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Grade 5
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Developing The Concept

Adding and Subtracting with Negative Numbers

Materials: Large number line up front for the class to see, student number lines

  • Say: We've been learning how to add and subtract with positive and negative numbers on a number line. Do the following additions on your number line: negative3 + (negative4); negative6 + (negative3); negative2 + (negative4).
  • Ask: Is there anything that is the same about all of the answers?
    Students will respond that all the answers are negative.
  • Ask: Do you think that when we add two negative numbers, the sum will always be negative? The answer is yes.
    Have students give some examples to support their answers, such as walking backwards 3 steps then backwards 4 steps more or borrowing 5 dollars and then borrowing 3 dollars more.
  • Ask: When we add two positive numbers, do we always get a positive number? (Yes)
    If students ask about the sign of the sum when adding a positive and a negative number, you can tell them that it will vary depending on the numbers being added. If your students seem adept with the basic concepts, point out that the number which is farther from zero determines the sign of the answer.
  • Ask: If the sum of two negative numbers is negative8, what could those two numbers be?
    If the sum of a positive and a negative number is negative3, what could those two numbers be?
    If the sum of a positive and a negative number is +4, what could those two numbers be?

    A good homework project would be to find all the pairs of numbers between negative8 and 8 whose sum is negative3.
  • Ask: How does the sum of 5 + (negative9) compare to the sum of negative9 + 5?
    How does the sum of 6 + (negative4) compare to the sum of negative4 + 6?
    What property do these illustrate?

    Make sure that students recognize that the commutative property for addition is true for integers. Similarly, emphasize that the associative property for addition is true for integers.
  • Have the students do the following subtraction problems using their number lines:
    negative7 – (+2) and negative7 + (negative2)
    negative3 – (+4) and negative3 + (negative4)
    negative6 – (+1) and negative6 + (negative1)
    and
    negative5 – (+4) and negative5 + (negative4).
  • Ask: What was true about the answers for each pair of problems?
    It should be stated by them or by you that subtracting a positive number from a negative number always gives a difference of which is negative, and that subtracting a positive number is like adding the opposite of that number.
  • Ask: If the difference between a positive and a negative number is negative7, what could those two numbers be?
    (Possible answers: negative5 – (+2); negative6 – (+1); negative3 – (+4))
    If the difference between a positive and a negative number is negative4, what could those two numbers be? (Possible answers: negative3 – (+1); negative2 – (+2))

Wrap-Up and Assessment Hints
Students should be allowed to create and use number lines during assessment. You may want to encourage more advanced students to practice adding and subtracting with negative numbers without using a number line. Also, give students problems that test their understanding of the properties of addition using negative numbers.

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

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