Representing Relationships as Expressions, Equations, and Inequalities
Without realizing it, your students simplified expressions and solved equations when they were asked to add and subtract given numbers. They probably didn't know that 5 + 3 is an expression and 7 + 2 = 9 is an equation. When working with inequalities, it is important for students to understand these terms. This will allow them to clearly understand the similarities and differences between equations and inequalities.
By third grade, students have had prior work comparing and ordering whole numbers. Some students may have already been introduced to some inequality symbols, such as > (greater than) or < (less than). It is extremely important that children fully understand the meaning of these and other inequality symbols such as (not equal to), (greater than or equal to), and (less than or equal to). Therefore, getting children to use the correct mathematical language as well as learning the appropriate symbols to use is essential.
Materials: Overhead projector or front board
Preparation: None
Prerequisite Skills and Concepts: Students should have a working knowledge of simplifying expressions using addition and subtraction.
 Write 5 + 3 and 5 + 3 = 8 on the board or overhead. Have a student real aloud the expression 5 + 3 and the equation 5 + 3 = 8.
 Ask: What is the difference between 5 + 3 and 5 + 3 = 8?
Many students will quickly respond by stating that one has an answer and the other does not.
 Ask: Besides the numerical answer, what else is different between 5 + 3 and 5 + 3 = 8?
The goal is for students to realize that 5 + 3 = 8 has an equal sign.
 Say: 5 + 3 is called an expression. An expression consists of a number or a combination of numbers joined by operation symbols. An expression does not have an equal sign.
Erase 5 + 3. Point to 5 + 3 = 8.
 Ask: What is on the left side of the equal sign? What is one the right side?
Elicit from students that an expression is on both sides of 5 + 3 = 8. Try to have students describe the numbers as well as the operation. The left side has 5 + 3 while the right side only has 8.
 Say: 5 + 3 = 8 is called an equation. The left side of an equation equals the right side.
 Ask: Does the left side of the equation 5 + 3 = 8 equal the right side?
The goal is for students to notice that the expression on the left side of the
equation equals the expression on the right side of the equation.
 Write 3 + 4 ____ 10 on the board.
 Ask: What is the value of the expression on the left side of the blank? What is the value of the expression on the right side?
The goal is for students to realize that the expression on the left side is less than the value of the expression on the right.
 Ask: Does it make sense if I write the words "equal to" in the blank of 3 + 4 ____ 10? Why not?
We want students to make connections between the mathematical symbols and language used.
 Ask: What words would make sense in the blank?
You are trying to get students to use the words "less than" in the blank. Write < in the blank.
 Write 7 + 6 ____ 5 on the board or overhead.
 Ask: What words would make sense in the blank for 7 + 6 ____ 5?
You are trying to get the students to use the words "greater than" in the blank. Write > in the blank.
 Continue with additional examples using different inequalities. Try using two numbers on each side as well. When introducing the concept, use the words "less than" and "greater" than before using the symbols.


