The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 5.1: Applying Monomial Vocabulary Accurately

Although the study of monomials is relatively easy, students often have trouble with the

terminology. Consistent reinforcement of the terms can help clarify confusion.

1. Discuss the following facts with your students:
   
   
   • A monomial is a numeral (called a ‘‘constant’’), a variable, or a product of a numeral and
     one or more variables. The exponent of each variable must be a positive integer.
   
   
   • The coefficient of the monomial is the numerical factor of the monomial (usually the first
     number). If a coefficient is not written, it is understood to be 1. For example, ‘‘1’’ is the
     coefficient of the monomialx.
   
   
   • The degree of each variable in a monomial is the number of times the variable occurs as a
     factor.
   
   
   • The degree of the monomial is the sum of the degrees of the variables in the monomial.
   
   
   
   


2. To summarize these facts, discuss the examples on the first chart on the worksheet with your
   students. Especially point out that 3xand

1

5

xare examples of similar monomials because

they have the same variable and degree.

EXTRA HELP:

Monomials are never sums or differences.

ANSWER KEY:

(1)10, 5, 6, 11 (2)1, 1, 1, 2 (3)−5, 3, 1, 4 (4)−

1

2

,3,2,5 (5) 5 xy,2 (6)

1

2

x^3 y^4 ,3

------------------------------------------------------------------------------------------

(Challenge)The commutative property of multiplication.

------------------------------------------------------------------------------------------

176 THE ALGEBRA TEACHER’S GUIDE