Representing Relationships as Expressions, Equations,
and Inequalities
The terms expression, equation, and inequality have different mathematical meanings. It is very important in the mathematical development of your students to clearly explain and model the significant differences between these terms. Each term will appear more and more as children progress through school and life. The understanding of each term allows students to take important steps in laying the proper foundations for algebra. An expression consists of a number, variable, or a combination of numbers and variables joined by operation symbols. Examples of expressions are:
3 + 4
2a
3c + 8
 7
Notice that expressions do not contain an equality or inequality sign. An equation is a mathematical sentence in which two expressions are joined by an equal sign (=). Examples of equations are:
5 + 2 = 7
3 + y = 8
12 = 4a
4 + 6 = 9 + c
An inequality is a mathematical sentence in which two expressions are joined by relations symbols such as  (not equal to), > (greater than), < (less than),  (greater than or equal to),  (less than or equal to). Examples of inequalities are:
| x + 4 5 | x plus 4 is not equal to 5 |
| 5 > 1 | 5 is greater than 1 |
| 10 < 10.5 | 10 is less than 10 and 5 tenths |
| 12 9 + 8 | 12 is less than or equal to 9 plus 8 |
| c 10 | c is greater than or equal to 10 |
Students begin working with expressions, equations, and inequalities before third grade. When learning basic addition facts, children learn that 5 + 3 = 8. This is an example of an equation. When students use flash cards to learn these facts, one side of the card shows 5 + 3 and the other side shows 8. Each side of the card is an expression.
When solving equations, children can think of an equation as a balanced scale. Each pan on the scale represents an expression, and the center support of the scale represents an equal sign. For the scale to be balanced, both sides of the scale must be equal. For example, the scale below is balanced because we have a total of 5 on each side of the scale: 4 + 1 = 5 and 5 = 5.
A scale can also be used to demonstrate inequalities. Each pan on the scale below represents an expression. The goal is to place an inequality sign at the center support of the scale to make a true mathematical sentence.
The left side of the scale shows the expression 4 + 1 + 2. The right side shows 5. Since 4 + 1 + 2 = 7, and 7 > 5, we need to use the > symbol at the center support.
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