Lesson Plan | Traditional Methodology | Translations in the Cartesian Plane

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to introduce students to the concept of translation in the Cartesian plane and establish the foundations for understanding and practical application of this concept. By clearly outlining the objectives, it ensures that students know what is expected of them, facilitating the assimilation of content and the execution of proposed activities.

Main Objectives

1. Recognize and describe the concept of translation in the Cartesian plane.

2. Identify figures that have been translated in a Cartesian plane, specifically by moving a figure two units to the right and three units down.

Introduction

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to introduce students to the concept of translation in the Cartesian plane and establish the foundations for understanding and practical application of this concept. By clearly outlining the objectives, it ensures that students know what is expected of them, facilitating the assimilation of content and the execution of proposed activities.

Context

To start the class on translations in the Cartesian plane, it is important for students to understand that the Cartesian plane is a fundamental tool in various fields, such as engineering, physics, and computer science. The Cartesian plane allows us to represent and analyze different phenomena, such as movements and transformations, in a visual and clear manner. Translation, specifically, is a way of moving a figure from one point to another without changing its shape, size, or orientation. This skill is essential both in academic contexts and in everyday situations, such as reading maps or graphs.

Curiosities

Did you know that the concept of translation is widely used in movie animations and video games? When a character moves from one place to another on screen, it is being translated. This technique helps animators create smooth and realistic movements, making characters appear to be moving through space.

Development

Duration: (35 - 40 minutes)

The purpose of this stage of the lesson plan is to provide a deeper and practical understanding of the concept of translation in the Cartesian plane. Through detailed explanations and practical examples, students will be able to visualize and apply the concept of translation, consolidating their learning. The proposed questions aim to reinforce the theory presented and ensure that students can solve translation problems autonomously.

Covered Topics

1. Introduction to the concept of translation: Explain that translation is a type of geometric transformation that moves each point of a figure or object a constant distance in a specific direction. 2. Cartesian plane: Briefly review the concept of the Cartesian plane, the X and Y axes, and how to plot points in the plane. 3. Translation vectors: Detail what translation vectors are, how they are represented (e.g., (a, b)), and how they affect the position of points in the Cartesian plane. 4. Practical examples: Demonstrate with specific examples how to translate figures in the Cartesian plane, for example, moving a square two units to the right and three units down. Show step by step how each point of the square is moved. 5. Problem solving: Work with students on solving problems involving translation, showing how to apply the translation vector to each point of a figure.

Classroom Questions

1. What will be the new position of point A(3, 4) after a translation of 2 units to the right and 3 units down? 2. If a triangle with vertices at (1, 2), (3, 5) and (6, 2) is translated by a vector (4, -1), what will be the new coordinates of the vertices? 3. A figure is translated by a vector (-2, 3). What will be the new position of point B(-1, -1)?

Questions Discussion

Duration: (20 - 25 minutes)

The purpose of this stage of the lesson plan is to review and consolidate the knowledge acquired by students through the discussion of the resolved questions. This section allows students to revisit concepts, clarify doubts, share their resolution strategies, and reflect on the practical application of translations in the Cartesian plane. Additionally, it promotes a collaborative learning environment where students can learn from each other.

Discussion

• Question 1: What will be the new position of point A(3, 4) after a translation of 2 units to the right and 3 units down?

Explanation: To solve this question, the translation vector (2, -3) should be added to the original coordinates of point A. Thus, the new position will be calculated as:

A' = (3 + 2, 4 - 3) = (5, 1)

Therefore, the new position of point A after translation is (5, 1).

• Question 2: If a triangle with vertices at (1, 2), (3, 5) and (6, 2) is translated by a vector (4, -1), what will be the new coordinates of the vertices?

Explanation: For each vertex, the translation vector (4, -1) should be added to the original coordinates:

Vertex 1: (1 + 4, 2 - 1) = (5, 1) Vertex 2: (3 + 4, 5 - 1) = (7, 4) Vertex 3: (6 + 4, 2 - 1) = (10, 1)

Therefore, the new coordinates of the triangle's vertices are (5, 1), (7, 4), and (10, 1).

• Question 3: A figure is translated by a vector (-2, 3). What will be the new position of point B(-1, -1)?

Explanation: To solve this question, the translation vector (-2, 3) should be added to the original coordinates of point B. Thus, the new position will be calculated as:

B' = (-1 - 2, -1 + 3) = (-3, 2)

Therefore, the new position of point B after translation is (-3, 2).

Student Engagement

1.  What strategy did you use to add the translation vector to the coordinates of the points? 2. 樂 Was any of the results obtained different from what you expected? Why? 3.  How did you verify that the new coordinates were correct? 4.  Can you think of any everyday situation where translation could be applied? 5.  How can understanding translations help in other subjects, such as Physics or Geography? 6.  Can someone explain to the class how they solved one of the questions?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to review and consolidate the knowledge acquired during the class, ensuring that students have a clear understanding of the concepts addressed. Additionally, it reinforces the practical importance of the content by connecting it to real-life situations and future applications.

Summary

• Translation is a geometric transformation that moves a figure without changing its shape, size, or orientation.
• The Cartesian plane consists of two perpendicular axes, X and Y, that allow us to plot points and figures.
• Translation vectors indicate the amount and direction of movement for each point of a figure.
• Movements in the Cartesian plane can be represented by vectors, such as (2, -3) to move a figure two units to the right and three units down.
• The practical application of the concept of translation was demonstrated through examples and guided problem-solving.

The lesson connected theory with practice by presenting fundamental concepts of translation and the Cartesian plane, followed by practical examples and problem-solving. This allowed students to visualize how the coordinates of points are altered by the translation vector, consolidating their understanding of the concept through applied practice.

The concept of translation is relevant to students' everyday lives, as it is present in various situations such as reading maps, graphs, and even in animations in movies and video games. Understanding how to translate figures in the Cartesian plane helps develop analytical and spatial skills, essential in many disciplines and professions.