Objectives (5 - 7 minutes)

1. The students will be able to define and identify a composite figure. They will learn that a composite figure is made up of two or more shapes.
   • The teacher will provide various examples of composite figures, such as a figure made up of a rectangle and a half-circle, or a figure made up of a triangle and a parallelogram.
2. The students will understand that to find the area of a composite figure, they need to break it down into its individual shapes, calculate the area of each shape, and then add the areas together.
   • The teacher will use a visual aid, such as a large cut-out of a composite figure, and demonstrate how to break it down into its individual shapes.
3. The students will practice applying this concept to solve mathematical problems involving composite figures, such as finding the area of a garden that has a rectangular main section and a circular pond.
   • The teacher will provide several problem-solving activities during the lesson to help students practice this skill in a variety of contexts.

Secondary Objectives:

• The students will enhance their spatial reasoning skills as they mentally manipulate shapes to calculate areas.
• The students will improve their collaborative learning skills as they work in pairs or small groups to solve problems.

Introduction (10 - 15 minutes)

1. The teacher begins the lesson by reminding the students of the previous lesson on the area of basic shapes, such as rectangles, triangles, and circles. The teacher asks a few questions to refresh the students' memory and ensure they have a solid foundation for the current topic. (2 - 3 minutes)

2. The teacher then presents two problem situations to the students:

   • The teacher draws a figure on the board that's a combination of a rectangle and a semicircle, and asks, "How would you find the area of this figure if someone told you that the rectangular part is a garden and the semicircular part is a pond?"
   • The teacher uses a second figure that is a combination of a triangle and a parallelogram, and asks, "If this figure represents a park with a triangular playground and a rectangular field, how could you find the total area of the park?" (3 - 4 minutes)

3. The teacher contextualizes the importance of the subject by explaining how understanding the area of composite figures can be useful in real-life situations. For example:

   • The teacher might discuss how an architect would need to calculate the area of a room that has an irregular shape due to a bay window or an angled wall.
   • The teacher could mention that a landscaper might need to find the area of a garden that has a pond or a pool, which would involve calculating the areas of different shapes. (3 - 4 minutes)

4. To grab the students' attention and spark their interest in the topic, the teacher shares two intriguing facts or stories related to the area of composite figures:

   • The teacher could mention that the concept of finding the area of a composite figure is used in digital image editing, where images are made up of many small pixels, each of which can be considered a shape.
   • The teacher could tell a story about how ancient architects and builders used the concept of the area of composite figures to design and construct buildings with irregular shapes, such as the pyramids or the Colosseum. (2 - 3 minutes)

5. The teacher concludes the introduction by stating the objectives of the lesson and assuring the students that by the end of the lesson, they will be able to confidently calculate the area of any composite figure. (1 minute)

Development (20 - 25 minutes)

Activity 1: "Break It Down!" (10 - 12 minutes)

In this hands-on activity, students will work collaboratively in pairs to break down a given composite figure into its constituent basic shapes. They will then calculate the area of each shape before summing them up to determine the total area of the composite figure.

1. The teacher distributes a set of composite figure cards to each pair of students. Each card depicts a different composite figure, with the constituent shapes clearly labeled. The figures are a mix of shapes studied in previous lessons, such as rectangles, triangles, and circles. (2 - 3 minutes)

2. The students, as a pair, choose one card and use a ruler to measure the dimensions of the constituent shapes. They record these measurements in their notebooks. To promote critical thinking, the teacher encourages the students to identify which measurements they need to calculate the area of each shape accurately. (3 - 4 minutes)

3. The students then calculate the area of each shape and write down their results. The teacher circulates the room, providing guidance and checking the students' calculations. (3 - 4 minutes)

4. Once the students have calculated the areas, they add the areas of the individual shapes together to determine the total area of the composite figure. The teacher ensures that the students understand that they need to sum the areas and not the measurements. (2 - 3 minutes)

5. After completing the task, each pair of students shares their findings with the class, including the steps they took and the total area of their composite figure. The teacher uses this opportunity to correct any misconceptions and reinforce the correct process. (1 - 2 minutes)

Activity 2: "Design Your Dream Garden" (10 - 13 minutes)

In this creative activity, students will work in pairs to apply the concept of finding the area of composite figures in a practical, real-world scenario. They are tasked with designing a dream garden that includes various basic shapes, thereby creating a composite figure. They will then calculate the garden's total area, which will be used to estimate the cost of sodding the garden.

1. The teacher provides each pair of students with a large sheet of graph paper, colored pencils, and a list of prices for sod per square unit, differentiating between the types of shapes. (2 - 3 minutes)

2. The students, as a pair, draw their dream garden on the graph paper, ensuring it includes rectangles, triangles, circles, and other shapes. They label the dimensions of each shape that they plan to use on their garden. The teacher encourages the students to use their creativity and think about real-world gardens as they design. (3 - 4 minutes)

3. Once the garden is designed, the students calculate the area of each shape and then sum the areas to find the total area of their garden. They then multiply the total area by the price of sod per square unit to estimate the cost of sodding their garden. (3 - 4 minutes)

4. After completing the task, each pair of students presents their design to the class, explaining the steps they took to calculate the garden's area and the estimated sodding cost. The teacher uses this opportunity to assess the students' understanding and provide feedback. (2 - 3 minutes)

Throughout these activities, the teacher circulates the classroom, providing assistance, clarifying concepts, and ensuring that all students are actively engaged. The teacher should also encourage cooperation and discussion among the students, fostering an interactive and collaborative learning environment.

