Objectives (5-10 minutes)

1. Understand the concept of Composite Figures: Students should be able to identify and understand composite figures, shapes formed by combining two or more figures. They should also be able to differentiate composite figures from simple figures.

2. Calculate the Area of Composite Figures: With an understanding of the concept, learners should be able to calculate the area of composite figures. To do so, they will need to correctly apply the area formulas of the various individual shapes making up the composite figure.

3. Solve Real-World Area Problems involving Composite Figures: The ultimate goal for students is to be able to apply the learned knowledge to solve real-world problems that involve calculating the area of composite figures. This will help strengthen the understanding of the concept and calculation skill.

Secondary Objectives:

1. Develop Logical and Analytical Thinking: Through solving problems with composite figures, students should improve their logical and analytical thinking skills, essential in mathematics and other areas of life.

2. Encourage Collaboration and Communication: By working together in teams to solve problems, students will have opportunities to build their collaborative and communication skills, crucial to succeeding in various life scenarios.

3. Spark Interest in Mathematics: The lesson plan, by making the class interactive and practical, aims to encourage a liking towards mathematics, showing them how the subject can be both interesting and applicable in everyday life situations.

Introduction (10-15 minutes)

1. Review of Previous Knowledge: The teacher should start by recalling basic geometric ideas, especially the notions of area, shapes and geometric figures. Revisiting these concepts before advancing to composite figures is crucial for student success. This can be done by way of quick questions or a short class review on the board.

2. Introduce Problem Scenarios: The instructor may introduce a couple of real-world scenarios that involve calculating the area of composite figures. One could involve finding the area of a backyard that consists of several distinct shapes like rectangles, triangles, and circles. Another example could be finding the area of a map of a town, where buildings are indicated as various geometric figures. These problem scenarios will be used to engage student interest and show them how important the topic is practically.

3. Put into Context: The teacher can now go on to explain how composite figures are useful in daily life. They can mention, for example, how architects and engineers need to calculate areas of composite figures when working. Another approach to put this into context is by discussing how calculating areas of composite figures finds uses in video games and graphic design.

4. Lead-in to Topic Discussion: To introduce the topic of composite figures, the instructor may present a few fun facts or trivia. They could mention that the idea of composite figures dates back to Ancient Greece, where mathematicians explored the properties of shapes formed by the superimposition of others. Another fun fact to intrigue the class is that many famous paintings, such as Pablo Picasso's Guernica, are composed of multiple geometric figures placed one over the other.

5. Grab Student Attention: To further capture students' attention, the instructor can put on a short video explaining or showing the concept of composite figures with animations. They can also do an example on the class whiteboard, drawing various overlapping geometric shapes on the board and having their class try to calculate the total area.

Development (20-25 minutes)

1. Activity 1: Building Composite Figures: For this activity, students should form teams of 3-4 members. Provide each team with a sheet of large paper where they will have to draw various basic geometric shapes such as squares, rectangles, triangles, and circles. Once drawn, they should cut these shapes. The next step is for the students to use these cut-out shapes and superimpose them in various ways so they create interesting composite figures. Finally, they will have to find the total areas of the composite figures they have made. This activity aims to be enjoyable and engaging, all the while having the students explore the composite figures concept and practice finding the areas. (10-15 minutes)

   • Step by step walkthrough
     1. Give each team a sheet of paper, pencils, ruler, scissors and glue.
     2. Instruct the students to draw and cut-out the basic geometric shapes.
     3. Have them put together these shapes in various ways which result in composite figures.
     4. Encourage the teams to discuss and collaborate towards creating the best ways of combining the shapes.
     5. Once the composite figures are complete, instruct them to find the total area of each.
     6. Finally, ask each team to showcase one of their composite shapes to the class and explain how they calculated its total area.

2. Activity 2: Composite Figures Challenge: In this activity, the teams will be given a set of cards with various composite figures drawn on them. Each card is missing one of the simple figures which make up that composite figure. Using their new-found understanding, students should be able to recognize the missing shape needed to complete that composite figure and find the total area. To make this a bit more engaging, the teacher may set a timer and give bonus points to the teams who can answer the most cards correctly. (10 minutes)

   • Step by step walkthrough
     1. Prepare cards with composite figures and the missing component shapes.
     2. Give each team the set of cards.
     3. Explain the challenge rules including any time limit.
     4. Encourage group work and discussion for finding solutions.
     5. When time runs out, collect the card sets, and count how many were solved correctly for each group.
     6. Award bonus points for the winning team.

