Date: May 31, 1999

Grade Level(s): 6, 7, 8, 9, 10, 11, 12, Adult/Continuing Education

Subject(s):

• Mathematics/Algebra

Description: I cannot take credit for the "smiling man." It was presented to me in a pre-algebra class many years ago. It is used in factoring an expression as well as a FOIL method substitute.

Goals: Students will engage in factoring problems.

Objectives: The students will factor trinomials with 90% accuracy and use the "smiling man" to check if the factoring is done correctly.

Materials:

• pencils and paper

Usually given by board examples and teacher lead discussions.

FOIL: (x+2) (x+3)

1. The student draws an arched line from the top of one x to the top of the other x. [x multiplied by x equals x² ]

2. Next, the student draws a U-shaped line from the bottom of the first x to the bottom of the 3. [x multiplied by 3 equals 3x]

3. Then the student draws a U-shaped line from the bottom of the 2 to the bottom of the second x. [2 multiplied by x equals 2x]

4. Lastly, the student draws an arched line from the top of the 2 to the top of the 3. [2 multiplied by 3 equals 6]

If done correctly you see two arched lines forming something like eyebrows. The outer facing ( ) form loosely the ears, and the lines facing up in a U-shaped pattern where the two numbers are added form the nose and mouth. Students should get the following result when combining terms: x² +5x +6.

Give students the following trinomial and have them factor it, checking their results using the "smiling man": x² -5x +6

Assessment: Informally assess students during class work. Ask for volunteers to go to the board to demonstrate the "smiling man" technique.