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

Teaching Notes 4.1: Graphing on a Number Line

Many students experience confusion when graphing inequalities on a number line. Knowing the

meanings of ‘‘closed’’ as opposed to ‘‘open’’ circles and the directions of arrows can eliminate

confusion.

1. Present an example of a number line and review its characteristics with your students. Note
   that every point on the number line can be paired with a real number, which is called the
   ‘‘coordinate’’ of the point.


2. Discuss the properties of the number line. Larger numbers are located to the right of smaller
   numbers. Provide examples such as 5>4, 3>−1, and− 5 >−6. Smaller numbers are
   located to the left of larger numbers; for example, 4<5,− 1 <3, and− 6 <−5.


3. Review the information and examples on the worksheet with your students.
   
   
   • Explain that a closed circle on the number line is the graph of the number that is paired
     with the point; for example,x=3. If a number line is shaded to the right, for example, as
     x≥3, the graph shows 3 and all numbers that are greater than 3, including decimals and
     fractions. Note thatx ≤3 shows 3 and all the numbers less than 3.
   
   
   • Explain that an open circle on the number line does not include the number that is paired
     with the point on the number line. If a number line is shaded to the right, for example
     x>3, the graph shows all the numbers that are greater than 3. If a number line is shaded
     to the left, for examplex<3, the graph shows all the numbers less than 3.
   
   
   
   

EXTRA HELP:

Rewrite the inequalities so that the variable is on the left. Then the tip of the arrow points in the

direction the number line is shaded.

ANSWER KEY:

Asketchofeachgraphisshown.

(1)

− 4

(2)

0

(3)

2

(4)

− 1

(5)

− 2

(6)

7

(7)

− 6

(8)

5

(9)

1

(10)

0

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(Challenge)Because the inequalities are not equal to 5, the graph is a number line with an open

circle on the point paired with 5. The number line is shaded to the right of 5 and to the left of 5.

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138 THE ALGEBRA TEACHER’S GUIDE