Objectives (5 - 7 minutes)

1. Understanding Numerical Expressions: The students should be able to define and understand what numerical expressions are. They should be able to distinguish numerical expressions from algebraic expressions and equations.
2. Interpreting Numerical Expressions: The students should be able to interpret numerical expressions involving whole-number exponents. This includes understanding the order of operations and applying it correctly in numerical expressions.
3. Solving Numerical Expressions: The students should be able to solve numerical expressions involving whole-number exponents. This includes simplifying the expressions and finding the value of the expressions when given specific values for the variables.

Secondary Objectives:

• Increasing Engagement: The lesson should aim to increase student engagement with the topic by using interactive and hands-on activities.
• Promoting Collaboration: The lesson should encourage students to collaborate and work together on problem-solving activities, fostering a cooperative learning environment.
• Improving Communication: The lesson should provide opportunities for students to explain their thinking and solutions, improving their mathematical communication skills.

Introduction (10 - 12 minutes)

1. Recall Previous Lessons: To set the stage for the current lesson, the teacher should remind students of the basic concepts of operations (addition, subtraction, multiplication, and division) and the order of operations (PEMDAS - Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). The teacher can use a quick review activity or a brief discussion to ensure that students have the necessary foundational knowledge for the current lesson.

2. Problem Situations: The teacher should present two problem situations to the students. The first situation could involve calculating the number of books in a library with a given number of shelves and books on each shelf. The second situation could involve determining the amount of money a person would have after a given number of days if they double the amount of money they have each day. These problem situations should hint at the concept of numerical expressions and encourage students to think about the order of operations.

3. Real-World Applications: The teacher should highlight the importance of numerical expressions in real-world applications. For example, they can mention how numerical expressions are used in computer programming to perform complex calculations, in engineering to design structures and machines, and in financial planning to make investment decisions. This can help students see the relevance of the topic and motivate them to learn.

4. Topic Introduction and Curiosities: The teacher should introduce the topic of numerical expressions, explaining that they are mathematical expressions that contain only numbers and mathematical operations. The teacher can then share some interesting facts or curiosities to pique the students' interest. For example, the teacher can mention that the world's fastest computer can perform over 200 quadrillion calculations per second, most of which involve numerical expressions. The teacher can also share that a numerical expression can be as simple as 5 + 2 or as complex as (3^2 - 4) x (5 + 7) and that mastering numerical expressions is an important step towards understanding algebra and higher mathematics.

5. Linking the Topic to Everyday Life: To make the topic more relatable, the teacher can explain that we encounter numerical expressions in our daily lives without even realizing it. For example, when we calculate our grocery bill, determine how long it will take us to reach a destination given a certain speed, or figure out our monthly savings based on our income and expenses, we are using numerical expressions. The teacher can also mention that understanding numerical expressions can help us make sense of the world around us, such as understanding how interest rates work or how much time it will take for a population to double given a certain growth rate.

Development (20 - 25 minutes)

1. Lecture and Note-Taking (7 - 10 minutes)

1. Numerical Expression Definition: The teacher will first define a numerical expression as an expression that contains only numbers and operations such as addition, subtraction, multiplication, and division. It can also contain parentheses and exponents.
2. Numerical Expression Components: The teacher will then break down a numerical expression into its components. For example, in the expression 3 + 4 × 2, the three is a number, the plus and times are operations, and the 4 and 2 are also numbers.
3. Order of Operations: The teacher will explain the importance of the order of operations (PEMDAS) in numerical expressions. This means that in expressions involving multiple operations, we must perform the operations in a specific order: parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
4. Examples and Counter-Examples: The teacher will provide a few examples of numerical expressions and ask students to identify the components and apply the order of operations. The teacher should also present a few common misconceptions or counter-examples to challenge students' understanding and promote active learning.

2. Activity - "Expression Builders" Game (8 - 10 minutes)

1. Preparation: The teacher will have prepared "Expression Builders" kits for each group of students. Each kit will contain number cards (1-9), operation cards (+, -, ×, ÷), parentheses, and exponent signs. The goal of the game is for teams to use the cards to build the largest numerical expression possible.
2. Game Rules: The teacher will explain the rules of the game. Each team will choose one card from each category in their kit and place them in front of them. When the teacher says, "Go!", each team will use the cards to construct a numerical expression. The team with the largest expression (after applying the order of operations) wins the round.
3. Game Rounds: The teacher will facilitate multiple rounds of the game, encouraging students to apply the order of operations correctly. After each round, the teacher will ask the winning team how they built their expression and guide them to explain the order of operations they used. This will provide a fun and interactive learning experience and allow for peer learning and assessment.

