Lesson Plan | Traditional Methodology | Volume: Contextualized Rectangular Prism

Objectives

Duration: (10 - 15 minutes)

The aim of this stage is to provide a clear and detailed overview of the content that will be covered during the class, establishing the skills that students will need to develop. This prepares students for learning, allowing them to know what to expect and which specific objectives will be achieved by the end of the lesson.

Main Objectives

1. Introduce students to the formula for calculating the volume of rectangular prisms and right prisms with a triangular base.

2. Demonstrate how to solve practical problems involving the calculation of volumes of prisms, using everyday examples such as water tanks and cisterns.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage is to capture students' attention and contextualize the theme of the lesson, making a direct connection between theoretical content and its practical applications in the real world. This helps to motivate students and demonstrate the relevance of what will be taught, creating a conducive environment for learning.

Context

Start the lesson by asking students about everyday situations where they may have encountered objects of different sizes and shapes, such as boxes, cans, and bottles. Explain that many of these objects are examples of prisms. Introduce the idea that volume is a measure of how much space these objects occupy. Use concrete examples, like a shoebox, a water tank, or a swimming pool, to illustrate the importance of calculating volume.

Curiosities

Did you know that civil engineers use volume calculations to determine the amount of concrete needed to build building foundations? Additionally, volume is an essential measure in various other professions, such as in pharmacies for measuring doses of liquid medications, and even in the manufacturing of packaging to ensure that products fit perfectly within boxes.

Development

Duration: (50 - 60 minutes)

The aim of this stage is to deepen students' understanding of the calculation of the volume of rectangular prisms and triangular base prisms through detailed explanations and practical examples. This will allow students to apply the concepts learned to solve real-world and contextualized problems, reinforcing the relevance of the content and facilitating learning.

Covered Topics

1. Definition of Rectangular Prism: Explain that a rectangular prism is a geometric solid with two congruent rectangular bases and sides that are parallelograms. It is important to highlight that rectangular prisms are also known as parallelepipeds. 2. Volume Formula: Present the formula for calculating the volume of a rectangular prism, which is given by V = length x width x height (V = c x l x h). Write the formula on the board and explain each of the variables. 3. Practical Example 1: Use a shoebox to demonstrate the application of the formula. Measure the length, width, and height of the box and calculate the volume step by step, involving students' participation. 4. Triangular Base Prism: Explain that a triangular base prism is a geometric solid with two congruent triangular bases and three rectangular faces. Show a model or an image to illustrate. 5. Volume Formula for Triangular Prism: Introduce the formula for the volume of a triangular base prism, which is given by V = (base area x height). Write the formula on the board and explain how to calculate the area of the triangular base. 6. Practical Example 2: Use a concrete example, such as a triangular prism made of cardboard. Calculate the base area and then the volume, step by step, with students' participation. 7. Contextualized Problems: Present everyday problems involving the calculation of the volume of prisms, such as calculating the volume of a water tank or cistern. Discuss the importance of these applications.

Classroom Questions

1. Calculate the volume of a rectangular prism with a length of 8 cm, a width of 5 cm, and a height of 10 cm. 2. A triangular base prism has a base with an area of 12 cm² and a height of 7 cm. What is the volume of this prism? 3. A water tank is shaped like a rectangular prism with dimensions 2 m x 1.5 m x 1 m. What is the volume of the water tank in liters?

Questions Discussion

Duration: (15 - 20 minutes)

The aim of this stage is to ensure that students have correctly understood how to calculate the volume of rectangular prisms and triangular base prisms. Through the discussion of responses and reflections, students are encouraged to review their calculations, clarify doubts, and understand the practical application of the content. This also promotes active participation and student engagement, reinforcing learning.

Discussion

• Question 1: Calculate the volume of a rectangular prism with a length of 8 cm, a width of 5 cm, and a height of 10 cm.

Explanation: To calculate the volume of a rectangular prism (or parallelepiped), the formula V = length x width x height is used. Substituting the provided values:

V = 8 cm x 5 cm x 10 cm = 400 cm³.

Therefore, the volume of the rectangular prism is 400 cm³.

• Question 2: A triangular base prism has a base with an area of 12 cm² and a height of 7 cm. What is the volume of this prism?

Explanation: To calculate the volume of a triangular base prism, the formula V = (base area x height) is used. Substituting the provided values:

V = (12 cm² x 7 cm) = 84 cm³.

Therefore, the volume of the triangular prism is 84 cm³.

• Question 3: A water tank is shaped like a rectangular prism with dimensions 2 m x 1.5 m x 1 m. What is the volume of the water tank in liters?

Explanation: First, calculate the volume in cubic meters using the formula V = length x width x height. Substituting the provided values:

V = 2 m x 1.5 m x 1 m = 3 m³.

Since 1 cubic meter equals 1000 liters, we convert:

V = 3 m³ x 1000 = 3000 liters.

Thus, the volume of the water tank is 3000 liters.

Student Engagement

1. What difficulties did you encounter when solving the questions? 2. How can you check if the volume calculation is correct? 3. Why is it important to know how to calculate the volume of objects in daily life? 4. Can you think of other practical situations where calculating volume is necessary? 5. How can you apply volume knowledge in other subjects or contexts?

Conclusion

Duration: (10 - 15 minutes)

The aim of this stage is to review and consolidate the main points covered during the lesson, ensuring that students have a clear and complete understanding of the content. Additionally, the conclusion reinforces the practical importance of the topic and motivates students to apply the knowledge acquired in everyday situations.

Summary

• Definition of rectangular prism and triangular base prism.
• Formulas for calculating the volume of rectangular prisms (V = length x width x height) and triangular base prisms (V = (base area x height)).
• Practical examples of calculating volume using everyday objects, like shoeboxes and cardboard triangular prisms.
• Contextualized problems involving the calculation of the volume of water tanks and cisterns.

The lesson connected theory with practice by using concrete examples from everyday life, such as shoeboxes and cisterns, to demonstrate the application of volume formulas. This allowed students to see the relevance of theoretical concepts in real situations, facilitating understanding and retention of content.

The calculation of the volume of prisms is fundamental in various areas of daily life, such as in construction for determining the necessary amount of materials, in pharmacies for dosing liquid medications, and in the industry for manufacturing packaging. Understanding these concepts helps students better understand the world around them and solve practical problems efficiently.