Objectives (5 - 7 minutes)

1. The teacher will introduce the topic of "Evaluating Expressions" and explain its relevance to real-life situations. They will make it clear that understanding how to evaluate expressions is fundamental to solving mathematical problems.

2. The teacher will outline the three main objectives of the lesson:

   • Objective 1: Students will learn how to substitute values for variables in numerical expressions and evaluate the expressions.
   • Objective 2: Students will understand the concept of order of operations (PEMDAS) and its role in evaluating expressions.
   • Objective 3: Students will practice evaluating expressions in various contexts to enhance their understanding and application of the topic.

3. The students will be informed of the expectations for the lesson. They should be prepared to engage in active learning during the class session, applying what they learned at home, and participating in group activities and discussions.

Introduction (10 - 15 minutes)

1. The teacher will start by reminding students of the basic mathematical concepts they have learned so far, such as the meaning of variables, the importance of parentheses, and the order of operations (PEMDAS). This will serve as a foundation for the new topic. The teacher may use a quick review game to make this process more engaging. (3 - 5 minutes)

2. The teacher will propose two problem situations that serve as a context for the lesson:

   • Problem 1: Imagine you have a part-time job at a bakery, and you are paid $7 per hour. If you worked for 3 hours, how much will you get paid?
   • Problem 2: A farmer has 15 cows and he wants to give each cow 3 apples. How many apples does he need in total? The teacher will then ask students how they would approach these problems, encouraging them to think about the role of variables and operations. This will help to bridge the gap between abstract mathematical expressions and real-life applications. (5 - 7 minutes)

3. To grab the students' attention, the teacher will share two interesting facts or stories related to the topic:

   • Fact 1: The teacher will explain that the concept of evaluating expressions is not only used in mathematics but also in computer programming and scientific calculations. For example, in computer programming, variables are often used to store and manipulate data.
   • Fact 2: The teacher will share a curiosity about the history of mathematics, such as how the concept of parentheses was introduced in the 16th century by a mathematician named Robert Recorde. This can lead to a brief discussion about the importance of notation in mathematics. (2 - 3 minutes)

4. To introduce the topic of "Evaluating Expressions", the teacher will say, "Today, we are going to learn a skill that will help us solve problems faster and more efficiently. We will learn how to evaluate expressions - a skill that is not only important in math class but also in real life. By the end of the lesson, you will be able to calculate how much you will earn at a part-time job or how many apples a farmer needs to feed his cows." (1 minute)

Development

Pre-Class Activities (At Home)

1. Reading and Video Material: The teacher will provide a reading assignment that explains the concept of "Evaluating Expressions" in a simple and engaging manner. This should cover the basics of substituting values for variables and using the order of operations (PEMDAS) to simplify numerical expressions. The reading material will be accompanied by a short, fun video that reinforces the concepts and provides examples for better understanding. (15 - 20 minutes)

2. Online Quiz: After reviewing the reading and video material, students will be required to take an online quiz. The quiz will consist of a series of multiple-choice and fill-in-the-blank questions to assess their understanding of the material. The quiz will be automatically graded, and the results will be sent to the teacher for review before the class session. (10 - 15 minutes)

In-Class Activities (20 - 25 minutes)

Activity 1: 'Expression Evaluation Relay Race'

1. The class is divided into groups of 4 or 5 students. Each group is given a set of numerical expressions and a stack of index cards. On each index card is a number or variable that appears in one of the expressions.
2. The objective of the game is for each group to evaluate their set of expressions by substituting the appropriate numbers or variables from the index cards. The challenge is that they can only evaluate one expression at a time, and they must pass the index cards down the line, one by one, to the next player who will use the cards to evaluate the next expression.
3. The teacher will shout out different orders of operations (e.g., 'Divide and Multiply first, then Add and Subtract' or 'Start with what is in Parentheses, then Exponents, then Multiply and Divide from left to right, and finally Add and Subtract') at different points during the game. This will test the students' understanding of the order of operations.
4. The first team to correctly evaluate all their expressions wins the relay race.

