Objectives (5 - 7 minutes)

• The teacher will ensure the students understand the concept of whole numbers and integers, including their basic properties and the number line representation.
• The teacher will guide the students to differentiate between whole numbers and integers, highlighting the importance of the sign in identifying integers.
• The teacher will provide example problems to help students apply the concepts of whole numbers and integers, and will encourage students to ask questions or seek clarification as needed.

Secondary Objectives:

• The teacher will aim to foster a positive learning environment, encouraging active participation and collaboration among students.
• The teacher will promote critical thinking by asking students to explain their thought process or reasoning behind their answers.
• The teacher will provide real-world applications of whole numbers and integers to help students understand the practical significance of these concepts.

Introduction (10 - 12 minutes)

• The teacher will start the lesson by reminding students of the previous lesson's content, which includes the basic concepts of numbers, such as counting, place value, and the addition and subtraction of whole numbers. This revision will provide a necessary foundation for the new topic of whole numbers and integers.

• To pique the students' interest, the teacher will pose two problem situations that will later be solved using the concept of integers. For example, "If a submarine is at a depth of 200 meters below sea level and then it moves up 100 meters, at what depth is it now?" or "If you owe your friend $5 and then she gives you $10, how much do you have now?".

• The teacher will then contextualize the importance of the new topic by explaining its real-world applications. They might say, "Understanding whole numbers and integers is crucial in many real-life situations. For instance, in finance, understanding negative numbers (which are a type of integer) is key to managing debts and credits. In science, the concept of integers is used to understand temperatures below zero. In sports, integers are used to represent scores in games where negative scores can occur."

• To grab the students' attention, the teacher will share two fun facts related to the topic. They might say, "Did you know that the concept of zero, which is a whole number, was first used in India around the 7th century? It was a revolutionary concept that changed the way we do math!" or "Have you ever wondered why the numbers on a thermometer go down below zero? That's because the temperatures below freezing are represented by negative numbers, which are a type of integer!"

• The teacher will then formally introduce the topic of the day: Whole Numbers and Integers. They will explain that whole numbers are the numbers we use to count things (starting from zero and going to infinity) and that integers include whole numbers as well as their negatives. The teacher will assure the students that by the end of the lesson, they will be able to understand and use these types of numbers confidently.

Development (20 - 25 minutes)

• Whole Numbers (5 - 6 minutes)

  • The teacher will start by defining what whole numbers are: non-negative numbers, including zero, that we use to count whole things.
  • The teacher will then explain the characteristics of whole numbers, such as they are closed under addition and multiplication (which means the sum or product of two whole numbers is always a whole number), but not division (as division can sometimes result in a fraction).
  • The teacher will illustrate the concept of whole numbers using the number line, where they can show that the whole numbers start at zero and continue indefinitely in both directions.

• Integers (5 - 6 minutes)

  • The teacher will then introduce the concept of integers, which includes whole numbers as well as their negatives. They will explain that the addition and subtraction of integers can result in numbers that are not whole, such as negative whole numbers or fractions.
  • The teacher will also explain the importance of the sign in identifying integers. For example, "If there's a minus sign in front of a number, it means that number is negative and therefore an integer. If there's no sign or a plus sign, it's a whole number, but not an integer."
  • Just like with whole numbers, the teacher will illustrate integers on the number line, reinforcing that it extends infinitely in both directions, with zero at the center.

• Comparing Whole Numbers and Integers (5 - 6 minutes)

  • The teacher will guide the students to distinguish between whole numbers and integers. They will use visual aids and examples to illustrate this difference, such as -5 being an integer but not a whole number.
  • The teacher will also explain that all whole numbers are integers, but not all integers are whole numbers. To demonstrate this, the teacher can write a few numbers on the board, such as 0, 1, -1, 2, -2, and ask the students to identify the whole numbers from the integers.

• Operations with Whole Numbers and Integers (5 - 7 minutes)

  • The teacher will then proceed to explain how to perform basic operations (addition, subtraction, multiplication, and division) with whole numbers and integers.
  • They will use examples and step-by-step procedures to demonstrate each operation, ensuring that students understand how the sign of each number affects the result.
  • For instance, the teacher might ask, "If we have the problem -2 + 3, what do you expect the answer to be? Why?" or "What about 5 - 7? What would you expect the answer to be? Why?"

