Objectives (5 - 7 minutes)

• Students will understand and be able to define what a composite figure is, and how it differs from a regular polygon or shape.
• Students will learn the necessary formulas and strategies for finding the area of composite figures.
• Students will be able to apply these formulas and strategies to solve various problems involving the area of composite figures.

Secondary Objectives:

• Students will develop critical thinking skills by analyzing and breaking down complex figures into simpler shapes to facilitate area calculation.
• Students will enhance their problem-solving skills by applying learned formulas and strategies in different scenarios.

Introduction (10 - 12 minutes)

• The teacher begins the lesson by reminding students of the concepts they have already learned that are essential for understanding the topic of the day. This includes revisiting the definitions of basic shapes (e.g., rectangles, triangles, circles) and their respective area formulas. (3 minutes)
• The teacher then presents two problem situations as starters to pique the students' interest and stimulate their thinking:
  1. The teacher shows a diagram of a soccer field which consists of a rectangle and two semicircles at the ends. The teacher asks, "How can we find the total area of this soccer field?" (3 minutes)
  2. The teacher displays a picture of a complex building with various shapes. The teacher asks, "If we were to paint the entire outside of this building, how much paint would we need?" (3 minutes)
• The teacher then contextualizes the importance of the subject by explaining its real-world applications. The teacher could discuss how architects and designers use these concepts in their work, or how understanding the area of composite figures can be useful in various fields such as landscaping, carpentry, and even in everyday tasks like planning a garden or making a pizza. (2 minutes)
• To grab the students' attention, the teacher shares two interesting facts related to the topic:
  1. The teacher can share that the concept of finding the area of composite figures was used in ancient Egypt when they had to calculate the area of land for farming.
  2. The teacher can also share a curiosity about how the area of a figure can change depending on how it is divided. For example, cutting a rectangular sheet of paper into two triangles and rearranging them can create a new shape with the same area, but a different perimeter. (1 minute)

Development (20 - 25 minutes)

1. Understanding Composite Figures (5 - 7 minutes)

• The teacher begins by defining a composite figure as a shape made up of two or more simple shapes. The teacher uses visual aids like a diagram or a drawing to illustrate this concept.
• The teacher then explains that to find the area of a composite figure, we can break it down into its simpler shapes, find the area of each shape, and then add up these areas.
• The teacher reinforces the concept by illustrating this process using a few simple composite figures, such as a figure made up of a rectangle and a triangle.
• The teacher then explains that the same principle applies to more complex composite figures, it's just a matter of breaking them down into simpler shapes and calculating their areas.

2. Finding the Area of Composite Figures (10 - 12 minutes)

• The teacher introduces the formula for finding the area of a rectangle (Area = Length x Width) and a triangle (Area = 1/2 x Base x Height) if they haven't done so already in previous lessons.
• The teacher then shows how to apply these formulas to find the areas of the individual shapes within a composite figure.
• The teacher demonstrates this calculation using a composite figure example, such as a figure made up of a rectangle and a triangle.
• The teacher emphasizes that care must be taken to ensure that the units of measurement are the same for all the shapes before adding up the areas.
• The teacher then explains the term “overlap area” – the area where the simple shapes overlap in a composite figure. The teacher states that this area should only be counted once in the total area.
• The teacher demonstrates how to find the “overlap area” and subtract it from the total area of the composite figure. They illustrate this using a diagram of a figure with overlapping shapes.

3. Problem-Solving Strategies (5 - 6 minutes)

• The teacher wraps up the lesson by sharing some problem-solving strategies for finding the area of more complex composite figures.
• The teacher suggests that students start by identifying the simple shapes in the composite figure and then calculate the areas of these shapes.
• The teacher then advises students to consider the “overlap area” and how many times it appears in the figure. This will determine whether they need to subtract it once, twice, or more times from the total area.
• The teacher reminds students to pay attention to units of measurement and to double-check their calculations to ensure accuracy.

During this stage, the teacher encourages active participation from the students by asking them to identify the individual shapes in the composite figure and calculate their areas. The teacher provides additional examples for the students to practice during the lesson. This step-by-step explanation helps students to understand the concept thoroughly and apply it to solve problems.

Feedback (8 - 10 minutes)

• The teacher assesses the students' understanding by asking them to share their thoughts about the lesson. The teacher encourages the students to make connections between the theoretical concepts learned and their real-world applications. (2 minutes)
• The teacher then conducts a quick review of the main points covered in the lesson, summarizing the definition of composite figures, the process of finding their areas, and the problem-solving strategies shared. This review helps to consolidate the information in the students' minds. (2 minutes)
• The teacher then proposes that the students take a moment to reflect on what they have learned today. The teacher suggests that students consider the following questions:
  1. What was the most important concept learned today?
  2. What questions do you still have about finding the area of composite figures? The teacher gives the students a minute to think and then invites a few volunteers to share their reflections. The teacher addresses any remaining questions or misconceptions. (2 minutes)
• The teacher then assesses the students' understanding through a formative assessment. This could be in the form of a quick quiz, a problem-solving task, or a group discussion where students are asked to solve a problem related to the topic. The teacher uses this assessment to gauge the students' comprehension and identify any areas that may need further clarification or review. (2 - 3 minutes)
• The teacher ends the lesson by providing constructive feedback to the students about their participation and understanding. The teacher also encourages the students to continue practicing the skills learned today and to approach the teacher with any further questions or difficulties. (1 minute)

This feedback stage is crucial as it allows the teacher to evaluate the effectiveness of the lesson and adjust future instruction accordingly. It also provides an opportunity for the students to reflect on their learning, ask questions, and receive clarification on any areas of confusion. By the end of this stage, both the teacher and the students should have a clear understanding of the progress made during the lesson.

Conclusion (5 - 7 minutes)

• The teacher starts the conclusion by summarizing the main contents of the lesson. They remind the students that a composite figure is a shape made up of two or more simpler shapes, and that its area can be found by breaking it down into its component shapes, calculating their areas, and summing them up. The teacher also reinforces the concept of "overlap area" and how it is accounted for in the total area. (2 minutes)
• The teacher then explains how the lesson connected theory, practice, and applications. They point out that the theoretical concepts were presented and defined, and the students got to practice applying these concepts through the various problem-solving tasks. The teacher also highlights how the lesson connected these mathematical concepts to real-world applications, such as in architecture, design, and everyday tasks. (1 minute)
• The teacher suggests some additional resources for the students to further their understanding and practice. This could include online interactive tools for visualizing and calculating the area of composite figures, worksheets with more complex problems, and educational games that make learning fun. The teacher also encourages the students to use their textbooks and class notes as references for studying the topic. (1 minute)
• Lastly, the teacher discusses the importance of the topic for everyday life. They explain that the ability to find the area of composite figures is not just a mathematical skill, but also a problem-solving skill that can be applied in many real-life situations. They give examples such as calculating the area of a garden, planning a room layout, or even designing a logo. The teacher emphasizes that understanding this concept can help students in various fields of study and in their future careers. (1 - 2 minutes)

By the end of the conclusion, the students should have a clear and concise summary of the lesson, understand the connections between theory, practice, and applications, know where to find additional resources for further learning, and appreciate the relevance of the topic in their everyday life.