Activity 2: 'Expression Evaluation Showcase'

1. Each team will be asked to choose one numerical expression from their set and write it on a large sheet of paper. They will then have to explain the process of evaluating that expression, step by step, in a clear and logical manner.
2. Once all the teams have completed their explanations, they will take turns presenting their expression and evaluation process to the rest of the class. This will not only allow them to revise and reinforce their understanding of the topic but also help them practice their public speaking and presentation skills.
3. As an additional challenge, the teacher can randomly select a card with a number or variable and ask the presenting team to evaluate the chosen expression on the spot. This will test their ability to apply the concept quickly and accurately.

Each activity will be followed by a brief discussion and feedback session where the teacher will clarify any misconceptions and highlight the key learning points of the activities. The teacher will also take this opportunity to link the activities back to the theory, emphasizing how the activities have helped the students to understand and apply the concept of evaluating expressions more effectively.

Feedback (8 - 10 minutes)

1. Group Discussion: The teacher will ask each group to share their solutions or conclusions from the activities. Each group will have up to 3 minutes to present their work. This will allow the students to learn from each other and see different approaches to evaluating expressions. (5 minutes)

2. Connecting Theory and Practice: After all the groups have presented, the teacher will facilitate a discussion to connect the activities with the theoretical concepts of evaluating expressions. The teacher will highlight how the activities demonstrated the importance of substituting values for variables and using the order of operations (PEMDAS) to simplify numerical expressions. The teacher will also clarify any misunderstandings and reinforce the key learning points of the lesson. (2 minutes)

3. Reflection: The teacher will then ask the students to take a moment to reflect on what they have learned in the lesson. The students will be prompted to consider the following questions:

   • Question 1: What was the most important concept you learned today?
   • Question 2: What questions or doubts do you still have about evaluating expressions?
   • Question 3: How can you apply what you learned today to other areas of your life or other subjects?

4. Sharing Reflections: The teacher will ask a few students to share their thoughts and reflections with the rest of the class. This will provide an opportunity for the students to express their understanding and for the teacher to address any remaining questions or doubts. (1 - 2 minutes)

5. Wrapping Up: The teacher will conclude the feedback session by summarizing the key learning points of the lesson and reminding the students of their homework assignment. This will ensure that the students leave the class with a clear understanding of the topic and what is expected of them for the next lesson. (1 minute)

This feedback stage is crucial as it allows the teacher to assess the students' understanding of the topic and to provide clarification or reinforcement where necessary. It also encourages the students to reflect on their learning, which can enhance their understanding and retention of the material.

Conclusion (5 - 7 minutes)

1. Summary and Recap: The teacher will start by summarizing the main points of the lesson. They will recap the concept of "Evaluating Expressions" and the process of substituting values for variables and using the order of operations (PEMDAS) to simplify numerical expressions. The teacher will also highlight the importance of these skills in solving mathematical problems and real-life situations. (2 minutes)

2. Connection of Theory, Practice, and Application: The teacher will then explain how the lesson connected theory, practice, and real-world application. They will refer back to the problem situations discussed at the beginning of the lesson and show how the activities helped the students to apply the theoretical concepts to solve these problems. The teacher will also mention the online quiz, the relay race, and the showcase, emphasizing how these activities allowed the students to practice and demonstrate their understanding of the topic. (1 minute)

3. Additional Materials: The teacher will suggest additional materials for the students to further their understanding of the topic. This could include interactive online games, math apps, or extra practice worksheets. The teacher will also remind the students of the textbook chapter that covers the topic and encourage them to review it if they have any remaining questions or doubts. (1 - 2 minutes)

4. Importance of the Topic: Lastly, the teacher will explain the importance of understanding and being able to evaluate expressions in everyday life. They will provide examples such as calculating expenses, understanding financial statements, or even programming a computer. The teacher will emphasize that the skills learned in this lesson are not only essential for their math class but also for many other areas of their lives. (1 - 2 minutes)

This concluding stage is essential as it helps to reinforce the main points of the lesson, clarify any remaining doubts, and provide the students with additional resources for further learning. It also serves to motivate the students by showing them the real-world relevance and applications of the topic.