THIS TEACHING GUIDE IS THE THIRD OF FIVE EXPERIMENTAL EDITIONS CONCERNING MATERIALS AND METHODS FOR TEACHING A REVISED MATHEMATICS PROGRAM IN GRADE 8. BACKGROUND MATERIAL FOR TEACHERS AS WELL AS QUESTIONS AND ACTIVITIES FOR CLASSROOM PRESENTATIONS ARE PROVIDED IN THE CONTENT AREAS OF POLYNOMIAL EXPRESSIONS (UNIT 8) AND POLYNOMIAL EQUATIONS (UNIT 9). UNIT 8 CONTAINS SECTIONS ON ADDITION, SUBTRACTION, MULTIPLICATION AND DIVISION OF POLYNOMIAL EXPRESSIONS, AND FACTORING POLYNOMIAL EXPRESSIONS. UNIT 9 INCLUDES SECTIONS ON SOLUTION BY FACTORING, SOLUTION BY COMPLETING THE SQUARE, SOLUTION BY QUADRATIC FORMULA, GRAPHING QUADRATIC EQUATIONS, AND SIMPLE PROOFS. (RP)