There are three relationships that can exist between two quantities: The first is greater than the second, the first is less than the second or the first and the second are the same. The symbols that show these relationships between quantities are, as examples:

1. 3 > 1 Three is greater than 1
2. 1 < 3 One is less than 3
3. 3 = 3 Three is equal to three.

3 is greater than 1 (3>1) because 3 is to the right of 1 on the number line.
 

1 is less than 3 (1<3) because 1 is to the left of 3 on the number line. 3>1 and 1<3 mean the same and are equivalent statements. Students should use the number line to determine one of the three relationships between two numbers. The statement of an equation or an inequality is called a number sentence.
 

Expressions indicate an operation between numbers and represent a single numeric quantity. For example, 5+3 represents the quantity 8. There are many expressions that also represent the quantity 8. Students should be encouraged to explore the many expressions that can represent a numeric quantity. Students often confuse expressions with equations and use the symbol = along with the expression.

When writing expressions, students should be prompted to simply "express" the quantity described in the problem situation with numbers and operational symbols only. Once they have shown a fluency in writing numeric expressions for a given quantity, they should then determine one of the three relationships discussed above between these various expressions.