Objectives (5 - 7 minutes)

• Objective 1: The teacher will introduce the topic of the Law of Sines as a method to extend trigonometric concepts to non-right triangles. The students will understand the importance of this topic in the wider context of trigonometry and its real-world applications.
• Objective 2: The students will learn to identify when the Law of Sines should be applied. They will be taught the conditions where the Law of Sines is the most appropriate method to use for solving problems.
• Objective 3: The teacher will introduce the specific formula for the Law of Sines and explain each component in a simple, clear, and didactic manner. The students will learn how to apply this formula to solve for unknown side lengths and angles in non-right triangles.

Secondary Objectives:

• The teacher will ensure that students understand the concept of sine in relation to right triangles before extending the idea to non-right triangles.
• The students will be encouraged to ask questions in order to ensure a thorough understanding of the topic.

Introduction (8 - 10 minutes)

• The teacher will begin by reminding students about the basic trigonometric concepts, particularly focusing on sine, cosine, and tangent in the context of right-angled triangles. This review will involve a quick whiteboard sketch of a right triangle, marking the angles and sides, and then defining sine as the ratio of the length of the side opposite the angle to the length of the hypotenuse. (2 minutes)

• The teacher will next introduce two problem situations where the Law of Sines is applicable.

  1. The first problem could be a real-world scenario involving navigation: "A ship sets sail from a port and travels 20 miles at a bearing of 030 degrees. It then changes course and travels 30 miles at a bearing of 120 degrees. How far is the ship from the port, and what is its bearing from the port?"

  2. The second problem could be a geometrical problem: "In a triangle ABC, angle A is 50 degrees, angle B is 80 degrees, and side AB is 7 units. Find the lengths of sides AC and BC."

  The problems will be written on the board for students to see and consider. (3 minutes)

• The teacher will then contextualize the importance of the subject by explaining how the Law of Sines is used in various real-world applications such as in navigation, architecture, physics, engineering, and even in computer graphics and game design. This will help the students understand the practicality and significance of learning this topic. (2 minutes)

• To grab the students' attention, the teacher could share two interesting facts or stories related to trigonometry:

  1. The teacher can mention that the ancient Egyptians used a primitive form of trigonometry for building the pyramids. They didn't have the modern trigonometric functions, but they understood the concept of ratios in right triangles.

  2. Another interesting fact could be about the famous mathematician, Bhaskara II, who was one of the first to give a proof of the Law of Sines. The teacher can briefly explain how Bhaskara II’s work was way ahead of his time and how it still forms the basis of much of modern trigonometry. (3 minutes)

Development (25-30 minutes)

Pre-Class Activities (10-15 minutes):

• The students should watch an online video lecture (that would be previously selected and provided by the teacher) on the introduction to the Law of Sines. This should be a simple and easy-to-understand video explaining the basic terms and concepts of the Law of Sines and how it extends trigonometric concepts to non-right triangles. The students should note down any questions they have while watching the video for discussion in class.

• Afterwards, the students should individually attempt a set of basic Law of Sines problems given by the teacher. These problems are to be solved at home and are designed to be introductory tasks that allow the students to experiment with the Law of Sines before diving into more complex problems in the classroom. This helps prepare the students for the in-class activities and primes their thinking towards the Law of Sines.

In-Class Activities (15-20 minutes):

Activity 1: Board Race (8-10 minutes):

• The teacher can start a fun and competitive board race involving problems that require the use of the Law of Sines to solve.

• The class will be divided into groups of 3-5 students. Each group is assigned a whiteboard space. The teacher then presents a problem on the main whiteboard. Each team will collaboratively solve the problem on their own board, with the teacher checking for correctness. The first team to get the correct solution wins a point. The team with the most points at the end of the activity wins.

• Besides creating a fun, competitive atmosphere, this activity strengthens students' understanding of the principles of the Law of Sines and encourages them to make quick, but accurate calculations.

