Lesson Plan | Active Learning | Divisibility Criteria

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 section sets forth the main goals that the lesson aims to achieve, clearly outlining what students should be able to do by the end of the session. This step is crucial for guiding both preparatory and interactive activities in the classroom, ensuring that all efforts are aligned with the desired educational outcomes. Additionally, it helps guide students on the focus of their self-directed learning and the necessary preparation before the lesson.

Main Objectives:

1. Empower students to identify the divisibility criteria for numbers 2, 3, 4, 5, 6, 9, and 10, allowing them to quickly recognize if one number is divisible by another.

2. Develop skills to solve mathematical problems that involve the application of divisibility criteria, including determining remainders in divisions.

Side Objectives:

1. Encourage active participation and critical thinking among students during problem-solving.
2. Promote collaboration among students as they work on group activities to discuss and apply the divisibility criteria.

Introduction

Duration: (15 - 20 minutes)

The introduction aims to engage students through problem situations that stimulate the practical and relevant application of divisibility criteria, helping them make connections to the real world. Additionally, this step serves to contextualize the importance of divisibility criteria, showing how they are applied in everyday situations and throughout history, thereby increasing student interest in the topic.

Problem-Based Situations

1. Imagine you are organizing a party and need to divide 150 balloons equally among 6 tables. How can you quickly check if it is possible to divide the balloons without any leftover?

2. In a marathon, 528 runners are registered and the organization wants to form groups of 4 for each team. How can they use the divisibility criteria to determine if this number of runners can be equally divided among the groups?

Contextualization

The divisibility criteria are not just abstract mathematical rules; they play a crucial role in many practical situations, such as dividing resources into equal parts or organizing events. For example, knowing if one number is divisible by another can help in the fair distribution of items or in forming groups. Furthermore, the history of mathematics reveals that these criteria have been useful since ancient civilizations, which applied them in trade, land division, and other economic activities.

Development

Duration: (70 - 80 minutes)

The Development section is designed to allow students to apply the divisibility criteria in a practical and interactive way. By working in groups, they not only reinforce their individual learning but also develop collaboration and communication skills. Each proposed activity offers a playful and contextualized approach, ensuring that students engage deeply with the material and understand it holistically. This step is vital for transforming theoretical knowledge into applicable practical skills.

Activity Suggestions

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

Activity 1 - Divisibility Detectives

> Duration: (60 - 70 minutes)

- Objective: Develop the ability to apply divisibility criteria practically and collaboratively, strengthening understanding through explanation and justification of answers.

- Description: In this activity, students will become mathematical detectives. They will receive cards with different numbers and must investigate which numbers are divisible by 2, 3, 4, 5, 6, 9, and 10. Each group will have a set of cards and an answer sheet to record their findings.

- Instructions:

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

• Distribute a set of cards with numbers and an answer sheet to each group.

• Each group should analyze the numbers on the cards and determine the divisibility of each one using the learned criteria.

• Students must record their answers on the provided sheet, justifying each decision with the corresponding divisibility criteria.

• At the end, each group will present their findings to the class, discussing the methods used and lessons learned.

Activity 2 - The Supermarket of Numbers

> Duration: (60 - 70 minutes)

- Objective: Playfully apply divisibility criteria, developing calculation and strategy skills, as well as promoting teamwork.

- Description: Students will 'buy' and 'sell' numbers in a fictional supermarket, where the price of each number is determined by its divisibility. Each group will have a 'balance' to spend and must choose numbers based on their divisibility by 2, 3, 5, and 10, trying to maximize or minimize their balance according to the given instructions.

- Instructions:

• Organize the room into 'supermarket stands' with displayed numbers.

• Each group receives an initial balance and rules on how numbers can be 'bought' or 'sold' based on their divisibility.

• Groups must strategize to buy numbers that maximize or minimize their balance following the game rules.

• After a round of purchases, groups calculate their new balance and discuss the strategies used.

• The activity ends with a reflection on the strategies and the importance of divisibility criteria in decision-making.

Activity 3 - Divisible Race

> Duration: (60 - 70 minutes)

- Objective: Foster an energetic and competitive environment to apply divisibility criteria, improving students' speed and accuracy in recognizing divisibility patterns.

- Description: In this dynamic activity, students will participate in a relay race where each stage involves solving a divisibility challenge. Each group must go through stations where they solve divisibility problems to advance in the race.

- Instructions:

• Prepare stations around the room, each with a different divisibility challenge.

• Divide the class into groups and position each group at a starting station.

• At the signal, each group solves the divisibility challenge at the station and, upon success, advances to the next station.

• The first group to complete all challenges and return to the starting point wins.

• Conclude with a discussion about the strategies used and the challenges faced during the activity.

Feedback

Duration: (10 - 15 minutes)

This stage of the lesson plan is essential for consolidating students' learning, allowing them to articulate what they have learned and hear their peers' perspectives. The group discussion helps validate individual understanding and deepen the comprehension of the topic, while the key questions stimulate critical reflection on the applicability of divisibility criteria. Furthermore, this stage strengthens students' communication and argumentation skills.

Group Discussion

At the end of the activities, lead a group discussion for students to share their experiences and learnings. Start the discussion with a brief introduction: 'Now that everyone has had the chance to explore the divisibility criteria through various activities, let's share what we've learned. Each group will have the opportunity to discuss their strategies and findings. This will help us understand how the divisibility criteria can be applied in different situations and how each of you approached the proposed problems.'

Key Questions

1. Which divisibility criteria did you find easiest to apply and why?

2. Was there any number or situation that posed a greater challenge? How did you overcome that?

3. How can knowledge about divisibility help in other areas of mathematics or in practical everyday situations?

Conclusion

Duration: (5 - 10 minutes)

The conclusion stage is essential for consolidating learning, allowing students to reflect on what they have learned and how to apply that knowledge. Reviewing key points helps reinforce memory and understanding of the divisibility criteria, while discussing their practical applications motivates students to perceive the relevance of mathematics in their lives. This stage also serves to synthesize the connection between theory and practice, a fundamental approach in the flipped classroom method.

Summary

In this conclusion, we will recap the divisibility criteria for the numbers 2, 3, 4, 5, 6, 9, and 10, which were explored through practical and interactive activities. Students had the opportunity to apply these criteria in various situations, from solving problems to games and team challenges.

Theory Connection

Today's lesson connected the theory of divisibility criteria with real practices and applications, allowing students to see the relevance of mathematical concepts in everyday situations. Through the activities, they were able to experience the applicability of these criteria in practical scenarios, such as event organization and strategic games, facilitating understanding and memorization of the rules.

Closing

The ability to quickly recognize if one number is divisible by another is a valuable tool not only in mathematics but also in various everyday situations, such as dividing objects equally or organizing people into groups. This knowledge lays a solid foundation for studying more advanced mathematical concepts and helps develop logical reasoning and problem-solving skills.