Math Background

Lesson: Adding and Subtracting With Negative Integers
Introducing the Concept

Your students have worked with adding and subtracting integers on a number line, but it is a good idea to start by reviewing the basic skills of adding and subtracting on a number line. This will provide a visual model of what they are doing and should help them understand and remember the rules.

Materials: a large number line on the chalkboard or on an overhead transparency

Prerequisite Skills and Concepts: Students should know how to add and subtract positive numbers using a number line.

Use the large number line you made or the one you made on the overhead transparency.

  • Point to various points on the number line and Ask: What is this point? What is this point? What kinds of points lie to the left of zero on the number line?
  • Ask: Who would like to come up and show us how to add 5 + 3 using the number line?
  • Ask: Who would like to come up and show us how to add 5 +-3 on the number line?
    You may need to demonstrate this. Explain that you start with the 5 and then go the directed distance of the number that follows when adding, in this case   -3 units or 3 units to the left.

    Have students do the following examples of adding integers at their desks, and then have volunteers demonstrate the solutions for the class: 3 + (-7); -4 + (-3); -5 + 7; -6 + 2; 8 + (-4). Put a list of all the problems done on the board off to the side for students to refer to as you ask the following questions.

  • Ask: If we add two negative integers, is the sum positive or negative? If we add two positive integers, is the sum positive or negative?
  • Ask: If I add a positive integer and a negative integer, how can I tell if the sum is positive or negative?
    Stress that the sign of the sum of a positive integer and a negative integer depends on which number is farther from zero.
  • Ask: What is the relationship between addition and subtraction?
    Students will probably say that they are inverse operations or that subtraction “undoes” addition.
  • Ask: Since -3 + 5 would mean to go 5 units to the right from -3 on your number line, what does -3 − (+5) mean on your number line?
    Students should say to do the opposite of going 5 units to the right — in other words, go 5 units to the left. If they don't, tell them that subtraction means to go in the opposite direction of the number that is to be subtracted. Give them a new problem: 4 − (-3).
  • Ask: Who can show us how to do this new problem using the number line?
    Pose several more subtraction problems for them to do at their desks.
  • Ask: Who can summarize what you do when you add on the number line?
    Make sure students go to the first number on the number line, and then they go the number of units of the second number in the direction indicated by the number's sign.
  • Ask: Who can summarize how to subtract integers on the number line?
    Make sure students go to the first number, and then they go the number of units of the second number in the opposite direction indicated by the number's sign.

Houghton Mifflin Math Grade 6