## 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.