Contextualization

Introduction to Percents

Percents are a fundamental concept in mathematics that is applicable to a range of everyday situations. Understanding percents is essential for interpreting data, solving problems involving discounts, taxes, and tips, and for understanding interest rates.

A percent is simply a fraction with a denominator of 100. The word 'percent' means 'per hundred', so 50% is the same as 50 per hundred, or 50/100, which simplifies to 1/2. Percentages are used in many different areas, from finance to medicine, from cooking to sports.

Real-world Application of Percents

The concept of percents is not isolated to the classroom. It's a concept that we use every day, often without even realizing it. When we see a "50% off" sign in a store, we know it means half-price. When we hear that a team has a 75% win rate, we know that they win 75 out of every 100 games. When we look at a nutrition label and see that a food has 10% of the recommended daily intake of a certain nutrient, we can quickly understand how much that is.

Resources

To delve deeper into the concept of percents, the following resources are recommended:

1. Khan Academy’s Introduction to percent
2. Math is Fun’s Percentages Explained
3. BBC Bitesize: Percentages
4. Book: "Mathematics: A Very Short Introduction" by Timothy Gowers. Chapter 3: "Percents and Proportions".
5. Video: Math Antics - Percent

Please use these resources to not only understand the concept of percents but also to explore its applications in real-world scenarios.

Practical Activity

Activity Title: "Percents in the Real World: A Shopping Adventure"

Objective of the Project:

The objective of this project is to understand the concept of percents and their real-world applications. You'll be learning how to calculate discounts, taxes, and tips, which are all based on percents. This project will also improve your teamwork and problem-solving skills.

Detailed Description of the Project:

In this activity, your group will simulate a shopping adventure at a virtual store. Each group will be given a list of items with their respective prices. You will be presented with different scenarios where you need to calculate the discount, tax, and tip, and then determine the final price of the items. The aim is to understand how percents are used in real-world situations, like shopping.

Necessary Materials:

• Internet access to use the virtual store and other resources
• A calculator
• Notebooks and pens for note-taking

Detailed Step-by-Step for Carrying out the Activity:

1. Form your Groups: Form groups of 3 to 5 students. Make sure everyone in your group has access to a computer with an internet connection.

2. Set Up your Virtual Store: Each group will be given a link to a virtual store. This store will have a list of different items with their prices.

3. Scenario 1: Calculate the Discount: Your group will be given a scenario where there is a discount on certain items. Calculate the discount for each item and determine the new price.

4. Scenario 2: Calculate the Tax: In this scenario, you need to calculate the tax on the items. The tax rate will be given to you as a percent.

5. Scenario 3: Calculate the Tip: Here, you need to calculate the tip for a service. The tip rate will be given to you as a percent.

6. Scenario 4: Calculate the Final Price: Finally, you need to calculate the final price, which includes the original price, the discount, the tax, and the tip.

7. Document your Work: Throughout the activity, make sure to document your work. Take notes on the steps you took to calculate the percents and the final price.

8. Write your Report: After completing the shopping adventure, each group will need to write a report detailing the process and the results. The report should include the following sections:

   • Introduction: Briefly explain the concept of percents and its real-world applications. Also, mention the objective of this project.

   • Development: In this section, explain the theory behind percents in detail and how it relates to the activity. Describe the activity in detail, the methodology you used, and present the results of the shopping adventure. Use tables or graphs if necessary to present the data.

   • Conclusion: Revisit the main points of the project, state the learnings obtained, and draw conclusions based on the results.

   • Bibliography: Indicate the sources you used to work on the project, such as books, web pages, videos, etc.

9. Present the Project: Each group will present their project to the class. The presentation should summarize the report and highlight the main findings of the project.

Project Deliverables:

1. Completed shopping adventure, where you've calculated the discount, tax, and tip for different items.

2. A written report following the format mentioned above.

3. A group presentation summarizing the project and its findings.

This project should take about 5-8 hours to complete and will be due two weeks from the date of assignment. Remember, this isn't just about understanding the concept of percents, but also about applying it in real-world scenarios and learning to work effectively as a team. Good luck!