By the end of the development stage, the students should have a clear understanding of the differences between whole numbers and integers, their properties, and how to perform basic operations with them. Through the use of visual aids, real-world examples, and interactive discussions, the teacher will ensure that the students are actively engaged in the learning process.

Feedback (8 - 10 minutes)

• The teacher will initiate a class discussion by asking students to share their understanding of the lesson. They might say, "Can anyone explain in their own words what the difference is between whole numbers and integers?" or "Who would like to share a real-world situation where they might encounter negative numbers or integers?"

• The teacher will then provide feedback on the students' responses, correcting any misunderstandings and reinforcing the correct concepts. They will also praise students for their participation and effort in understanding the new topic.

• The teacher will then ask the students to reflect on the lesson and answer a few questions:

  1. "What was the most important concept you learned today?" - This question will help the teacher gauge the students' understanding of the lesson's key concepts and identify any areas that may need further clarification or reinforcement.
  2. "Can you think of any real-world situations where you might encounter whole numbers or integers?" - This question will encourage students to think about the practical applications of what they have learned.

• The teacher will give the students a few minutes to think about these questions and then ask for volunteers to share their answers. They will listen attentively to the students' responses and provide additional explanations or examples as needed.

• The teacher will conclude the feedback session by summarizing the key points of the lesson and highlighting the importance of whole numbers and integers in everyday life. They might say, "Today, we learned about whole numbers and integers. We learned that whole numbers are non-negative numbers that we use to count whole things, while integers include whole numbers and their negatives. We also learned how to perform basic operations with whole numbers and integers. These are important concepts in math, but they're also used in many real-life situations, like managing money, understanding temperatures, and even in sports. Great job today, everyone!"

• To wrap up the lesson, the teacher will assign a short homework task to reinforce the concepts learned in class. For instance, they might ask the students to solve a few problems involving whole numbers and integers, or to write a short paragraph explaining a real-world situation where they might encounter these types of numbers. They will also encourage the students to come to the next class with any questions or doubts they may have, assuring them that it's okay if they don't understand everything right away and that learning is a process.

By the end of the feedback stage, the teacher should have a clear understanding of the students' grasp of the lesson's concepts. The students, on the other hand, should feel confident in their understanding of whole numbers and integers, and understand their relevance in everyday life.

Conclusion (5 - 7 minutes)

• The teacher will start the conclusion by summarizing the key points of the lesson. They will remind the students that whole numbers are non-negative numbers that we use to count whole things, while integers include whole numbers and their negatives. They will also reiterate the importance of the sign in identifying integers and highlight that all whole numbers are integers, but not all integers are whole numbers. The teacher will also briefly recap the basic operations with whole numbers and integers.

• The teacher will then explain how the lesson connected theory, practice, and applications. They will mention that the initial discussion and problem situations helped to frame the theory of whole numbers and integers, and the subsequent guided exercises and real-world examples allowed students to apply this theory in practice. The teacher will emphasize that understanding the theory is important for solving problems and making sense of real-world situations.

• To further students' understanding of the subject, the teacher will suggest additional materials for study. These might include textbooks with more advanced problems, educational websites and apps that offer interactive lessons and exercises on whole numbers and integers, and educational videos that explain the topic in a fun and engaging way. The teacher will encourage the students to explore these resources at their own pace to reinforce their understanding of the topic.

• The teacher will then briefly discuss the significance of whole numbers and integers in everyday life. They will remind the students of the real-world situations where these types of numbers are used, such as in finance, science, and sports. They might also mention that the concept of zero, which is a whole number, is a fundamental concept in mathematics that underpins many other mathematical concepts and operations. The teacher will stress that understanding whole numbers and integers is not just important for math class, but also for life in general.

• Finally, the teacher will wrap up by encouraging the students to continue practicing with whole numbers and integers and to keep seeking out new learning opportunities. They might say, "Remember, learning is a journey, and it's okay if you don't understand everything right away. The important thing is to keep trying and to keep asking questions. I'm here to help you every step of the way, so don't hesitate to reach out if you need any clarification or further explanation. Great job today, and I look forward to seeing your continued progress!"

By the end of the conclusion, the students should have a clear and comprehensive understanding of whole numbers and integers, their properties, and their importance in everyday life. They should also feel motivated to continue learning and exploring the topic further.