Math Background

Lesson: Placing Negative Numbers on a Number Line
Developing the Concept

Now that students have created their own number lines and acquired an initial understanding of negative numbers, it is time to deepen that understanding by having them explore negative numbers further.

Materials: The number lines students created in the first lesson

  • Say: Take out your number lines, because we are going to use them to answer some questions.
  • Ask: Which two numbers are 5 units from zero?
    Which number is farther from zero, -7 or 5?
    Students should say that 5 and -5 are five units from zero and that -7 is farther from zero than 5 is.
  • Ask: Which two numbers are 5 units from 2?
    Which two numbers are 7 units from -3?
    Students will respond 7 and -3 and -10 and 4, respectively.
    Ask several other questions in which students identify numbers that are some set distance away from a given number.
  • Ask: What is the number 9 units to the left of zero?
    What is the number 7 units to the right of zero?
    What is the number 6 units to the left of 2?
    What is the number 5 units to the right of -8?
    What is the number 10 units to the right of -4?
    Questions like these and the ones above will prove helpful when students are asked to find the difference between two numbers such as -4 and 5.

    Draw a number line like the one shown below, with some of the numbers missing.

    number line
  • Ask: (pointing to each missing number) What is the name of this number?
  • Draw several other number lines that use a scale other than one. Ask students what some of the missing values are on the number lines you have drawn. Using a scale other than one is often needed when graphing numbers which vary greatly in size.

Wrap-Up and Assessment Hints
Create several true-or-false statements and have students use their number lines to tell you whether a statement is true or false.

The number 4 is 6 units to the right of -3. (False)
The number that is 8 units to the left of 3 is -5. (True)
The number -8 is to the left of -4. (True)
-4 and 3 are seven units apart on the number line. (True)
All negative numbers are to the right of zero on the number line. (False)

Houghton Mifflin Math Grade 5