Representing Relationships as Expressions, Equations, and Inequalities
When students have a strong grasp of the terms "less than" and "greater than", they are ready to develop an understanding of (less than or equal to) and (greater than or equal to).
Materials: Overhead projector or front board.
Preparation: Review symbols and meanings of =, <, and >.
 Ask: Does 6 + 4 equal 9 or 10?
Students will say 10.
 Ask: Is it true if I say, "6 + 4 equals 9 or 10"?
This should start a class discussion surrounding the fact that this is a true statement because 6 + 4 = 10. The question, "Does 6 + 4 equal 9 or 10?" allows one to choose between two possible answers. Therefore, it is true to say, " 6 + 4 equals 9 or 10."
 Ask: Which symbol in the blank makes this a true statement: 2 + 9 = or < 15? Why?
the "less than" symbol because the left expression equals 11 which is less than 15
 Ask: Which symbol in the blank makes this a true statement: 7 + 4 > or = 11? Why?
the "equal to" symbol because the left expression equals 11 which is equal to 11
 Ask: Which symbol in the blank makes this a true statement: 8 + 5 > or = 10? Why?
the "greater than" symbol because the left expression equals 13 which is greater than 10
 Ask: Is it true that 8 + 5 > or = 10? Why?
It is true since one of the symbols makes this a true statement.
 Say: The symbol allows us to combine the symbols > and = and means "greater than or equal to."
 Ask: What do you think the symbol means?
Students should respond that the symbol allows us to combine the symbols < and =. is read as "less than or equal too."
 Ask: Using only < or >, which symbol would satisfy 6 + 9 ___ 12? Why?
>, because 15 is greater than 12.
 Ask: Using only < or >, which symbol would satisfy 5 + 4 ___ 9? Why?
Either < or >, because 9 is equal to 9. Students need to see the connection between the equality and the inequality.
 Continue with additional examples.
 Ask: Using <, , >, or , which symbol or symbols would satisfy 12 + 4 ___ 19? Why?
< or . Students need to realize that more than one inequality symbol could be used.
 Take time to develop this concept. Many students are not comfortable with exercises that have multiple possibilities. By using examples with multiple solutions, students will develop a better understanding of the concept and use of the mathematical notation.