3. Activity 3: Area Game: For this activity, the students will play a board game that has been designed to help calculate the areas of composite figures. Each team will be given a game board which will have several composite figures on different squares. The class will take turns rolling dice to move tokens along their board. When they land on a square with a composite figure, the students will calculate its area. The first team to reach the last square on the game board is declared the winner. (10-15 minutes)

   • Step by step walkthrough
     1. Get the game boards, markers, dice, and area calculation cards ready.
     2. Explain the rules of the game and how to do area calculations.
     3. Begin the game, having the teams take turns.
     4. As the game proceeds, circulate the classroom, to monitor and provide support to the teams.
     5. When the game ends, congratulate the winners and take some time for a quick discussion about the strategies that were employed.

Closure (10-15 minutes)

1. Class Discussion (5-7 minutes): To wrap up, the instructor will have everyone come back together as a class and facilitate a group discussion. Each team will be provided up to 3 minutes to present their findings, solutions, and strategies from Activities 1: Building Composite Figures, Activity 2: Composite Figures Challenge, and Activity 3: Area Game. This is a chance for students to learn from their peers, for the teacher to evaluate understanding, and for all students to reflect on what has been covered.

   • Step by step walkthrough:
     1. Have each group take no more than 3 minutes to share their findings, solutions, or strategies.
     2. Facilitate peer-to-peer questioning or comments.
     3. Summarize and restate main points or connections back to the lesson content after each group's presentation.
     4. After presentations are completed, go over the main lesson points once more in review fashion.

2. Connect Theory (2-3 minutes): The teacher will now make connections between the activities completed in class with the content from the lecture. They will emphasize how going through these activities helped strengthen understanding of composite figures and calculating of area. They can also mention again which area formulas are used for the component figures and how these were put to use during the activities.

   • Step by step walkthrough
     1. Briefly recap activities that were completed in the lesson.
     2. Highlight how these strengthened the understanding of composite figures and calculating area.
     3. Re-iterate which area formulas were utilized and their application during the activities.
     4. Tie the class back to how these activities connect the theoretical side to practical applications.

3. Individual Reflections (3-5 minutes): To end the lesson, have the students do some self-reflection on what they learned. This can be guided by asking targeted questions like, "Which of today's concepts did you find most important?", and "What are your remaining questions about the topic?" This kind of reflective practice helps solidify the learning, and may also reveal any areas that need to be revisited.

   • Step by step walkthrough:
     1. Have the students take a moment to reflect individually about what was covered.
     2. Pose targeted questions to the class as a guide to their reflection.
     3. Give the students a minute or so to think through their answers.
     4. If students want to, have them share some of their responses with the group.
     5. Remind the class that any unanswered questions can be addressed during the next class session or office hours.

Conclusion (5-10 minutes)

1. Recap and Summary (2-3 minutes): To conclude, the instructor will summarize the key points of today's lesson content. This includes revisiting composite figures, how area calculations for basic figures can be combined to calculate the area of a composite, the real-life applications of this calculation, and so on. Doing so will help reinforce what has been learnt throughout the class, and to make sure students have grasped the main ideas of the lesson.

   • Step by step walkthrough:
     1. Quickly go over the main learning points again.
     2. Review composite figures and their calculations.
     3. Reinforce how finding area for composite figures is important and used in many real-world applications.

2. Connecting Theory, Practice and Applications (1-2 minutes): The teacher should now highlight how the class has blended together theory with practical learning and real-life applications. This will entail acknowledging that a theoretical component was taught early on which was then reinforced and strengthened by hands-on activities. They can also restate that the skill of finding the areas of composite figures is useful and used across many different aspects of daily life.

   • Step by step walkthrough:
     1. Explain how the class combined theory, hands-on practice and applications.
     2. Highlight how activities helped solidify the theory learned in class.
     3. Revisit how this skill can be used and is encountered across many aspects of life.

3. Supplemental Resources (1-2 minutes): The instructor can recommend supplemental materials for the students' further study. This may consist of textbooks, math websites, video tutorials or interactive geometry online games, and more area calculation problem sets. By utilizing these, they can go over concepts of the lesson, get additional practice, and enhance their understanding of the subject.

   • Step by step walkthrough:
     1. List some supplementary resources the class may find valuable for further learning.
     2. Explain how these materials can help review lesson concepts, provide extra practice, and enhance the students' learning.

4. Value and Encouragement for Further Practice (1-2 minutes): Finally, the teacher should underscore how important it is to have this ability to find areas of composite figures. They can offer real-world examples of where such a skill might come into play, such as in architecture or engineering, or graphic design and video game creation. Furthermore, encourage learners to practice finding the area of composite shapes on their own in daily situations, like when examining a map, estimating the total land area for different regions of the country or state.

   • Step by step walkthrough:
     1. Highlight how this skill of area calculation for composite figures is significant in daily life.
     2. Share examples of how the skill can be used in different career fields and professions.
     3. Motivate the students to practice this on a daily basis by observing their surroundings and looking at areas of different composite shapes in real life.