Lesson Plan | Lesson Plan Tradisional | Translations of Plane Figures

Objectives

Duration: (10 - 15 minutes)

The aim of this stage is to offer a clear and thorough comprehension of the fundamental concepts of translating 2D figures, ensuring that students grasp the theoretical background of how shapes move on the Cartesian plane. This understanding is essential for students to recognize and derive shapes resulting from translations, thereby facilitating their practical application in future activities.

Objectives Utama:

1. Explain the concept of translation of 2D shapes.

2. Demonstrate how to identify and obtain translated shapes.

3. Apply translation to different geometric figures such as triangles, squares, and rectangles.

Introduction

Duration: (10 - 15 minutes)

The aim of this stage is to provide a clear and comprehensive understanding of the fundamental concepts of translating 2D shapes, ensuring that students grasp the theoretical framework behind the movement of shapes on the Cartesian plane. This comprehension is essential for them to recognize and derive shapes resulting from translations, aiding practical application in their future tasks.

Did you know?

Did you know that translation plays a crucial role in the world of animations and video games? When a character moves across the screen without twisting or resizing, it's an example of translation. This concept is also vital in creating repetitive patterns in graphic design and architecture.

Contextualization

To kick off the lesson on translating 2D shapes, explain to the students that translation is a type of geometric movement whereby a shape is shifted from one location to another without changing its form, size, or orientation. Use the analogy of moving furniture from one corner of the room to another. The furniture’s position changes, but it remains the same. Emphasize that translation is one of the basic geometric transformations, similar to rotation, reflection, and dilation.

Concepts

Duration: (40 - 50 minutes)

The aim of this stage is to deepen students' comprehension of the concept of translating 2D shapes, providing practical examples and exercises that strengthen their learning. By the end of this section, students should be able to identify and accurately apply translations to geometric figures on the Cartesian plane.

Relevant Topics

1. Definition of Translation: Explain that translation is the movement of a geometric shape from one place to another on the plane, without altering its form, size, or orientation. Utilize visual examples to illustrate the concept.

2. Translation Vectors: Introduce the idea of translation vectors, which are used to detail the direction and magnitude of the movement. Show how to represent translations using vectors on the Cartesian plane.

3. Properties of Translation: Discuss the properties of translation, such as the preservation of angles and lengths, and how parallelism between lines is maintained. Highlight that both the original shape and its translated counterpart are congruent.

4. Practical Examples: Provide practical examples of translation involving varying geometric shapes such as triangles, squares, and rectangles. Utilize the Cartesian plane to demonstrate translation step by step.

5. Application in Problems: Present problems involving translation and guide students in resolving them. Use diverse geometric figures and various translation vectors to help students practise the concept.

To Reinforce Learning

1. 1. Draw a triangle ABC on the Cartesian plane with vertices A(1, 2), B(3, 2), and C(2, 4). Then, translate the triangle 4 units to the right and 3 units up. What are the coordinates of the new vertices of the triangle?

2. 2. A square DEFG has vertices D(2, 2), E(5, 2), F(5, 5), and G(2, 5). Translate this square 3 units to the left and 2 units down. What are the new coordinates of the square's vertices?

3. 3. Consider a rectangle HIJK with vertices H(0, 0), I(6, 0), J(6, 3), and K(0, 3). Translate the rectangle 2 units to the right and 4 units up. What are the coordinates of the new vertices of the rectangle?

Feedback

Duration: (25 - 30 minutes)

The aim of this stage is to review and strengthen students' understanding of translating 2D shapes, ensuring they can correctly implement the concept. Through an in-depth discussion of the questions and active student engagement with reflections and additional queries, it is anticipated that their skills in recognizing and obtaining translated figures will be enhanced.

Diskusi Concepts

1. Discussion of the questions solved by students: 2. Question 1: To translate triangle ABC with vertices A(1, 2), B(3, 2), and C(2, 4) 4 units to the right and 3 units up, the coordinates from the translation vector (4, 3) must be added to the original vertices. 3. New vertex A': (1+4, 2+3) = (5, 5) 4. New vertex B': (3+4, 2+3) = (7, 5) 5. New vertex C': (2+4, 4+3) = (6, 7) 6. Hence, the new coordinates of the translated triangle's vertices are A'(5, 5), B'(7, 5), and C'(6, 7). 7. 8. Question 2: To translate square DEFG with vertices D(2, 2), E(5, 2), F(5, 5), and G(2, 5) 3 units to the left and 2 units down, the coordinates from the translation vector (-3, -2) must be subtracted from the original vertices. 9. New vertex D': (2-3, 2-2) = (-1, 0) 10. New vertex E': (5-3, 2-2) = (2, 0) 11. New vertex F': (5-3, 5-2) = (2, 3) 12. New vertex G': (2-3, 5-2) = (-1, 3) 13. Thus, the new coordinates of the translated square's vertices are D'(-1, 0), E'(2, 0), F'(2, 3), and G'(-1, 3). 14. 15. Question 3: To translate rectangle HIJK with vertices H(0, 0), I(6, 0), J(6, 3), and K(0, 3) by 2 units to the right and 4 units up, the relevant coordinates from the translation vector (2, 4) must be added to the original vertices. 16. New vertex H': (0+2, 0+4) = (2, 4) 17. New vertex I': (6+2, 0+4) = (8, 4) 18. New vertex J': (6+2, 3+4) = (8, 7) 19. New vertex K': (0+2, 3+4) = (2, 7) 20. Thus, the new coordinates of the translated rectangle's vertices are H'(2, 4), I'(8, 4), J'(8, 7), and K'(2, 7).

Engaging Students

1. Student Engagement: 2. 1. Reflection: How would you verify that the translation was carried out correctly? (Hint: Compare distances and angles between vertices before and after the translation). 3. 2. Question: Why does translation not alter the shape, size, or orientation of the original figure? 4. 3. Discussion: Can you recall any practical scenarios where translation is applicable? Think of examples from your daily routines. 5. 4. Extra Exercise: If you had to translate a figure using a negative translation vector, how would you go about adjusting the coordinates? 6. 5. Challenge: Propose a translation using a diagonal vector (e.g., 3 units to the right and 3 units up). What would be the new coordinates for a figure of your choice?

Conclusion

Duration: (10 - 15 minutes)

The aim of this closing stage is to revisit and reinforce the knowledge gained during the lesson. Reviewing the key points helps solidify comprehension, while discussing the practical relevance of the topic enhances the significance of learning, preparing students to apply the concept of translation in diverse contexts.

Summary

['Translation refers to the movement of a geometric shape on the plane, without altering its form, size, or orientation.', 'Translation vectors indicate the direction and magnitude of the shift.', 'The properties of translation include the preservation of angles, lengths, and the maintenance of parallelism between lines.', 'Translated shapes are congruent to the original shapes.', 'Real-world applications of translation in various geometric figures include triangles, squares, and rectangles.']

Connection

The lesson effectively connected theory with practice by leveraging visual examples on the Cartesian plane to demonstrate translations of geometric figures. Students engaged in solving practical problems that solidified their theoretical understanding of translation, showcasing how to use translation vectors to move figures on the plane without affecting their inherent properties.

Theme Relevance

Grasping the concept of translation is paramount in our daily lives, as this principle is widely employed in domains such as movie animations, video games, and graphic design. Mastering the application of translations allows for a better grasp of how objects and patterns can be maneuvered and replicated, which is crucial for various practical and creative ventures.