Math Background

Lesson: Adding and Subtracting With Negative Numbers
Introducing the Concept

Your students have used number lines in the past to add and subtract whole numbers. Relating the addition and subtraction of negative numbers to that of whole numbers will help your students understand how to operate with negative numbers. It's important to reinforce the meanings of addition and subtraction in terms of moving left and right on the number line.

Materials: Large number line, student number lines

Prerequisite Skills and Concepts: Students need to be familiar with how to add and subtract whole numbers on a number line.

Place the large number line you created on a wall in front of the class so that all the students can see it. You could also use a number line drawn on an overhead transparency and shown on the wall.

  • Ask: Who can show us how to add 4 and 5 on the number line?
    Students should suggest starting at 4 and moving 5 places to the right to the number 9. Your students may object to this sort of work with basic facts they already know, but encourage them to “play along.”
  • Ask: What do you think I should do to add 4 and -5 on the number line?
    If no one suggests starting at 4 and going 5 units to the left, bring it up. Explain that it would be like going 4 steps forward and then 5 steps backward. You would end up one step back from where you began.
  • Say: Let's try another one. Use your own number lines and find the sum of -3 + 6.
    Have a student explain how to do it by using the number line up front. Do several other examples.
  • Ask: Who can tell us how to add any two numbers on the number line?
    Students should state that you start at one number and move the number of units indicated by the second number in the direction indicated by the sign of the second number, right if positive and left if negative. This is a very important concept. Students need to adjust their thinking about addition — addition does not always signal to go to the right!
  • Ask: Who can explain how to find 8 − 5 by using the number line?
    Students should say to start at 8 and move five units to the left to the number 3. Point out that the number subtracted was +5 and that to find the answer, we went in the opposite direction of +5. Do another example, such as 8 − 2. Stress that we had to move 2 units to the left of 8.
  • Ask: How would we do the following problem on the number line: -2 − (+5)?
    If students have trouble doing this problem, show them that since they are subtracting, they need to start at -2 and then move 5 units to the left.

Houghton Mifflin Math Grade 5