Lesson Plan | Active Learning | Base Change Problems

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 establishing a solid understanding before entering practical activities. By clarifying what is expected for students to learn, this section guides both the teacher in preparing the lesson and the students in reviewing previously studied content. This way, the focus is directed towards the theoretical and practical understanding of Base Change Problems, aligning expectations and maximizing efficiency in classroom time.

Main Objectives:

1. Ensure that students understand the concept of base and numbering system, identifying how these bases affect the representation of a number.

2. Empower students to perform conversions between different number bases, focusing especially on changing from base 2 to base 10 and vice versa.

Side Objectives:

1. Develop logical and critical reasoning skills through solving mathematical problems.

Introduction

Duration: (15 - 20 minutes)

The Introduction serves to engage students with the theme of the lesson, using problem-situations to revisit and apply prior knowledge about number bases in a practical and contextualized way. This approach seeks not only to activate students' memory but also to show the relevance of the content in everyday and professional situations. By doing this, students can recognize the usefulness and applicability of what they have learned, increasing interest and motivation for the lesson.

Problem-Based Situations

1. Imagine you are playing a board game where you need to move spaces according to decimal numbers, but the die you have is octal (base 8). How would you convert the rolled number to the base the game uses?

2. Consider that in a programming competition, the challenge is to write a piece of code that sums two integers, where these numbers are provided in binary. How should the participants convert the numbers to decimal before performing the sum?

Contextualization

The importance of understanding and being able to convert between number bases extends beyond the classroom, especially in areas such as computing and engineering, where binary, octal, and hexadecimal systems are widely used. For example, in programming, the ability to convert numbers between bases is essential for efficiently manipulating data and ensuring that digital systems function correctly. Additionally, historical curiosities, such as the use of the sexagesimal system by the Babylonians in antiquity, show how adapting different number bases is an ancient and still very relevant skill.

Development

Duration: (70 - 75 minutes)

The Development stage is designed to allow students to practically and engagingly apply the theoretical knowledge previously studied about conversion between number bases. Through playful and contextualized activities, students are encouraged to solve problems based on collaboration, logical reasoning, and direct application of content, thereby consolidating their learning. This approach not only facilitates understanding of the topic but also promotes an active and interactive learning environment.

Activity Suggestions

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

Activity 1 - The Space Base Challenge

> Duration: (60 - 70 minutes)

- Objective: Practice conversion between number bases in a playful and collaborative way, developing logical reasoning and teamwork skills.

- Description: Students are divided into groups of up to five people and are given the following scenario: they are scientists on an interplanetary mission who have discovered an ancient alien spaceship. To access its central computer, they need to decipher numerical sequences that are in different bases, and each sequence reveals a crucial part of the deactivation code for the spaceship's security systems.

- Instructions:

• Each group will receive a sealed envelope containing numerical codes in different bases (binary, octal, decimal, and hexadecimal).

• Students must convert each number to decimal and note the conversions.

• With the correct conversions, they must assemble a keyword that will open the next envelope with more codes.

• The first group to deactivate all security systems and access the central computer of the spaceship wins the challenge.

Activity 2 - The Bits and Bytes Race

> Duration: (60 - 70 minutes)

- Objective: Reinforce the ability to quickly convert between different number bases and promote a healthy competitive environment.

- Description: In this activity, students participate in a relay race, where each relay station contains a base conversion challenge. Each station with a correctly solved challenge allows the next group member to advance to the next station.

- Instructions:

• The room is divided into relay stations, each with a type of base to convert (binary, octal, decimal, hexadecimal).

• Each group starts at one station and has a time limit to solve the current base challenge.

• Upon correctly solving, the next group member runs to the next station and so on.

• The first group to complete all stations and cross the finish line wins the race.

Activity 3 - The Mystery of the Lost Base

> Duration: (60 - 70 minutes)

- Objective: Use logical reasoning and conversion skills between bases to solve a complex problem, encouraging collaboration and effective communication among group members.

- Description: Students, in groups, are detectives who need to decipher a series of codes to unravel the mystery of a lost number base. Each discovered code leads to a new clue until finally the base is revealed and the mystery is solved.

- Instructions:

• Groups receive a 'dossier' containing clues and codes in different bases.

• The clues lead to locations in the room where the next codes are hidden.

• Students must convert the codes to decimal to advance the investigation.

• The final clue reveals the lost number base and concludes the mystery.

Feedback

Duration: (10 - 15 minutes)

The purpose of this stage is to consolidate learning through reflection and sharing experiences. By discussing in groups, students have the opportunity to verbalize what they learned, identify gaps in understanding, and learn from the strategies and challenges faced by their peers. This exchange of ideas reinforces content comprehension and promotes communication and collaboration skills.

Group Discussion

After completing the activities, organize a group discussion with all students to share their experiences and learning. Start the discussion with a brief introduction: 'Now that everyone has completed the activities, let's reflect together on what we learned. Each group will have the opportunity to present what they found most challenging and how they managed to overcome the encountered obstacles. Let's use this exchange of experiences to enrich everyone's learning.'

Key Questions

1. What strategies did you use to convert numbers between different bases?

2. Was there a situation where collaboration in the group was essential to solve the problem? How did that happen?

3. How do you imagine that the ability to convert between number bases could be applied in other areas, such as technology or advanced mathematics?

Conclusion

Duration: (5 - 10 minutes)

The Conclusion stage is designed to consolidate the knowledge acquired during the lesson, ensuring that students can link theory with practice and understand the applicability of the content in real situations. Recapping key points helps reinforce students' memory and solidify learning, while discussing the importance of studying number bases in the real world motivates students to continue exploring and applying these concepts in various contexts.

Summary

In the final stage, the teacher should summarize and recap the main points covered during the lesson, emphasizing the different number bases (binary, octal, decimal, and hexadecimal) and the techniques for converting between them. It is essential that students understand and can recall the strategies discussed for converting numbers from one base to another, reinforcing learning through repetition and clarity in explanation.

Theory Connection

Today's lesson was structured to connect theory and practice effectively. The playful and contextualized activities allowed students to apply theoretical knowledge about number bases in a practical and enjoyable manner, solidifying understanding through real problem-solving and fictional scenarios. This approach not only facilitated learning but also highlighted the importance of conversion between number bases in real and technological contexts.

Closing

Finally, it is important to highlight the relevance of studying number bases in everyday life and in various professional areas, especially those related to technology and engineering. Understanding number bases and the ability to convert between them are essential for developing advanced computational and mathematical skills, as well as providing a new perspective on how information is represented and manipulated.