Feedback (8 - 10 minutes)

1. The teacher initiates a group discussion by asking each pair of students to share their solutions or conclusions from the activities. To ensure an inclusive environment, the teacher can randomly select pairs to share their work. This allows the students to learn from each other's approaches and understand different perspectives. (3 - 4 minutes)

   • During this discussion, the teacher should guide the conversation to connect the students' solutions with the theoretical concepts learned earlier in the lesson. For example, the teacher could ask, "How did you decide which shapes to use to break down your composite figure? How does this connect with our understanding of composite figures and their area?"

2. The teacher then assesses the students' understanding of the lesson's content. This can be done through a quick review of the key points, asking the students to explain in their own words how they would find the area of a composite figure. The teacher might also pose some quick problem-solving questions to gauge the students' understanding. (2 - 3 minutes)

   • For instance, the teacher could ask, "If you have a composite figure made up of a rectangle and a semicircle, how would you find its area?" or "What would you do if you were given a composite figure made up of a triangle and a parallelogram and asked to find its area?"

3. The teacher then encourages the students to reflect on their learning by posing a few questions:

   • What was the most important concept you learned today? (1 minute)
   • Which questions do you still have about finding the area of composite figures? (1 - 2 minutes)

4. The teacher collects the students' reflections and uses them to adjust future lessons or provide additional clarification as needed. This feedback loop helps to ensure that the students' learning needs are being met effectively. (1 - 2 minutes)

5. Lastly, the teacher provides a brief summary of the lesson's key points and expresses confidence in the students' ability to apply the concept of finding the area of composite figures in different scenarios. The teacher also encourages the students to continue practicing this skill at home using their textbooks or online resources. (1 minute)

Throughout the feedback stage, the teacher should maintain a positive and encouraging tone, reinforcing the students' efforts and achievements. The teacher should also be open to any further questions or doubts the students might have, providing additional help as necessary.

Conclusion (5 - 7 minutes)

1. The teacher starts the conclusion by summarizing the main points of the lesson. They reiterate that a composite figure is made up of two or more basic shapes and that to find its area, we need to calculate the area of each shape and then add them together. The teacher uses the examples from the lesson to illustrate these concepts. (2 - 3 minutes)

   • The teacher might say, "Today, we learned that when we have a composite figure, we can find its area by breaking it down into its component shapes, finding the area of each shape, and then adding them together. For example, if we have a garden that's a rectangle and a half-circle, we found that the total area is the sum of the area of the rectangle and the area of the half-circle."

2. The teacher then explains how the lesson connected theory, practice, and real-world applications. They mention that the theoretical concepts were introduced through the definition and identification of composite figures. These concepts were then practiced in hands-on activities like "Break It Down!" and "Design Your Dream Garden". Finally, the teacher highlights how the concept of finding the area of composite figures is not just a mathematical exercise but a practical skill that can be used in real-world situations, such as architecture, landscaping, and digital image editing. (1 - 2 minutes)

   • The teacher might say, "We started with the theory of composite figures and how to find their area, and then we put this theory into practice in our activities. By calculating the area of the composite figures in our hands-on tasks, you got to see how this concept works in real life. We also discussed how this skill is used in different professions and situations, making it a valuable skill to learn."

3. To further enhance the students' understanding of the topic, the teacher suggests additional materials for learning. These resources could include relevant sections from the students' textbooks, online tutorials, educational games, and worksheets for more practice. The teacher also advises the students to keep an eye out for composite figures in their everyday life and think about how they could calculate their areas. (1 - 2 minutes)

   • The teacher might say, "To strengthen your understanding of finding the area of composite figures, I recommend you to review the relevant sections in your textbooks. You can also find many online tutorials and educational games that can help you practice this skill. I'll also provide you with some worksheets for further practice. And don't forget to keep an eye out for composite figures around you. You can try calculating their areas in your head as a fun way to apply what you've learned."

4. Lastly, the teacher emphasizes the importance of the topic for everyday life and future learning. They explain that understanding the area of composite figures is not just a mathematical skill, but a tool for problem-solving in various real-world contexts. The teacher also assures the students that the skills they've learned in this lesson, such as breaking down complex problems into simpler ones and working collaboratively, will be valuable in their future academic and professional life. (1 - 2 minutes)

   • The teacher might say, "Remember that the skills you've learned today are not just about finding the area of composite figures. They're also about problem-solving, critical thinking, and collaboration. These skills are not only important for your math class but also for your everyday life and future learning. So keep practicing and applying these skills, and you'll be amazed at what you can achieve!"