Lesson Plan | Traditional Methodology | Congruent Figures

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage is to ensure that students understand the concept of congruent figures and know how to identify these figures in different types of grids. The initial explanation provided by the teacher will create a solid foundation for the practical activities and examples that will follow, ensuring that students are prepared to recognize and work with congruent figures in different contexts.

Main Objectives

1. Explain the concept of congruent figures clearly and in detail.

2. Demonstrate how to identify congruent figures in quadrangular and triangular grids.

3. Provide practical and guided examples to reinforce students' understanding.

Introduction

Duration: (10 - 15 minutes)

 Purpose: The purpose of this stage is to ensure that students understand the concept of congruent figures and know how to identify these figures in different types of grids. The initial explanation provided by the teacher will create a solid foundation for the practical activities and examples that will follow, ensuring that students are prepared to recognize and work with congruent figures in different contexts.

Context

️ Context: Start the class by asking students if they have ever played with puzzles or building blocks, like LEGO blocks. Explain that, just like puzzle pieces or blocks that fit perfectly together, there are geometric figures that are exactly the same in shape and size. These figures are called congruent figures. Use visual examples, such as paper cutouts or colored blocks, to demonstrate this equality.

Curiosities

 Curiosity: Did you know that engineers and architects use the concept of congruent figures to design and build buildings and bridges? They need to ensure that certain parts of their designs are exactly the same so that everything fits perfectly and the construction is safe and beautiful. Moreover, we encounter congruent figures in various objects in our daily lives, such as floor tiles, wall tiles, and even product packaging.

Development

Duration: (55 - 60 minutes)

 Purpose: The purpose of this stage is to deepen students' understanding of congruent figures through detailed explanations and practical examples. By the end of this section, students should be able to identify and justify the congruence of figures in different types of grids, thus consolidating theoretical learning with practice.

Covered Topics

1.  Definition of Congruent Figures: Explain that congruent figures are those that have the same shape and size. Even if they are rotated, reflected, or translated, they remain identical. 2.  Identification in Quadrangular Grids: Show how to identify congruent figures in a quadrangular grid. Use graph paper and draw two congruent figures. Explain that if placed one on top of the other, they overlap perfectly. 3.  Identification in Triangular Grids: Repeat the identification process but now using a triangular grid. Draw two congruent figures on triangular grid paper and demonstrate how they align exactly when overlaid. 4. ✂️ Practical Examples: Provide practical examples using paper cutouts. Cut out geometric figures and ask students to identify which are congruent. Show examples of figures that are not congruent for contrast.

Classroom Questions

1. Draw two congruent figures on a quadrangular grid and explain how you know they are congruent. 2. Draw two congruent figures on a triangular grid and explain how they overlap perfectly. 3. Given a set of cut-out geometric figures, identify which are congruent and justify your answer.

Questions Discussion

Duration: (15 - 20 minutes)

 Purpose: The purpose of this stage is to review and consolidate the knowledge acquired by students about congruent figures. Through detailed discussion of the questions and engaging students with reflective questions, the teacher ensures that the concepts have been understood clearly and that students are able to apply this knowledge in different situations. This stage also promotes active student participation, reinforcing learning and encouraging the exchange of ideas.

Discussion

•  Discussion of the Questions:

• Question 1: Draw two congruent figures on a quadrangular grid and explain how you know they are congruent. Explanation: The congruent figures on a quadrangular grid have the same size and shape. When overlaid, they align perfectly, leaving no parts out or overlapping differently.

• Question 2: Draw two congruent figures on a triangular grid and explain how they overlap perfectly. Explanation: In the triangular grid, the congruent figures also maintain the same size and shape. When overlaid, all their edges and vertices coincide exactly, showing that they are identical.

• Question 3: Given a set of cut-out geometric figures, identify which are congruent and justify your answer. Explanation: When observing the cut-out figures, the congruent ones will be those that, when placed one on top of the other, coincide completely at all their points. Those that do not coincide, even at just one point, are not congruent.

Student Engagement

1. 樂 Student Engagement: 2. How would you define congruent figures in your own words? 3. Why is it important to understand the concept of congruent figures in our daily lives? 4. Can you think of other everyday examples where we see congruent figures? 5. Do all congruent figures need to be in the same orientation to be identified as such? Why? 6. How does identifying congruent figures help in solving more complex mathematical problems?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the main points covered during the lesson, ensuring that students have a clear and comprehensive understanding of the concept of congruent figures. This stage also reinforces the importance of the topic and its practical applications in students' daily lives.

Summary

• Congruent figures are those that have the same shape and size, regardless of whether they are rotated, reflected, or translated.
• Congruent figures in quadrangular grids overlap perfectly when aligned on top of one another.
• Congruent figures in triangular grids also align exactly when overlaid.
• The importance of identifying congruent figures was demonstrated with practical examples using paper cutouts.

The lesson connected theory with practice by using visual examples and paper cutouts to demonstrate how to identify congruent figures in quadrangular and triangular grids. These practical examples helped students visualize and understand the concept of congruence in a concrete and applied manner.

Understanding congruent figures is essential in various areas of everyday life, such as in construction, where engineers and architects need to ensure that parts of their constructions are identical so they fit perfectly. Additionally, congruence appears in common objects such as tiles, bricks, and packaging, demonstrating the practical relevance of the concept.