Contextualization

Mathematics, as an essential tool for logical reasoning, is a critical subject for learning various concepts that are applicable in our everyday life. One of those fundamental concepts is the 'Percent,' an ubiquitous element in diverse instances such as calculating discounts, computing interest rates, managing income tax, and even understanding statistical data. The term 'percent' is derived from the Latin 'per centum,' which means 'per hundred.'

Percentage is a way of expressing a number as a fraction of 100. It's a universal tool that allows us to compare, analyse, and generalise data, making it easier for us to understand the world. This concept is indispensable as it offers a concise way to represent proportions and ratios.

In any financial transaction, percentages play a significant role. It's essential for calculating sales tax, computing discounts during sales, or understanding interest rates on loans and credit cards. Understanding this concept provides students with a better grasp of how finances work, enabling them to make informed decisions in the future.

In our information-laden society, data is everywhere. Be it weather forecasts, pandemic statistics, or sports achievements, percentages are widely used. They aid in the interpretation of data and information, making it easily understandable and comparable.

Introduction

To fully appreciate the magic of percentages, we will delve into their theoretical concepts. In the realm of mathematics, a percent is a ratio or fraction that represents a number out of 100. If we say 50%, it means 50 out of every 100, or simply half of the total.

Percentages are often used to express proportions. For instance, if a test score is 95%, it indicates that 95% of the total possible points were earned. This single figure provides a concise and understandable metric of performance, irrespective of whether the total possible points are 100, 500, or 1000.

Mathematically, we can express percentages in the form of fractions or decimals, and vice versa. This interchangeability provides us the flexibility in operations, depending on the requirements of the problem at hand.

In the coming project, we will explore the world of percents, understanding their theory, and applying the concept to solve real-world problems. Through group collaboration and creative thinking, the project will be a journey from understanding the percentage as a theoretical concept to its practical applications.

Resources

For an in-depth understanding, students can refer to the following resources:

1. Maths is Fun: This website covers definitions, explanations, and exercises about percentages.
2. Khan Academy: This platform provides educational videos and exercises to understand percentages.
3. Book: Percents and Ratios: A Way to Make Mathematics Visual by David Adler. This book explains percentages and their applications in daily life.
4. Book: Math on the Job: Working in Sports by Richard Wunderlich. This book shows how percentages are used in sports.
5. BrainPOP: An online platform depicting educational animated movies about percentages.
6. Math Antics: YouTube video for clear and interactive understanding on Percentages.

Practical Activity

Activity Title: "The Percent Hunt: A Walk Through Real Life Percent Problems"

Objective of the Project

The project is aimed to strengthen the students’ understanding of the practical application of percent problems by engaging them in real-world scenarios. Furthermore, this project helps to develop students' collaborative and problem-solving skills, promoting effective communication and creative thinking within the group.

Detailed Description of The Project

The project encourages students to explore their surroundings to find and analyze different scenarios where percentages are applied. For the execution of the project, students will be divided into groups of 3 to 5. Over a span of around two weeks, the students are expected to document different percent problems from various walks of life, including but not limited to shopping, sports, finance, and public statistics.

For each identified application, they are expected to provide a detailed mathematical breakdown of how the percentage problem is solved and how it is applicable in their daily lives.

The practical activity would cover key theoretical topics including

1. Understanding the concept of percentage.
2. Conversion between fractions, decimals, and percentages.
3. Solving percent problems in real-world scenarios.
4. Applying the knowledge of percentages in calculating discounts, interests, and tax rates.
5. Using percentages to interpret and comprehend data.

By the end of this project, students should be able to successfully incorporate their mathematical knowledge to solve percent problems and comprehend their relevance and application in real-world situations.

Necessary Materials

1. Notebook or Digital Journal (for documentation)
2. Pen/Pencil or Digital tools (for sketching diagrams, if required)
3. Calculator
4. Camera (for taking relevant pictures, optional)

Detailed Step-by-step for Carrying Out The Activity

1. Formation of Groups: Divide the students into groups of 3 to 5 students each. Assign each group a unique identifier for easy reference.

2. Introduction and Instructions: Provide a brief about the project and its objectives. Discuss the importance of teamwork, time management, and the effective division of tasks.

3. Activity Initiation: Encourage students to begin by brainstorming about the different areas of life where percent is used. They should then decide which areas they would like to explore during the project.

4. Documentation: Each group is required to investigate and document at least 10 real-life percent problems with detailed solutions. They should clearly define the problem, show the mathematical calculations and how the concept of percentage is applied in that context. Use of diagrams, charts, and tables to explain their findings is encouraged.

5. Compilation: All of the documented tasks should be compiled into a final report following the defined structure: Introduction, Development, Conclusions, and Used Bibliography.

6. Presentation: Each group will present their findings to the class. This will encourage peer learning and improve presentation skills.

Project Deliverables

1. Final Report: Each group will prepare a final report detailing their findings and learnings. The report must include four significant sections:

   • Introduction: This section should contain a brief about the project, including its relevance, real-world application, and the objective of the project.
   • Development: Detail the theoretical background of the project's central themeof the project, elaborate on the activities, illustrate the methodology used, and finally discuss the results obtained.
   • Conclusion: Conclude the work by revisiting its main points, stating the learnings obtained and the conclusions drawn about the project.
   • Bibliography: Indicate all the sources that they relied on for the project.

2. Presentation: Each group will present their project in front of the class, explaining each percent problem identified and solved by them. They should also exhibit teamwork and presentation skills.

3. Peer Evaluation: Each student will evaluate their group members based on their contribution to the project, which will help develop the skill of constructive feedback.

By the end of the project, students are expected to have a solid grasp of the theoretical aspects of percentages and their practical applications, along with improved collaboration, problem-solving, and creative thinking skills.