What is an Equation?
A statement that two quantities (two mathematical objects) are equal
An equation is a math sentence that says two things are equal. It uses an equal sign (=) to show that what’s on the left has the same value as what’s on the right.
You can think of an equation like a balance scale—both sides need to be equal for it to work.
Let’s look at a few examples:
- 3 + 2 = 5 → Both sides equal 5, so the equation is balanced.
- 7 = 7 → This simply shows that 7 is equal to 7.
- x + 4 = 10 → This means “What number plus 4 equals 10?” (The answer is x = 6.)
Equations can use numbers, symbols, or variables. When a variable is used (like x), we often solve the equation to figure out what the variable must be to make the equation true.
When students learn how equations work, they can use them to:
- Represent real-world problems: Equations help us turn word problems into math problems we can solve. For example, “I have 12 apples and give away some. Now I have 7” becomes 12 − x = 7.
- Show mathematical relationships: Equations describe how numbers are connected. For instance, the equation A = l × w shows how the area of a rectangle depends on its length and width.
- Find unknown values: When something is missing in a problem, we can use an equation to solve for it. For example, x + 5 = 9 helps us find that x = 4.
When Do Students Learn About Equations?
Students are introduced to equations early in elementary school through simple math sentences and build their understanding step by step.
Grades 1–2 – Math Sentences and Equality
Students begin working with number sentences and balancing simple equations like 3 + 2 = 5 and 5 = 5.
Grades 3–5 – Solving for Unknowns
Students use equations with symbols or variables (like □ or x) and solve simple one-step word problems.
Grades 6+ – Multi-Step and Algebraic Equations
Students solve more complex equations with multiple steps, variables, and operations. They also write their own equations to model real-world situations.
