Identify What Changes

Welcome to Make Sense of Expressions and Inequalities, and congratulations on taking the first step in this course! This is the first lesson out of four, so you are right at the beginning of your journey into the world of pre-algebra! In this lesson, you will learn how to look at an everyday situation, spot the quantity that changes, and represent it with a clearly defined variable. This skill is the foundation for everything else we will build together. By the end, you will be able to:

• Distinguish fixed quantities from varying quantities in everyday situations.
• Identify the quantity that changes and choose a variable letter to represent it.
• Write a clear variable definition that states what the variable represents and includes its units.

Let's think about something we all do naturally. When you glance at a grocery receipt, you instinctively know that the store's name at the top never changes, but the total at the bottom depends on what you bought. In daily life, you constantly separate things that stay the same from things that shift.

Once you can pinpoint what is changing in a situation, you can describe the entire pattern in a compact, reusable way. That is exactly the skill you are building in this lesson.

Every real-world situation contains quantities, and these quantities fall into two camps:

• Fixed (constant) quantities stay the same within the situation. For example, a monthly subscription fee of $15 does not depend on how much you use the service.
• Varying (changing) quantities can take on different values. The number of extra gigabytes of data you use each month, for instance, is different from one month to the next.

A helpful question to ask yourself is: "Could this number be different next time?" If the answer is yes, you are looking at a varying quantity.

In this lesson, you learned how to scan a real-world situation for the quantity that changes, assign it a meaningful variable letter, and write a clear definition that includes the quantity's name and units. These three small steps may seem simple, but they set the stage for every expression, equation, and inequality you will encounter later in this course.

Up next, you will put these ideas into action with a set of hands-on practice tasks. You will sort fixed and varying quantities, fill in variable-definition templates, and even critique a vague definition to make it better, so get ready to roll up your sleeves!