks.

• The teacher projects the results and keeps an updated scoreboard during the activity.

Feedback

Duration: (15 - 20 minutes)

This stage of the lesson plan primarily aims to consolidate students' learning, allowing them to articulate the knowledge acquired and reflect on its applicability. Group discussion helps develop communication and argumentation skills, as well as providing a space for students to learn from each other, sharing different resolution strategies and views on the topic. This exchange of ideas helps reinforce knowledge and understanding of the median concept.

Group Discussion

At the end of the activities, organize a group discussion with all students. Start the discussion with a brief introduction, emphasizing the importance of the median as a useful tool in many real-life contexts, such as defining education policies or planning business strategies. Ask each group to share their findings and challenges faced during the activities. Encourage students to discuss how the concept of median can be applied in different situations beyond those carried out in the activities.

Key Questions

1. What were the main challenges your group faced when calculating the median in the activities?

2. How did the median help solve the proposed problem in each activity?

3. What other situations do you imagine where calculating the median would be useful?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage serves to consolidate learning, ensuring that students have a clear and complete understanding of the topic addressed. By summarizing and recapping the content, the teacher helps students retain the knowledge acquired. Additionally, by emphasizing the applicability of the median in real contexts, this section of the lesson plan reinforces the importance of studying mathematics in practical day-to-day situations.

Summary

In the conclusion of the lesson, the teacher should summarize the main points covered regarding the median, including its definition, calculation, and practical application. It is essential to recap the activities carried out, such as 'The Median Fair' and 'The Mystery of the Missing Median', highlighting the results obtained and the calculation strategies employed.

Theory Connection

During the lesson, the connection between the theory studied at home and the practice in class was established through interactive and contextualized activities. Students were able to directly apply the concept of median in scenarios simulating real situations, such as defining cutoff scores and solving problems involving codes and secrets.

Closing

At the end, it is imperative to highlight the relevance of studying the median in everyday life, showing how this measure of central tendency influences decisions in various areas, from education to the market. This final reflection helps students perceive mathematics as a practical and essential tool in daily life.