Math Background

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

Your students will have used a number line before, but it may not have included negative numbers. Your students will also have had experiences with real-life applications that could be modeled by the set of integers. Spend some time discussing applications involving opposite directions, such as walking forward or backward, temperature going up and down, or profits and losses in a business. This will help your students better understand the concept of negative numbers.

Materials: large model of a number line from -10 to +10 with only zero and the numerals 1 to 10 written beneath their marks (see below); strips of paper for students to make their own number lines


Preparation: Construct a large number line and post it where students can see it. Cut out strips of paper for your students to construct their own number lines.

Prerequisite Skills and Concepts: Students will have worked with number lines before. They should be able to locate an unmarked number on the number line. They should also be able to add and subtract whole numbers by using the number line.

Show them the number line you made. Tell them that there are other numbers to the left of zero.

  • Ask: Who knows what the numbers to the left of zero are called?
    Students may say these are negative numbers. If they don't, tell them what they are.
  • Ask: Does anyone know what this number is called?
    (Point to the mark for -1.)
    Someone will probably respond, “negative one.” If not, give the answer.
  • Ask: (pointing to each of the negative integers one by one) What is the name for this number?
    Students should identify each number as you point to it on the number line. Write the appropriate numeral on the number line as you proceed.
  • Ask: How far away from zero is the number -4? -7? -9?
    Students should say 4 units, 7 units, and 9 units, respectively.
  • Ask: Tell me something that is the same about the numbers -5 and 5.Tell me something that is different about the two numbers.
    Students should reply that -5 and 5 are both 5 units from zero. They might say that both have a 5 in them, which could lead you to point out how each is 5 units from zero. Students may also say that what is different about -5 and 5 is that one is to the left of zero and one is to the right of zero.
  • Ask: Which is farther from zero, -4 or 7?
    Which is farther from zero, -8 or 3?
    The number 7 is seven units from zero, and -4 is only four units from zero. Therefore, 7 is farther from zero than -4 is. The number -8 is eight units from zero, and 3 is only three units from zero. Therefore, -8 is farther from zero than 3 is.
  • Show students the number line below and ask them what number is represented by each of the question marks.
  • Say: Now that you have a good idea of what a number line with negative numbers looks like, each of you will make a number line, using the strip of paper I will pass out to you.
    Tell them to write neatly and take care to place the numbers appropriately on their number line, so that it looks like the one you have modeled.

Houghton Mifflin Math Grade 5