Lesson Plan | Traditional Methodology | Expansion and Reduction of Figures

Objectives

Duration: (10 - 15 minutes)

The purpose of this stage of the lesson plan is to establish a clear and focused foundation on the concepts of enlarging and reducing geometric figures. Understanding how the values of areas and perimeters are affected by proportional changes in the sides of the figures is essential for the development of students' mathematical skills, allowing them to apply these concepts in practical and theoretical problems.

Main Objectives

1. Describe how the areas and perimeters of geometric figures are affected when the sides of these figures are proportionally increased or decreased.

2. Correctly calculate the areas and perimeters of geometric figures after enlarging or reducing their sides.

Introduction

Duration: (10 - 15 minutes)

📚 Purpose: The purpose of this stage is to create a clear and interesting context that captures students' attention and prepares them to understand how the areas and perimeters of geometric figures are affected by proportional changes in their sides. Establishing this foundation is essential for students to proceed with confidence in the next stages of the lesson.

Context

👋 Welcome to Math class! Today we will explore a very interesting and useful concept: enlarging and reducing geometric figures. Imagine you have a photo and want to enlarge it to put in a larger frame or reduce it to fit in a smaller frame. What happens to the dimensions of the photo? And with the area it occupies? This is the concept we will learn and apply during our class.

Curiosities

🔍 Curiosity: Enlarging and reducing figures do not only apply to photos. In the world of architecture, for example, engineers and architects use scales to create reduced models of buildings and then enlarge them to real size during construction. Similarly, on maps, we use scales to represent vast areas on a small piece of paper.

Development

Duration: (40 - 50 minutes)

📚 Purpose: The purpose of this stage is to provide students with a detailed and practical understanding of the concepts of enlarging and reducing geometric figures. By addressing specific topics and solving practical problems, students will be able to apply the knowledge gained to calculate areas and perimeters of figures after proportional changes in the sides.

Covered Topics

1. Concept of Proportionality: Explain that proportionality is the relationship between two quantities that change in a constant manner. Show how this applies to the enlargement and reduction of figures, meaning all sides of a figure increase or decrease in the same proportion. 2. Enlargement of Figures: Detail that when enlarging a figure, the sides are multiplied by a factor greater than 1. Present visual examples of enlarged squares and rectangles, and explain how to calculate the new area and new perimeter. 3. Reduction of Figures: Explain that when reducing a figure, the sides are multiplied by a factor less than 1. Show visual examples of reduced figures and how to calculate the new area and new perimeter. 4. Calculation of Areas and Perimeters: Demonstrate how to calculate the area (side x side for squares, base x height for rectangles) and perimeter (sum of the sides) of figures before and after enlargement or reduction. 5. Practical Examples: Solve problems step by step on the board, showing in detail how to apply the concepts of proportionality to find the new area and new perimeter after changing the sides.

Classroom Questions

1. If a square with a side of 4 cm is enlarged with a scale factor of 3, what will be the new area and new perimeter? 2. A rectangle has sides of 6 cm and 8 cm. If it is reduced with a scale factor of 0.5, what will be the new area and new perimeter? 3. A triangular figure has sides of 5 cm, 5 cm, and 5 cm. If the sides are enlarged with a scale factor of 2, what will be the new perimeter of the figure?

Questions Discussion

Duration: (20 - 25 minutes)

📚 Purpose: The purpose of this stage is to review and consolidate the knowledge acquired during the lesson, ensuring that students understand how to apply the concepts of enlarging and reducing geometric figures. The detailed discussion of the solutions and student engagement with reflective questions help reinforce understanding and practical application of the concepts learned.

Discussion

• 📌 Question 1: If a square with a side of 4 cm is enlarged with a scale factor of 3, what will be the new area and new perimeter?

• ➡️ Solution:

• To find the new sides, simply multiply the original side by the scale factor: 4 cm * 3 = 12 cm.

• The new area is calculated by raising the new side to the power of two: 12 cm * 12 cm = 144 cm².

• The new perimeter is found by adding all the sides: 12 cm * 4 = 48 cm.

• 📌 Question 2: A rectangle has sides of 6 cm and 8 cm. If it is reduced with a scale factor of 0.5, what will be the new area and new perimeter?

• ➡️ Solution:

• To find the new sides, multiply each side by the scale factor: 6 cm * 0.5 = 3 cm and 8 cm * 0.5 = 4 cm.

• The new area is calculated by multiplying the new sides: 3 cm * 4 cm = 12 cm².

• The new perimeter is found by adding all the sides: (3 cm + 4 cm) * 2 = 14 cm.

• 📌 Question 3: A triangular figure has sides of 5 cm, 5 cm, and 5 cm. If the sides are enlarged with a scale factor of 2, what will be the new perimeter of the figure?

• ➡️ Solution:

• To find the new sides, multiply each side by the scale factor: 5 cm * 2 = 10 cm.

• The new perimeter is found by adding all the sides: 10 cm + 10 cm + 10 cm = 30 cm.

Student Engagement

1. 🔍 Question 1: Why does the area of a figure increase faster than the perimeter when the sides are enlarged? 2. 🔍 Question 2: How would you apply the concept of proportionality to solve everyday problems, such as adjusting the size of a recipe? 3. 🔍 Question 3: If a scale factor is a fractional number less than 1, what does that tell us about the resulting figure? 4. 🔍 Question 4: What is the importance of understanding scales and proportionality in professions such as engineering and architecture?

Conclusion

Duration: (10 - 15 minutes)

The purpose of this stage is to review and consolidate the main concepts presented during the lesson, reinforcing students' understanding of enlarging and reducing geometric figures. This stage also emphasizes the practical application and relevance of the concepts, preparing students to use this knowledge in various everyday situations.

Summary

• Concept of proportionality and its application in enlarging and reducing geometric figures.
• How to calculate the new area and new perimeter of enlarged and reduced figures.
• Resolution of practical problems involving the enlargement and reduction of geometric figures.

During the lesson, the theory was illustrated with practical examples that showed how to calculate the new area and new perimeter of geometric figures after enlargement or reduction. This allowed students to visualize the application of theoretical concepts in real situations, such as creating and adjusting models in architecture and engineering.

Understanding how the enlargement and reduction of geometric figures affect their areas and perimeters is crucial for various everyday and professional applications. This knowledge is especially useful in fields such as architecture, engineering, and even in tailoring and crafting projects, where it is common to work with scales and proportions.