Objectives (5 - 7 minutes)

During this stage, the teacher will:

1. Introduce the topic of "Triangles: Similarity" and the learning objectives to the students. The teacher will explain that the objective of this lesson is for students to understand the concept of similarity in triangles and how to use this concept to solve problems.

2. Define the key terms related to the topic, such as "similar triangles," "proportional sides," and "corresponding angles." The teacher will also explain the difference between similar and congruent triangles.

3. Outline the skills that students should be able to demonstrate by the end of the lesson, including the ability to identify similar triangles, determine the ratio of their sides, and solve problems involving similar triangles.

Secondary objectives:

• Encourage students to ask questions and participate in class discussions. This will help ensure that they are actively engaged in the lesson and understanding the material.

• Foster a collaborative learning environment by encouraging students to work together on hands-on activities and problem-solving exercises.

• Develop students' critical thinking and problem-solving skills by presenting them with real-world applications of the concept of similarity in triangles.

Introduction (8 - 10 minutes)

During this stage, the teacher will:

1. Remind the students of the previous lessons on basic geometry, especially the properties of triangles such as the sum of angles in a triangle and the Pythagorean theorem. The teacher will explain how these concepts are fundamental to understanding the concept of similarity in triangles.

2. Present two problem situations as starters:

   • The teacher will draw two triangles on the board, one large and one small, and ask the students to identify any similarities they see. This will prompt the students to start thinking about the concept of similarity.
   • The teacher will then ask the students to consider how they could determine the height of a tall building without actually measuring it. This will introduce the idea of using similar triangles and the concept of proportionality.

3. Contextualize the importance of the topic with real-world applications:

   • The teacher will explain that architects and engineers often use the concept of similarity in triangles to design buildings and bridges. They can use a small-scale model to predict how a larger structure will behave.
   • The teacher will also mention that artists use similar triangles to create perspective in their drawings, making objects appear smaller as they move further away.

4. Grab the students' attention by sharing two interesting facts or stories related to the topic:

   • The teacher will share the story of Thales, an ancient Greek mathematician who used the concept of similar triangles to measure the height of the pyramids in Egypt. This will demonstrate the long history and practical applications of the concept.
   • The teacher will also mention the use of similar triangles in modern technology, such as in the construction of cell phone towers. This will show the students that the concept is not just theoretical, but is actually used in many real-world applications.

Development (25 - 30 minutes)

During this stage, the teacher will:

1. Activity 1: "Shape Shifter" (10 - 12 minutes)

   • The teacher will provide each group of students with a large triangle made from a string and three straws/rods, and several smaller triangles made from the same materials but of different sizes.
   • The groups will be tasked to construct a smaller triangle that's similar to the larger one provided. They can only use the straws/rods and the string as tools.
   • Once the groups have achieved this, the teacher will have them compare the lengths of the corresponding sides of the two triangles.
   • The teacher will then ask the students to divide the length of a side in the large triangle by the length of the corresponding side in the smaller triangle, and observe what they find.
   • The teacher will explain that the ratio they found is constant for all corresponding sides of similar triangles, and this ratio is called the "scale factor".

2. Activity 2: "The Enlargement Machine" (10 - 12 minutes)

   • The teacher will provide each group with a set of triangular cardboard cutouts of different sizes and a projector.
   • The teacher will instruct the groups to place one of their triangles on the projector and trace its shadow onto a piece of paper.
   • The teacher will then tell the students to change the triangle to a different size and trace its new shadow onto the same paper.
   • The groups will be asked to compare the two shadows and identify any similarities.
   • The teacher will explain that the shadows are similar to the triangles because the corresponding angles are the same. The students will be encouraged to measure the angles and sides to verify this.
   • The teacher will then ask the students to determine the ratio of the lengths of corresponding sides of the two different-sized triangles and compare it to the ratio of the lengths of the two shadows.
   • The teacher will explain that the ratios are the same, which is a property of similar triangles.

3. Activity 3: "Geometry Detectives" (5 - 6 minutes)

   • The teacher will provide each group with a set of cards containing different triangles, some of which are similar.
   • The teacher will instruct the groups to sort the triangles into two piles: similar and not similar.
   • The teacher will then ask the groups to explain their reasoning for their choices.
   • The teacher will correct any mistakes and clarify any misconceptions as necessary.
   • The teacher will emphasize the importance of looking for proportional sides and corresponding angles when determining whether two triangles are similar.

