Lesson Plan | Active Learning | Volume: Rectangular Prism

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 clear foundation of what is expected for students to learn and master by the end of the lesson. By defining specific goals, the teacher guides the students' focus and prepares the ground for the practical activities that will follow. This clarity of goals helps students engage more effectively with the content, ensuring a deeper understanding and practical application of the mathematical concepts addressed.

Main Objectives:

1. Empower students to calculate the volume of rectangular prisms using the concept of unit cubes to determine how many fit inside the prism.

2. Develop the ability to solve practical problems involving volume calculation by applying the concept of rectangular prism and identifying the necessary measurements.

Side Objectives:

1. Encourage collaboration and communication among students during class activities, promoting an active and participatory learning environment.

Introduction

Duration: (15 - 20 minutes)

The Introduction stage serves to activate students' prior knowledge and contextualize the importance of studying the volume of rectangular prisms. The proposed problem situations encourage students to apply previously studied concepts practically and relate them to their daily lives, facilitating the transition to the more complex activities that will follow. The contextualization highlights the relevance of the theme, showing how the volume of rectangular prisms is essential in various practical applications, increasing students' interest and motivation.

Problem-Based Situations

1. Imagine you have a rectangular shoe box and need to know how many 1 cm³ cubes fit inside it, considering its dimensions are 30 cm in length, 15 cm in width, and 10 cm in height. How would you solve this problem?

2. Think of a fish tank that you want to fill with water. You know that the tank is a rectangular prism with measurements of 60 cm in length, 30 cm in width, and 40 cm in height. How many liters of water are needed to fill the tank completely?

Contextualization

Calculating the volume of rectangular prisms is a fundamental mathematical skill that applies to various everyday situations, such as planning space in furniture, packaging, or even filling reservoirs. For example, architecture and engineering constantly use these calculations to size structures and design spaces. Furthermore, math can be fun and practical, such as solving three-dimensional puzzles or participating in construction projects like models.

Development

Duration: (65 - 75 minutes)

The Development stage is designed to allow students to apply the concepts of volume of rectangular prisms they have previously studied in a practical and contextualized manner. The suggested activities aim not only to reinforce theoretical learning with practice but also to develop collaboration, communication, and problem-solving skills. By solving problems in groups, students are encouraged to discuss and justify their approaches, promoting a deeper understanding of the content and more meaningful learning.

Activity Suggestions

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

Activity 1 - Cube Party: Planning the Dance Space

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of volume of rectangular prisms to solve a practical space problem.

- Description: Students are challenged to organize a party where the space for the dance floor must be a rectangular prism, and the challenge is to calculate how many people can dance simultaneously in that space, considering that each person occupies a volume of 1 m³.

- Instructions:

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

• Provide each group with the dimensions of the available space for the dance floor, which will be a rectangular prism, for example, 10 m in length, 5 m in width, and 3 m in height.

• Ask them to calculate the total volume of the dance floor space.

• Determine that each person occupies a volume of 1 m³.

• Students should then calculate how many people can dance at the same time on the dance floor using the total volume and the 1 m³ cubes.

• Each group must present their conclusions and the method used to arrive at them.

Activity 2 - Cube Builders: Building a City

> Duration: (60 - 70 minutes)

- Objective: Develop volume calculation skills and apply geometry concepts in a practical and collaborative activity.

- Description: In this activity, students will work in groups to design and build a model of a city, where each building is represented by a rectangular prism. They will use 1 cm³ cubes to represent different buildings, and the challenge will be to calculate the total volume of the city and how many cubes are needed for each type of building.

- Instructions:

• Organize students into groups of up to 5 people.

• Distribute to each group a floor plan of the city, which includes different types of buildings (school, hospital, residential building, etc.), each represented by a rectangular prism with specific dimensions.

• Students must calculate the total volume of the city and then the volume of each type of building.

• Using 1 cm³ cubes, students should build the buildings in the model, ensuring that the number of cubes corresponds to the calculated volume.

• At the end, each group presents their model, explaining the calculations made and the design decisions taken.

Activity 3 - Treasure Hunt: Volume Calculation in Pirate Adventure

> Duration: (60 - 70 minutes)

- Objective: Apply the concept of volume of rectangular prisms in a playful problem-solving context, stimulating logical reasoning and teamwork.

- Description: Students, organized in groups, will participate in a treasure hunt where they need to calculate the volume of different boxes that can contain clues. Each box is a rectangular prism with unknown dimensions that will be described in clues to be solved.

- Instructions:

• Divide the class into groups of no more than 5 students.

• Give each group a set of clues that describe the size and shape of different boxes that might contain the treasure clues.

• Students should use the clues to calculate the volume of each box and determine where the treasure clues are hidden.

• Each group must record their calculations and justify their conclusions based on the calculated volumes.

• The first team to find all the clues and the treasure, with correct calculations, wins the activity.

Feedback

Duration: (15 - 20 minutes)

This feedback stage aims to consolidate students' learning, allowing them to reflect on the practical activities carried out and articulate the knowledge acquired. Group discussion helps to identify gaps in understanding, promotes the exchange of ideas, and enriches learning through the diversity of approaches presented. This stage also serves to assess the students' level of understanding of volume calculation of rectangular prisms and to reinforce the importance of teamwork and effective communication in solving mathematical problems.

Group Discussion

At the end of the activities, gather all the students for a group discussion. Start the conversation with a brief introduction, reminding them of the lesson objectives. Then, ask each group to share their experiences, challenges faced, and the solutions they developed. Encourage students to discuss the different approaches and what they learned from their peers' activities. Use questions such as 'What was the most challenging aspect of this activity?' and 'How did you solve this problem?' to guide the conversation and ensure everyone participates actively.

Key Questions

1. How does the concept of volume of rectangular prisms help solve practical everyday problems?

2. What were the main difficulties encountered when calculating the volume of rectangular prisms in the activities? How did you overcome them?

3. In what way did collaboration and communication in the group help solve the problems?

Conclusion

Duration: (5 - 10 minutes)

The purpose of the Conclusion stage is to ensure that students have a clear and consolidated understanding of the concepts addressed during the lesson, connecting theory with practice and highlighting the relevance of volume calculations in everyday life. Additionally, this stage serves to reinforce learning, allowing students to see the applicability of what they have learned and the importance of continuing to explore and refine this knowledge.

Summary

In the conclusion, the teacher should summarize the concepts addressed regarding the calculation of volume of rectangular prisms, recalling the calculation methods and formulas used. Emphasize the use of unit cubes to visualize and perform calculations practically.

Theory Connection

Explain how practical activities, such as 'Cube Party' and 'Building Cubes,' connected the theory studied at home with practice in the classroom, showing the application of mathematical concepts in everyday and playful situations.

Closing

Finally, highlight the importance of studying the volumes of rectangular prisms in the real context, such as in space planning and engineering. Reinforce how mastering these concepts helps solve practical problems and think more critically and structurally.