Lesson Plan | Active Methodology | Area and Perimeter: Comparison

Premises: This Active Lesson Plan assumes: a 100-minute class duration, prior student study both with the Book and the beginning of Project development, and that only one activity (among the three suggested) will be chosen to be carried out during the class, as each activity is designed to take up a large part of the available time.

Objective

Duration: (5 - 10 minutes)

The Objectives section aims to clearly define the learning goals for students, directing the focus of classroom activities. By detailing expected student learning outcomes, this section serves as a guide for effectively implementing practical activities, ensuring that students understand and apply the concepts of area and perimeter in a meaningful and contextualized way.

Objective Utama:

1. Equip students with the skills to calculate the areas and perimeters of basic geometric figures like squares, rectangles, and triangles.

2. Develop the ability to compare different figures that share the same perimeter but have different areas, drawing conclusions about their properties and real-world applications.

Objective Tambahan:

1. Encourage logical reasoning and analytical skills among students when comparing the properties of different geometric figures.

Introduction

Duration: (15 - 20 minutes)

The introduction aims to engage students with practical scenarios they may have encountered or can easily relate to, using the concepts of area and perimeter to solve real or hypothetical problems. Furthermore, the contextualization seeks to demonstrate the importance of studying these measurements by linking them to everyday situations and curiosities, thus boosting student interest and motivation.

Problem-Based Situation

1. Imagine you have a rectangular garden measuring 6 metres by 4 metres and you're looking to add a path around it. How could you calculate the length of the necessary path if it must have the same width on all sides?

2. If a farmer has 24 metres of fencing to enclose a rectangular plot and wants to maximize the planting area, how should they size the rectangle to achieve the largest possible area?

Contextualization

Understanding the area and perimeter of geometric figures is crucial in many everyday situations. For example, when decorating a room and needing to figure out how much paint or flooring is required, or in gardening competitions where space needs to be used efficiently. Additionally, we can explore interesting questions, such as why some professional soccer fields have different shapes, to illustrate the relevance and importance of these concepts.

Development

Duration: (75 - 80 minutes)

The Development phase of the lesson plan allows students to apply the concepts of area and perimeter learned previously to practical and engaging activities. By collaborating in groups, they reinforce their mathematical understanding while also developing communication, collaboration, and critical thinking skills. The proposed activities are designed to be challenging and enjoyable, encouraging students to think creatively and analytically while having fun.

Activity Suggestions

It is recommended that only one of the suggested activities be carried out

Activity 1 - Geometric Park Challenge

> Duration: (60 - 70 minutes)

- Objective: Apply the concepts of area and perimeter in the practical context of park design, fostering teamwork and mathematical reasoning skills.

- Description: Students will be divided into groups of up to 5 and tasked with designing a park on graph paper. They should apply the rules of area and perimeter calculation to determine the size and arrangement of different areas in the park, such as a pond, a playground, and pathways, while ensuring that everything fits within a specified perimeter.

- Instructions:

• Form groups of up to 5 students.

• Draw a rectangle on the graph paper representing the park.

• Decide which areas the park should include (pond, playground, green spaces, pathways, etc.).

• Calculate the total perimeter available for the park and allocate it among the different areas based on their function in the design.

• Use area and perimeter formulas to calculate the space taken up by each park feature.

• Present the design to the rest of the class, explaining the decisions made and the calculations carried out.

Activity 2 - The Mystery of Equal Areas

> Duration: (60 - 70 minutes)

- Objective: Develop the ability to compare and analyze figures based on their areas, even with differing shapes, while fostering critical thinking and mathematical argumentation.

- Description: In this activity, students will form groups and receive cards with various geometric figures drawn on them, all having the same perimeter but different areas. The challenge will be to determine which figures have equal areas irrespective of their distinct shapes, and to justify their findings.

- Instructions:

• Form groups of up to 5 students.

• Receive the cards with the geometric figures.

• Classify the figures by shape (squares, rectangles, triangles, etc.).

• Use rulers and area formulas to calculate the areas of the figures.

• Discuss in groups to identify which figures, despite having different shapes, have equal areas.

• Prepare a presentation for the class explaining the findings and reasoning used.

Activity 3 - City Builders

> Duration: (60 - 70 minutes)

- Objective: Utilize area and perimeter concepts to tackle a spatial optimization problem, developing calculation, logical reasoning, and teamwork skills.

- Description: Working in groups, students will be given a map of a developing city with designated areas for different types of constructions. The challenge is to optimize space usage, keeping the perimeter of each area constant while reshaping the plots to maximize the area of each construction.

- Instructions:

• Form groups of up to 5 students.

• Receive the city map with the designated areas.

• Identify the available perimeter for each type of construction.

• Redesign the marked areas to maximize the area of each construction while maintaining the same perimeter.

• Use area and perimeter formulas to calculate and justify their redesigns.

• Present the new city layout and explain the decisions made.

Feedback

Duration: (15 - 20 minutes)

This phase of the lesson plan is vital for consolidating students' learning, allowing them to reflect on their experiences, share insights, and learn from one another. Group discussions help identify gaps in understanding and reinforce area and perimeter concepts, while also developing communication and argumentation skills. This collaborative feedback can also be used to assess student progress and the effectiveness of the activities.

Group Discussion

At the end of the activities, encourage a group discussion among all students, giving each group the chance to share what they learned and the solutions they found. Start with a brief introduction to the importance of teamwork and sharing ideas for collective learning. Encourage students to reflect on the challenges they faced and the strategies they used to overcome them.

Key Questions

1. What were the biggest challenges you encountered when applying the concepts of area and perimeter in the activities?

2. How did working with your peers help in solving the problems encountered?

3. Was there a moment where you needed to adjust your initial reasoning? How did that happen?

Conclusion

Duration: (5 - 10 minutes)

The conclusion phase aims to solidify learning, ensuring students grasp the key concepts and their real-world applications. By summarizing and connecting theory to practice, this section reinforces memory retention and emphasizes the relevance of the topics discussed. Furthermore, discussing the practical implications of mathematical concepts motivates students to perceive mathematics as a valuable tool rather than merely a set of abstract formulas.

Summary

To wrap up, recap the key topics discussed regarding the area and perimeter of geometric figures like squares, rectangles, and triangles, while highlighting the central discovery that figures with the same perimeter can still have different areas. Reinforce the mathematical concepts and practical applications discussed during the activities to ensure that students leave with a clear understanding of the material.

Theory Connection

Discuss how the practical activities in class connected the theory studied at home to real-world applications and engaging scenarios. Emphasize how teamwork and solving problems in groups helped to solidify their theoretical understanding, making learning a dynamic and interactive experience.

Closing

Finally, highlight the significance of area and perimeter concepts in everyday life, such as urban planning, architecture, interior design, and various other practical domains. Demonstrate how these learnings are fundamental in developing analytical and critical skills that are essential for students' academic and professional success.