During these activities, the teacher will move around the classroom, observing and facilitating the students' work. The teacher will ensure that each group has a clear understanding of the concept of similarity in triangles and can apply it to solve problems.

Feedback (7 - 10 minutes)

During this stage, the teacher will:

1. Group Discussion and Reflection (3 - 5 minutes)

   • The teacher will ask each group to share their findings and solutions from the activities. This will allow students to learn from each other and see different approaches to solving problems related to similarity in triangles.
   • The teacher will encourage groups to explain how they determined if two triangles were similar in the "Geometry Detectives" activity. This will help reinforce the concept in a different context.
   • The teacher will also ask groups to explain how they used the concept of similarity to solve the problem in the "The Enlargement Machine" activity. This will help students see the practical application of the concept.

2. Connecting Theory with Practice (2 - 3 minutes)

   • The teacher will summarize the key points from the students' discussions, clarifying any misconceptions and reinforcing the correct use of the terms "similar triangles," "proportional sides," and "corresponding angles."
   • The teacher will also highlight how the activities connected with the theoretical aspects of the lesson, emphasizing the importance of understanding the concept of similarity in triangles and how to use it to solve problems.

3. Reflective Questions (2 - 3 minutes)

   • The teacher will propose that the students take a moment to reflect on the lesson. The teacher will ask the students to think about the most important concept they learned today and any questions they still have.
   • The teacher will ask the students to consider how they could apply the concept of similarity in triangles in other areas of their studies or in real-world situations. This will help students see the relevance of the concept beyond the classroom.

4. Final Wrap-up (1 minute)

   • The teacher will thank the students for their active participation and engagement in the lesson. The teacher will remind the students that understanding the concept of similarity in triangles is an important foundation for future geometry and trigonometry topics.
   • The teacher will also encourage the students to continue exploring the concept of similarity in triangles on their own, for example, by trying out additional problems from their textbook or online resources.

During the feedback stage, the teacher will take notes on the students' understanding and performance, which can be used for future instruction and assessment. The teacher will also provide individual feedback to each group, praising their efforts and providing constructive criticism when necessary.

Conclusion (5 - 7 minutes)

During this final stage, the teacher will:

1. Summarize and Recap (2 - 3 minutes)

   • The teacher will summarize the main points of the lesson, emphasizing the definition of similar triangles, the concept of proportionality, and the importance of corresponding angles and sides.
   • The teacher will recap the activities that were conducted during the lesson, reminding students of the "Shape Shifter" activity that demonstrated the constant ratio of corresponding sides in similar triangles, the "Enlargement Machine" activity that highlighted the similarity between shadows and triangles, and the "Geometry Detectives" activity that required students to apply their understanding of similarity to sort triangles.

2. Connecting Theory, Practice, and Applications (1 - 2 minutes)

   • The teacher will reiterate how the lesson connected theory with practice, explaining that the hands-on activities helped students to visualize and understand the concept of similarity in triangles.
   • The teacher will emphasize the real-world applications of this concept, such as in architecture, engineering, and art, which were discussed during the introduction. The teacher will also mention that this concept is foundational for more advanced topics in geometry and trigonometry.

3. Suggested Additional Materials (1 minute)

   • The teacher will suggest additional resources for students to further explore the topic, such as relevant sections of their textbook, online video tutorials, and interactive geometry games.
   • The teacher will also encourage the students to practice more problems involving similarity in triangles, and to try to apply this concept to real-world situations.

4. Relevance of the Topic (1 minute)

   • The teacher will conclude by reminding the students of the importance of understanding the concept of similarity in triangles. The teacher will explain that this concept is not only fundamental for geometry, but also has numerous practical applications in various fields.
   • The teacher will encourage the students to keep exploring and discovering the interesting and useful aspects of mathematics.

During the conclusion, the teacher will also take the opportunity to assess the students' overall understanding of the lesson. The teacher will ask the students if they feel they have a good grasp of the topic and if they have any remaining questions. This will help the teacher to identify any areas that may need to be revisited in future lessons.