Lesson Plan | Active Learning | Unequal Partition

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)

This stage of the lesson plan is crucial for establishing the foundations of students' understanding of unequal sharing, a fundamental mathematical concept. The defined objectives aim to ensure that students not only understand the theory behind unequal sharing but are also able to apply this knowledge practically in various situations. Through this approach, it is expected that students will develop a deep understanding and practical skill to solve problems involving unequal shares, preparing them for future mathematical challenges.

Main Objectives:

1. Empower students to solve problems involving the unequal sharing of quantities, identifying the ratio between the parts and their relation to the whole.

2. Develop logical and mathematical reasoning skills through the practical application of concepts of unequal sharing.

Side Objectives:

1. Encourage collaboration and teamwork during practical activities in the classroom.
2. Foster students' confidence in their mathematical abilities through group problem-solving.

Introduction

Duration: (20 - 25 minutes)

The introduction aims to engage students in the lesson theme through problem situations that they can relate to their experiences and lives. These situations are designed to activate prior knowledge and stimulate curiosity, paving the way for deeper exploration of the concept of unequal sharing. The contextualization seeks to show the relevance of the topic in everyday life, increasing students' interest and facilitating the connection between mathematical theory and practical application.

Problem-Based Situations

1. Imagine that you and a friend have a box of chocolates, and decide to share it unequally: you get twice as many as your friend. If the box contains 24 chocolates, how many chocolates will each of you get?

2. Maria and João went to a party and won a large quantity of candies. They decide to divide the candies, but Maria, who helped with the organization, will get twice as many candies as João. If Maria got 36 candies, how many candies did they win in total and how many did João get?

Contextualization

Unequal sharing is a mathematical concept that we encounter in many aspects of real life, from dividing a snack with a friend to solving large engineering problems. Understanding how to divide quantities unequally can help resolve conflicts in a fair and efficient manner. Additionally, this concept is essential for understanding proportions and ratios in mathematics, which are used in many other areas of knowledge.

Development

Duration: (75 - 80 minutes)

The Development stage is designed to allow students to apply the concepts of unequal sharing in a practical and engaging way. Through playful and contextualized activities, students will have the opportunity to solve real and imaginary problems, developing their mathematical, logical reasoning, and teamwork skills. This practical approach aims to solidify the theoretical understanding previously acquired and prepare students for real situations where unequal sharing is a necessity.

Activity Suggestions

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

Activity 1 - Unequal Flavors Festival

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of unequal sharing in a practical scenario, developing calculation, logical reasoning, and teamwork skills.

- Description: Students will be divided into groups of up to 5 people and each group will receive a 'picnic basket' with different types of food in unequal quantities. The challenge is to plan a picnic where each group member receives a total amount of food proportional to their weight. Each type of food represents a different proportion of the total.

- Instructions:

• Form groups of up to 5 students.

• Distribute the 'picnic baskets' to each group, containing items such as apples, oranges, sandwiches, and cookies, each with unequal quantities.

• Explain that each student must receive a total amount of food proportional to their weight. For example, if one student weighs double another, they should receive double the food.

• Students should calculate and decide how to divide the food so that each group member receives the correct proportion.

• Each group will present their planning, explaining the reasons and calculations made for the division.

• Class discussion about the different division methods and the reasons used.

Activity 2 - Bridge Builders

> Duration: (60 - 70 minutes)

- Objective: Understand the concept of unequal sharing through a simple engineering challenge, developing calculation, planning, and execution skills.

- Description: Students, organized into groups, will receive construction materials such as popsicle sticks, glue, and string. The challenge is to build a bridge that supports unequal weights. Each group will receive 'loads' (weight boxes) that must be distributed on the bridge unevenly, requiring the calculation of the weight distribution ratio so that the bridge does not collapse.

- Instructions:

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

• Distribute construction materials to each group: popsicle sticks, glue, and string.

• Each group receives 'loads' of different weights that must be distributed on the bridge unequally.

• Groups must calculate and build the bridge to support the loads, considering the unequal distribution of weights.

• Test the bridges at the end of the construction time by carefully placing the loads on the bridge to see if it holds.

• Discussion about the strategies used and the reasons for the weight distribution.

Activity 3 - Mathematical Cinema: The Treasure Division

> Duration: (60 - 70 minutes)

- Objective: Use storytelling to engage students in the concept of unequal sharing, promoting critical thinking and argumentation.

- Description: In this playful activity, students, divided into groups, will watch a short video where a group of pirates must divide a treasure unequally. After the video, each group must discuss and propose a fair division of the treasure, based on the weight, value, and utility of the items.

- Instructions:

• Organize students into groups of up to 5.

• Present the video where the pirates divide the treasure.

• After the video, each group should discuss and decide how to divide the treasure unequally, justifying their decisions based on the characteristics of the items.

• Each group presents their division and justifications to the class.

• Class discussion about the different approaches and justifications given by the groups.

Feedback

Duration: (15 - 20 minutes)

This stage of the lesson plan is fundamental to consolidating students' learning, allowing them to reflect on what they have learned and share insights with their peers. Group discussion helps develop communication and argumentation skills, as well as providing an opportunity to deepen understanding of the concept of unequal sharing through the exchange of experiences and perspectives. This collective reflection also helps assess how well students have internalized the content and identify areas that may require additional review.

Group Discussion

To initiate the group discussion, the teacher should ask each group to share their findings and strategies used during the activities. It is important for the teacher to encourage students to explain not only the final result but also the reasoning process and challenges faced. The discussion should be structured to allow all groups to have the opportunity to speak and learn from each other.

Key Questions

1. What were the biggest challenges your group faced when trying to divide the quantities unevenly?

2. How did understanding the ratio between the parts help in solving the problems?

3. Can you think of any everyday situation where the concept of unequal sharing could be applied?

Conclusion

Duration: (5 - 10 minutes)

The purpose of this stage of the lesson plan is to ensure that students have a clear and consolidated view of the content addressed, connecting theory to practice and recognizing the importance of the topic in daily life. The conclusion helps students synthesize the knowledge acquired and understand its applicability, preparing them for future mathematical applications and encouraging reflection on the usefulness of the concepts learned.

Summary

In the final stage of the lesson, the teacher should summarize and recap the main points addressed about unequal sharing, emphasizing the understanding of the ratio between the parts and their relation to the whole. This recap will help reinforce learning and ensure that students have a clear and consolidated understanding of the topic.

Theory Connection

To connect theory with practice, the teacher should highlight how the activities conducted in the classroom, such as the 'Unequal Flavors Festival' and 'Bridge Construction', illustrate the application of mathematical concepts in real and playful situations. This practical approach not only reinforces theoretical understanding but also prepares students to apply these concepts in everyday situations and more complex mathematical problems.

Closing

Finally, it is important for the teacher to highlight the relevance of studying unequal sharing in students' daily lives. This mathematical concept not only helps to solve practical problems but also develops logical reasoning and teamwork skills, essential in various real-life situations.