Contextualization

Mathematics is the language of the universe, and it forms the basis for many of our daily activities. Whole numbers and integers are the building blocks of this language. Understanding whole numbers (the set of zero and positive numbers) and integers (which include negative numbers as well) helps us in various aspects of life, including finance, physics, engineering, computer science, and much more!

The number "zero" was one of the last numbers to be invented, and it plays a pivotal role in understanding whole numbers and integers. Then come the Positive numbers or the numbers that we generally count in our daily life. Integers, on the other hand, introduce a broader concept, including not only zero and positive numbers but also negative numbers.

Understanding the difference between whole numbers and integers, mastering operations with them such as addition, subtraction, multiplication, and division, and knowing properties of these numbers are vital skills that will aid you in mathematical problem-solving.

The significance of learning about whole numbers and integers is not confined to math alone. When you look around, the world is filled with examples where knowledge of whole numbers and integers is needed. In the shopping mall, when we calculate discounts or pay for what we purchase, we use whole numbers and integers. When it's cold and the temperature falls below zero, you're dealing with negative integers.

In the world of finance and banking, whole numbers and integers are used to calculate profit and loss, interest rates, mortgages, and so on. Engineers use integers for measurements and calculations. Computer programmers use numeric operations for creating software and apps. As such, a thorough understanding of whole numbers and integers opens the door to a broad range of real-world applications and fields of study.

To start your exploration of whole numbers and integers, consider the following resources:

• "Numberphile", a YouTube channel dedicated to all things numbers.
• Khan Academy offers comprehensive video courses on whole numbers and integers, as well as interactive exercises.
• "A Very Short Introduction to Mathematics" by Timothy Gowers is an engaging and accessible book that covers basic mathematical concepts, including whole numbers and integers.
• MathIsFun.com provides straightforward and engaging explanations and online exercises on whole numbers and integers.

Remember these are only starting points, feel free to go beyond these resources and to question and explore as much as you can. The world of whole numbers and integers is fascinating and wide, and it's now yours to discover!

Practical Activity

Activity Title: "Exploring Whole Numbers and Integers: Through the Lens of Elevators and Temperature"

Objectives:

• To understand the concept and properties of whole numbers and integers.
• To understand the applications of whole numbers and integers in real-world scenarios.
• To effectively use whole numbers and integers in operations such as addition, subtraction, multiplication, and division.
• To practice teamwork, communication, problem-solving, and creative thinking.

Project Description:

You will be divided into groups of 3-5 students. Your group will use the concepts of whole numbers and integers to create a two-part project:

1. Design an Elevator System: where each floor level is a whole number and the elevator movement is represented by integers.
2. Temperature Tracking Activity: where you will analyze and describe temperatures over a week, which can go above or below zero.

Both parts of the project aim to provide hands-on learning experience of how whole numbers and integers are used and operate in real-world contexts.

Necessary Materials:

• Poster paper or cardboard
• Markers, colored pencils, etc.
• Rulers
• Thermometer (optional)
• Access to internet or library for research

Detailed Steps:

Part 1: Design an Elevator System

1. Decide how many floors your building will have. Remember, the ground floor is represented by the whole number "zero" while the floors above and below it are represented by positive and negative integers respectively.
2. Draw your building and the elevator system on the poster paper. Clearly mark the floor levels with the corresponding numbers.
3. Develop scenarios where the elevator moves from one floor to another. Use addition and subtraction of integers to show the operation. For example, if the elevator moves from floor 2 (positive integer) to floor -1 (negative integer), the operation would be 2 - 1 = 1 and then 1 - 2 = -1.
4. Make sure your scenarios include situations where the elevator moves up (addition) and down (subtraction).

Part 2: Temperature Tracking Activity

1. Choose a location (your city, a foreign city, etc.). Find and record the daily temperatures for a week. You can use a weather website for this.
2. On a separate poster paper, create a temperature line graph representing each day's temperature. Use integers to represent the temperatures, with negative numbers for temperatures below zero.
3. Describe the temperature changes using addition and subtraction of integers. For example, if Monday's temperature was 3 degrees and Tuesday's was -2 degrees, you could represent the drop in temperature as 3 - 2 = 1 and then 1 - 3 = -2.

Your completed project should include the two poster boards with their respective activities and a written report detailing your work process, observations, and conclusions. The report should include:

• Introduction: Explain the purpose of the project and the relevance of whole numbers and integers.
• Development: Detail what you did in each part of the project, the theory you used, the methodology, and the results you obtained.
• Conclusion: Revisit the main points of the project, state what you learned, and draw conclusions about the project.
• Bibliography: List the resources that you used for the project (websites, books, videos, etc.).

Project Duration:

The project is intended to be completed over two weeks, with each group member spending at least twelve hours on the project tasks.

Deliverables:

Each group will deliver two poster projects and a written report. The posters should clearly display the elevator system and the temperature graph with their respective whole numbers and integers. The report should reflect your understanding of the topic, the process you followed, and the conclusions you drew from the project.