Context

Introduction

Percentages form an essential part of mathematics and are regularly used in the real world. They provide a way of expressing a number as a fraction of 100 and are extremely useful in a variety of situations. Each percentage is equivalent to a fraction with a denominator of 100. For example, 25% is the same as the fraction 25/100 or one quarter.

The key concepts that will be covered in this project focus on understanding and calculating the most common percentages: 10% (a tenth), 25% (a quarter), 50% (a half), 75% (three quarters) and 100% (the whole). These percentages form the basis for many of the more complex percentages that can be encountered and, once these foundational percentages are understood, they can be used to calculate other percentages.

Calculating percentages of a number is also a crucial concept that will be covered. It is a concept that is used frequently in mathematics and in many real-world applications, so fully understanding how to calculate percentages is an extremely valuable skill.

Why are Percentages Important?

Percentages are used in a range of real-world contexts. They are used to help make sense of data, such as in opinion polls where the responses of a group of people are often expressed as a percentage of the total. They are also used extensively in financial literacy to help understand concepts such as interest, discounts and tax. In short, percentages are an essential tool in communicating information in a clear and understandable way.

In more practical terms, dealing with percentages is used to calculate discounts, understand the nutritional content of food and assess performance in sports, just to name a few examples. Having a good understanding of percentages will help us to better navigate many everyday situations.

Percentage Shopping Practical Activity

Project Aim

The aim of this project is to familiarise students with the concepts of percentages through a practical shopping and budgeting activity. The students will be assessed on their understanding of the theoretical concepts as well as the effectiveness of their collaboration and teamwork.

Project Description

For this activity, students will be split into groups of 3-5. Each group will be given a pretend amount of money and a list of items with varying prices to "buy". In addition, each item will be on "sale", with discounts ranging from 10%, 25%, 50% and 75%. Some items will have more than one discount applied sequentially.

The groups will need to calculate the price of each item after applying the discount(s), plan their purchases to ensure that they do not spend more than the amount of money they have been given, and finally produce a report detailing the process they used to come to their purchasing decisions.

Required Resources

1. Paper and pens for calculations and note-taking.
2. Calculators
3. A list of items to "buy" with prices and discounts marked.
4. Pretend "money".

Step-by-Step Process

1. Preparation: The teacher will prepare lists of items with varying prices and discounts of 10%, 25%, 50% and 75%. Each student will be given a pretend amount of money.
2. Planning: The groups of students will discuss which items they want to "buy" and will calculate the price of each item after the discount has been applied. They should ensure that the total of their planned purchases does not exceed the amount of money they have been given.
3. Shopping: The students will carry out their "shopping" based on their plan. The teacher will check that their discount calculations are correct.
4. Report: Each group will produce a detailed report of their purchasing decisions and the process they used to calculate the discounts. The report should include an Introduction, Development, Conclusions and Bibliography.

Project Deliverables

At the conclusion of this project, each group will submit:

1). A written report: Each group will prepare a written report detailing their purchasing decision-making process and discount calculations. The report should be structured as follows:

• Introduction: In this section, the students will provide context for the project, explaining its relevance and real-world application.
• Development: The students will explain the theory behind percentages, detail the process they used to plan their purchases, calculate the discounts and finally, compare the outcome to their plan. They should state the methodology used and discuss the results.
• Conclusion: The students should summarise the main points, highlight their learning and state their conclusions about the project.
• Bibliography: The students should reference any sources they used to complete the project, if applicable.

2. An oral presentation: Each group will present their purchasing decisions orally and explain the process they used to calculate the discounts. They should explain how they collaborated and worked as a team to complete the activity.