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Grade 5
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Introducing the Concept

Placing Negative Numbers on a Number Line

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 which 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 relate to the concept of negative numbers.

Materials: large model of a number line from negative10 to +10 with the numerals for 0 to 10 written beneath their marks and the marks for the numbers negative1 to negative10, but not the numerals (See the number line below); strips of paper for students to make their own number lines

 

    Placing Negative Numbers
    on a Number Line
    Adding and Subtracting
    with Negative Numbers

 

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 should 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 using the number line.

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

  • Ask: Does anyone know what the numbers to the left of zero are called?
    Students may say they 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 negative1.)
    Someone will probably say, "negative one." If they don't, tell them what it is.
  • Ask: (Point 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 down the appropriate numeral on the number line as you proceed.
  • Ask: How far away from zero is the number negative4? negative7? negative9?
    Students will say 4 units, 7 units, and 9 units, respectively.
  • Ask: Tell me something which is the same about the numbers negative5 and 5. Tell me something that is different about the two numbers.
    Students will reply that negative5 and 5 are both 5 units from zero. They might say that they both have a "5" in them, which could lead you to point out how they are both 5 units from zero. Students will say that what is different about negative5 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, negative4 or 7?
    Which is farther from zero, negative8 or 3?
    The number 7 is seven units from zero and negative4 is only four units from zero. Therefore, 7 is farther from zero than negative4 is. The number negative8 is eight units from zero and 3 is only three units from zero. Therefore, negative8 is farther from zero than 3 is.
  • Show them the number line below and ask them what number is represented by each of the "?" 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 so they can read their number lines and to be careful to place the numbers appropriately on their number line, so that it looks like the one up front.
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