3. Group Discussion and Problem-Solving (5 - 7 minutes)

1. Problem Situations: The teacher will present a few problem situations involving numerical expressions. For example, if 3 friends have 2 apples each and they share them equally, how many apples will each friend have? Or, if a car is traveling at 50 miles per hour and it has to travel 200 miles, how long will it take to reach its destination?
2. Group Work: The students will work in groups to solve these problems using numerical expressions and the order of operations. The teacher will walk around the room, providing guidance and feedback as needed.
3. Group Discussion: After a specified time, the teacher will call the class back together for a group discussion. Each group will share the problem they worked on and their solution. The teacher will facilitate a discussion, helping students to correct any misconceptions and reinforcing the correct use of numerical expressions and the order of operations.

Through these activities, the students will not only understand the concept of numerical expressions but will also be able to apply the order of operations correctly. They will also learn to work collaboratively, communicate mathematically, and think critically and creatively.

Feedback (8 - 10 minutes)

1. Group Sharing (3 - 4 minutes): The teacher will ask each group to share their solutions or conclusions from the "Expression Builders" game and the problem-solving activity. This will provide an opportunity for students to explain their thought process and the strategies they used. The teacher should guide this discussion, ensuring that the focus is on understanding the order of operations and applying it correctly in numerical expressions.

2. Connection to Theory (2 - 3 minutes): The teacher will then facilitate a discussion to connect the group's findings and solutions to the theoretical concepts discussed in the lesson. This can involve discussing how the order of operations was applied in the different expressions, how the components of a numerical expression were identified, and how the numerical expressions were simplified. The teacher should highlight the correct use of the order of operations and point out any common mistakes or misconceptions that were addressed during the activities.

3. Reflection (3 - 4 minutes): The teacher will then propose that students take a moment to reflect on the lesson. The teacher can ask guiding questions such as:

   • What was the most important concept you learned today?
   • What questions do you still have about numerical expressions and the order of operations?
   • How do you plan to study and practice numerical expressions on your own?
   • Can you think of any real-world situations where you might encounter numerical expressions?
   • How can you apply what you learned today in your daily life or in other areas of study?

4. Addressing Questions and Concerns (1 - 2 minutes): The teacher will address any remaining questions or concerns that students may have. This can involve providing further clarification on a concept, giving additional examples, or suggesting resources for further study. The teacher should also take note of any common misconceptions or areas of difficulty that emerged during the lesson for future remediation.

This feedback stage is crucial for consolidating the learning from the lesson, addressing any lingering questions or misunderstandings, and preparing students for independent practice and study. It also provides an opportunity for the teacher to assess the effectiveness of the lesson and make any necessary adjustments for future lessons.

Conclusion (5 - 7 minutes)

1. Summary and Recap (2 - 3 minutes): The teacher will summarize the main points of the lesson, reiterating the definition of numerical expressions, the components of numerical expressions, and the order of operations (PEMDAS). The teacher will also recap the activities done during the lesson, including the "Expression Builders" game and the problem-solving activity. The teacher will emphasize the correct application of the order of operations in these activities and how it helped in simplifying numerical expressions and finding their values.

2. Connecting Theory, Practice, and Applications (1 - 2 minutes): The teacher will explain how the lesson connected theory, practice, and applications. The theoretical part of the lesson focused on understanding numerical expressions and the order of operations. This was then put into practice through the hands-on activities, where students had to construct numerical expressions and solve problems using the order of operations. The real-world applications were highlighted in the problem situations, where students had to apply numerical expressions and the order of operations to solve real-world problems.

3. Suggested Additional Materials (1 minute): The teacher will suggest additional materials for students to further their understanding and practice of numerical expressions and the order of operations. This could include textbooks, online resources, educational games, and worksheets. The teacher can also recommend specific exercises or problems for students to practice, based on their individual learning needs and abilities.

4. Relevance to Everyday Life (1 - 2 minutes): Finally, the teacher will reiterate the importance of understanding numerical expressions and the order of operations in everyday life. The teacher can provide a few more examples of how we use numerical expressions in various situations, such as calculating cooking recipes, determining travel distances and times, and understanding sports statistics. The teacher can also mention that many professions, such as engineers, architects, and financial analysts, use numerical expressions in their work, further emphasizing the relevance of the topic. The teacher will conclude by encouraging students to continue practicing and exploring numerical expressions in their daily life and studies, and to always keep an eye out for situations where they can apply what they learned.