## Representing Relationships as Expressions, Equations, and Inequalities

• Why should I bother learning this?
This is an excellent opportunity to connect mathematics with reading and language arts. In these subjects, children are frequently asked to learn the definition and spelling of new vocabulary words. This holds true for mathematics as well. Children need to understand the meaning of expression, equation, and inequality in order to further their experiences in mathematics.

• Is an expression the same as an equation?
No! An expression consists of a number, a symbol that stands for a number, or a combination of numbers and their symbols joined by operation symbols. Examples of expressions are:
3 + 5
6
12 + ___
An equation is a mathematical statement that shows two expressions to be of equal value. An equation contains two expressions and an equal sign. Examples of equations are:
2 + 6 = 4 + 4
7 - 2 = 5
4 + ___ = 3 + ___

• Why is 3 not a correct solution for 6 + ___ > 9?
Many children will expect 3 to be a solution for 6 + ___ > 9, because 6 + 3 = 9, and 9 = 9. One way to clarify this mistake is to have students read orally the inequality 6 + ___ > 9 as "six plus what number is greater than nine?" If 3 was a solution, the inequality would read "nine is greater than nine." Nine is not greater than nine, it is equal to nine. Therefore, we are looking for any number that would cause the expression on the left side of the inequality sign to be greater than nine.

• Is 3 the next number greater than 2?
For many younger students, whole numbers are all they think of when they think of mathematics. As fractions and decimals are introduced, children will begin to understand that 3 is greater than 2, but there are other numbers between 2 and 3, such as 2 1/2 and 2.6.

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