Context

Modular Equations is a branch of mathematics that deals with solving equations which include the absolute value expression also known as the modulus. These types of equations are fundamental to mathematics and once understood can be a powerful tool to help you solve more complex maths problems in high school and even beyond.

Modular Equations involve equations using the absolute value which is the real number line and a great stepping stone to help understand more complex equations in subjects such as physics and engineering. Exploring the topic of modular equations gives you a greater understanding of the properties of the real number system and can lead to solving many more questions across the mathematics curriculum and its applications.

It is important to note that the modular equations have significant real world applications. In the field of Engineering for example, they are used to model situations where only the magnitude of a quantity is important rather than its direction. In the business world and economics modular equations are often used in risk analysis where the size of the error is more important than the direction of the error. In Economics modular equations can be used to understand issues surrounding inequality of income and wealth.

There are several resources available to students who wish to enhance their knowledge of this subject:

1. Khan Academy: Intro to Absolute Value Equations and Inequalities

2. Purplemath: Absolute Value Equations and Inequalities

3. Varsity Tutors: Intro to Absolute Value Inequalities

Practical Activity: "Cracking the Code to Modular Equations"

Project Aim:

To solve a range of problems involving modular equations, understanding and applying their theoretical concepts to practical situations whilst experiencing collaborative teamwork, exchange of ideas and building knowledge as a team.

Project Outline:

Teams of 3 to 5 students will each produce a "Modular Equations Problem Solving Kit" which includes:

1. An instruction manual explaining how to solve modular equations, in a step by step format.

2. At least three fully worked examples, demonstrating how to use the steps.

3. A five question quiz on solving modular equations.

4. Five real world problem solving examples which can be solved using the application of modular equations.

Resources:

• Computers with internet access for research purposes.
• A4 paper.
• Coloured pens/pencils.

Step by Step:

1. Research: Using the suggested websites and any others you think are useful, research modular equations, their properties, how they are solved and where they are used in the real world.

2. Discuss: Meet as a team either online or in person to discuss your findings and build a shared understanding of modular equations, clarifying any uncertainties.

3. Produce the Manual: Using your shared understanding create an easy to understand step by step instruction manual for solving modular equations, including worked examples.

4. Create the Quiz: Produce a quiz of five questions on modular equations which can be used to test understanding of those using the kit.

5. Create Real World Examples: As a team, think about and develop five real world examples of where modular equations can be applied as part of the solution.

6. Review and Finalise: Review the work you have done, correcting any errors and finalise your "Modular Equations Problem Solving Kit".

Submission: Each group will submit their "Modular Equations Problem Solving Kit" along with a written report (which can be either typed or handwritten) including:

1. Introduction: An explanation of what modular equations are, their importance and real world applications.

2. Methods: A step by step explanation of how to solve modular equations along with a detailed account of your team's journey, showing the methods you used and including the examples, quiz and real world examples you created.

3. Conclusion: Summarise the main points of your work, highlight what you have learnt and reflect on the experience of working on this project as a team.

4. Bibliography: List the sources you consulted during your project.

Students should expect to spend 2 to 4 hours working on this project individually, and the project should be completed within one week of the start date.

In completing this project, aside from developing their mathematical knowledge around modular equations, students will also develop key employability skills such as time management, effective communication, problem solving, critical thinking, initiative, and teamwork.