Activity 2: Build Your Own Scenario (7-10 minutes):

• For the second activity, the teacher will challenge each group to create their own "real-world" scenario where the Law of Sines can be applied. Each group must also come up with the corresponding trigonometric problem that relates to their scenario.

• Once each group has written their scenario and math problem, they exchange with another group. Each group then solves the problem they've been given, using the Law of Sines. If they solve it correctly, both groups present their scenario and solution to the class.

• This activity not only reinforces the application of the Law of Sines but also exercises the students' creativity and ability to contextualize abstract mathematical concepts to real-world situations.

Towards the end of the lesson, the teacher can conduct a quick recap of the Law of Sines in a non-right triangle and how it has been applied during the activities. The teacher can then summarize the main points, address any remaining doubts, and prepare the students for the next topic in trigonometry.

Feedback (8 - 10 minutes)

• The teacher will begin the feedback stage by facilitating a group discussion. Each group will have a maximum of 3 minutes to present their solutions to the class. This includes explaining their real-world scenario, the trigonometric problem associated with the scenario, and their solution to the problem. (approx. 15 minutes)

• The teacher will then use the remaining time to assess the group activities, focusing on how well the students have understood the Law of Sines and its applications. The teacher will review the most common mistakes made during the activities and explain how to rectify them, if any. This process will provide an opportunity for students to compare their work with others and learn from each other's mistakes and successes. (approx. 5 minutes)

• The teacher will then propose that students take a moment to reflect on answers to questions such as:

  1. What was the most important concept learned today?
  2. What questions remain unanswered?

• The teacher will collect these reflections in written form for future reference and to gauge the students' understanding of the lesson. (approx. 5 minutes)

• The teacher will close the session by summarizing the key takeaways of the lesson, reinforcing the importance of the Law of Sines, and preparing students for the upcoming lessons on further trigonometric concepts. The teacher will also remind students to review the day's lesson and to prepare for the next class by reading and doing some preliminary exercises on the next topic. (approx. 5 minutes)

• Lastly, the teacher will collect student feedback on the lesson. This could be done through a quick survey or an open discussion, depending on the teacher's preference and the classroom culture. This is important to understand what teaching methods were effective, which ones could be improved, and how students are feeling about their progress. This will be valuable in planning future lessons and ensuring that the teaching methods used are as effective as possible. (approx. 5 minutes)

This feedback stage is crucial for both the teacher and the students. It provides an opportunity for clarification, reinforcement of concepts, and reflection on learning. It also helps to build a supportive and responsive learning environment where students feel valued and heard.

Conclusion (5 - 7 minutes)

• The teacher will start the conclusion by summarizing the main points covered in the lesson. They will reiterate the definition and application of the Law of Sines, and how it extends trigonometric concepts to non-right triangles. They will recap the formula for the Law of Sines and remind students of the conditions under which it can be used to solve problems. (2 minutes)

• Next, the teacher will explain how the lesson has connected theory, practice, and applications. They will refer back to the introductory real-world problems to illustrate this connection. They will explain how the theoretical concept of the Law of Sines was put into practice during the in-class activities and was used to solve the real-world problems. (1 minute)

• The teacher will then suggest additional resources for students to further their understanding of the Law of Sines. This could include online interactive platforms, educational YouTube channels, or specific chapters in textbooks. They will encourage students to explore these resources at their own pace and come prepared with any questions they might have for the next class. (1 minute)

• Lastly, the teacher will briefly discuss the importance of the Law of Sines in everyday life. They will explain how it is used in different fields such as architecture, engineering, and navigation for calculating distances and angles. They will also mention that it's used in computer graphics and game design for creating realistic movements and animations. The teacher will emphasize that understanding the Law of Sines is not just about learning a mathematical concept, but also about gaining a tool that can be used to solve real-world problems. (1-2 minutes)

• To close, the teacher will remind students of their homework assignment and provide a glimpse into the next lesson, creating anticipation and curiosity for future topics. They will also encourage students to approach them after class or during office hours if they have any further questions or need additional help with the topic. (1 minute)