In arithmetic, we work with numbers we know, like $2 + 2 = 4$. But what happens when we don't know a number? What if you have a bag of apples, but you haven't counted them yet? In math, we have a way to talk about that unknown amount.

We use a symbol to stand in for the missing number. This placeholder is called a variable.

Think of a variable as a box. You might not know what's inside, but you know it's holding something. The most common letters used for variables are $x$, $y$, and $z$, but you can use any letter.

Once we have variables, we can combine them with numbers and operations to create mathematical phrases called algebraic expressions. An expression doesn't have an equals sign. It's just a statement of value.

This expression describes your age without knowing exactly how old your brother is. If he's 10, the expression's value is 15. If he's 12, it's 17. The expression works for any age.

Here are some other examples of expressions:

If an expression is like a phrase, an equation is like a complete sentence. An equation sets two expressions equal to each other using an equals sign ($=$).

The key idea is balance. Both sides of the equals sign must represent the same value, just like a balanced scale.

The diagram above represents the equation:

This equation makes a claim: "Some unknown number, when added to 2, equals 5." It's a mathematical statement that can be true or false depending on the value of $x$. Our goal in algebra is often to find the value of the variable that makes the equation true.

Let's check your understanding of these new concepts.

Variables are the building blocks of algebra, allowing us to turn word problems into math and generalize patterns.