Objectives (5 - 7 minutes)

1. Understand the Concept of Equations with Variables on Both Sides: The teacher will explain that equations with variables on both sides are mathematical statements that involve unknown quantities (variables) on both sides of the equal sign. The students will be able to identify such equations and understand their basic structure.

2. Learn to Simplify Equations: The teacher will outline the process of simplifying equations with variables on both sides, including the steps of combining like terms and isolating the variable. The students will be able to apply these steps to simplify and solve equations.

3. Develop Problem-Solving Skills: The teacher will stress the importance of problem-solving and critical thinking in mathematics. The students will be encouraged to think through each step of the solution process and to ask questions if they are unsure.

Secondary Objectives:

• Promote Collaborative Learning: The teacher will encourage students to work together and help each other understand the material. This will foster a collaborative learning environment and help students develop their communication and teamwork skills.

• Enhance Technology Skills: The flipped classroom model requires students to use technology to access the lesson at home. The teacher will ensure that students are comfortable using the necessary technology and can access the lesson materials. This will also help students develop their technology skills, which are important in today's digital world.

Introduction (8 - 10 minutes)

1. Recap of Previous Knowledge: The teacher will remind students of the basic concepts of equations, variables, and the equal sign. They will ask students to provide examples of simple equations they have learned in the past. The teacher will also review the concept of "balance" in equations, emphasizing that whatever is done to one side of the equation must also be done to the other side to maintain balance.

2. Problem Situations: The teacher will present two problem situations to the students. The first problem could be: "If you have 5 apples and want to share them equally with your 3 friends, how many will each of you get?" The teacher will guide the students to form an equation from this situation. The second problem could be: "A number plus 3 is equal to the number plus 7. What is the number?" The students will be asked to solve these problems in their heads and share their solutions with the class.

3. Real-World Contextualization: The teacher will explain the importance of equations with variables on both sides in real life. They will give examples of situations where such equations might be used, such as in business (to calculate profits or losses) or in physics (to calculate forces or velocities). The teacher will emphasize that understanding and being able to solve these types of equations is a valuable skill that can be applied in many areas of life.

4. Topic Introduction: The teacher will introduce the topic of "Equations: Variables on Both Sides" by showing a short, engaging video. This video could be a fun, animated explanation of the concept, or a real-world application of the concept, such as a video about how engineers use these types of equations to design bridges. The teacher will use this video to grab the students' attention and to show them the relevance and applicability of the topic.

5. Curiosity and Engagement: The teacher will share a couple of interesting facts or stories related to the topic. For example, they could share that the concept of equations with variables on both sides was first used by ancient Egyptian mathematicians. They could also share a fun puzzle or riddle that can be solved using these types of equations. This will help to pique the students' interest and make the topic more engaging.

Development (20 - 25 minutes)

Pre-Class Activities:

1. Video Lesson: The teacher will assign a short video lesson for the students to watch at home. This video should provide a clear explanation of the concept of equations with variables on both sides and demonstrate the process of simplifying and solving such equations. The video should be engaging and easy to understand. The teacher will make sure to provide the link to this video on the school's e-learning platform or through email.

2. Interactive Online Exercises: After watching the video, the students will be required to complete an online interactive exercise on a trusted educational platform. This exercise will provide them with practice in identifying equations with variables on both sides and solving them step by step. The teacher will ensure that the students are comfortable with using this online platform.

In-Class Activities:

1. Group Discussion and Problem Solving (10 - 12 minutes):

   • The teacher will divide the class into small groups of 4-5 students each. They will be asked to discuss the video lesson and the online exercise they completed at home.

   • Each group will be given a set of equations with variables on both sides. The equations will be at varying degrees of difficulty to cater to different student levels.

   • The groups will be asked to solve these equations together, applying the steps of simplifying and solving equations that they learned from the video.

   • The teacher will circulate the room, offering guidance and support as needed. They will encourage students to explain their thinking and solution steps to their group members, fostering a collaborative and supportive learning environment.

   • After the groups have solved their equations, each group will be asked to select one problem and present their solution to the class. This will allow for a variety of equations and solution strategies to be discussed.

2. Hands-on Equations Game (10 - 13 minutes):

   • The teacher will introduce a fun, hands-on game called "Equation Jigsaw". This game is designed to reinforce the concept of equations with variables on both sides and to make learning fun and engaging.

   • The teacher will prepare sets of equation jigsaw puzzles before the class. Each puzzle will be a complete equation cut into pieces. Each piece will have either a variable, a number, or an operation symbol on it.

   • The students will be divided into their groups again. Each group will receive a jigsaw puzzle and a blank piece of paper.

   • The groups will have to solve their puzzle by putting the equation back together correctly on the blank piece of paper. To do this, they will need to simplify and solve the equation.

   • The first group to correctly solve their puzzle and write down the complete equation will be the winner. The teacher will oversee the game, offering hints and guidance as needed.

   • After the game, the teacher will lead a class discussion, asking each group to share the equation they solved and the strategy they used. They will also discuss any common mistakes and misconceptions that arose during the game, providing the students with valuable feedback and learning opportunities.

The teacher will conclude the development stage by summarizing the main points of the lesson, emphasizing the steps to simplify and solve equations with variables on both sides, and highlighting the importance of balance in equations. They will also remind the students of the real-world applications of these types of equations, and how the skills they are learning in class can be applied outside of the school context.

Feedback (10 - 12 minutes)

In-Class Activities:

1. Group Discussion (3 - 4 minutes):

   • The teacher will facilitate a group discussion where each group will share their solutions and the strategies they used to solve the problems or complete the "Equation Jigsaw" game.
   • The teacher will encourage other students to ask questions and provide feedback on the presented solutions. This will not only give the presenting group a chance to reflect on their work but also provide the other students with alternative approaches and insights.

2. Connection to Theory (3 - 4 minutes):

   • The teacher will then connect the group activities to the theoretical understanding of equations with variables on both sides. They will highlight how the strategies used by the students in the group activities align with the steps outlined in the video lesson.
   • For instance, if a group used the strategy of combining like terms first and then isolating the variable, the teacher will explain how this aligns with the step-by-step process of simplifying and solving equations.

3. Reflection (3 - 4 minutes):

   • The teacher will then ask the students to reflect on their learning experience. They will be given a moment to think about their answers before sharing them with the class.
   • The teacher will pose questions such as:
     1. "What was the most important concept you learned today?"
     2. "What was the most challenging part of today's lesson?"
     3. "How do you plan to practice and reinforce what you learned today?"
   • The teacher will remind the students that it's okay to find some concepts challenging at first, and that the most important thing is to keep practicing and asking questions. They will also encourage the students to share their thoughts and questions with the class, creating a supportive and collaborative learning environment.

Feedback and Assessment:

1. Assessing Learning (2 - 3 minutes):

   • The teacher will use this feedback session to assess the students' understanding of the topic. They will observe which groups were able to solve the equations correctly and identify any common mistakes or misconceptions.
   • The teacher will also assess the students' ability to explain their thinking and solution steps, their collaboration and communication skills, and their engagement and participation in the activities. This will provide the teacher with valuable information about each student's progress and learning needs.

2. Providing Feedback (1 - 2 minutes):

   • The teacher will provide constructive feedback to the students, highlighting their strengths and areas for improvement. They will praise the students for their effort, collaboration, and creative problem-solving.
   • If any common mistakes or misconceptions are identified, the teacher will address these, providing a clear explanation of the correct concept or step. They will also encourage the students to ask questions and seek clarification if they are unsure about any part of the lesson.

By the end of the feedback stage, the teacher will have a comprehensive understanding of each student's learning progress and needs. The students will have had a chance to reflect on their learning, receive feedback on their work, and ask questions to clarify their understanding. This will set the stage for the next lesson and ensure that all students are on track with their learning.

Conclusion (5 - 7 minutes)

1. Lesson Recap: (2 - 3 minutes)

   • The teacher will summarize the main points of the lesson, reinforcing the concept of equations with variables on both sides, and the steps to simplify and solve these equations.
   • They will also recap the importance of maintaining balance in equations, reminding the students that whatever is done to one side of the equation must also be done to the other side.
   • The teacher will use the equations and solutions presented by the groups during the lesson to illustrate these points.

2. Connection of Theory, Practice, and Applications: (1 - 2 minutes)

   • The teacher will then discuss how the lesson connected theory, practice, and applications. They will explain that the video lesson provided the theoretical understanding of equations with variables on both sides and the steps to solve them.
   • The online interactive exercise and the in-class group activities allowed the students to practice these concepts and steps in a fun and engaging way. The "Equation Jigsaw" game, in particular, made the learning process more interactive and hands-on.
   • The real-world problem situations and the discussion of real-world applications helped the students to see the practical relevance and applicability of the concepts they were learning.

3. Additional Materials: (1 minute)

   • The teacher will recommend additional resources for students who want to further their understanding of the topic. These could include online math games, interactive worksheets, or educational math apps that provide more practice in solving equations with variables on both sides.
   • The teacher will also suggest that students use their math textbooks for additional exercises and explanations. They can also review the video lesson if they need further clarification on any part of the topic.

4. Importance of the Topic: (1 - 2 minutes)

   • Finally, the teacher will emphasize the importance of the topic for everyday life. They will explain that equations with variables on both sides are not just abstract mathematical concepts, but tools that can be used to solve real-world problems.
   • The teacher will give examples of how these types of equations might be used in different fields, such as in business, physics, or engineering.
   • They will also stress that the problem-solving and critical thinking skills that the students are developing through learning about these equations are valuable skills that can be applied in many areas of life, not just in math.

By the end of the conclusion stage, the students will have a clear understanding of the main points of the lesson and their relevance. They will also have the resources they need to further their understanding and practice of the topic. This will help to consolidate their learning and prepare them for the next lesson.