Math Background

Lesson: Comparing and Ordering Integers and Decimals
Developing the Concept

Now that students have created their own number lines and acquired an initial understanding of ordering and comparing decimals, they can expand their understanding by comparing and ordering integers.

Materials: your model number line and the number line students completed from the first lesson; large model of a number line from 0 to −5; blank number line with write-on lines, for each student (see below)

number line

Preparation: Post your model number line from 0 to 5 where students can see it. Construct a model number line from 0 to −5. Prepare student number lines with write-on lines. Use Learning Tool 5 in the Learning Tools Folder.

  • Say: Take out your number lines, because we are going to use them to answer some questions.
  • Ask: Where would you find 4, or positive 4, on your number line? (Write 4 and +4 on the board.)
    Your students should say that +4 is to the right of 0 on the number line. Explain that positive numbers can be written with or without a positive sign and are found to the right of 0. Have your students put positive signs in front of 1, 2, 3, 4, and 5 on their number lines while you put positive signs on your model number line from 0 to 5.
  • Ask: Where would you find negative 4? (Write −4 on the board.)
    Students should say that −4 is to the left of 0 on the number line. If they don't, tell them that negative numbers are found to the left of 0. Show students the model number line from 0 to −5. Attach it to your model number line from 0 to +5, overlapping the number lines so that only one zero is showing. Explain that negative numbers must always have a negative sign in front of them. Point out that zero is neither positive nor negative, so neither sign is used with zero.
  • Say: These two number lines together make up the set of integers. Integers include zero, the positive numbers, and the negative numbers. (Point to zero, positive numbers, and negative numbers as you name them.)
  • Ask: Where is the number +1.5 on the number line? Where is the number −1.5 on the number line?
    Your students should use their number lines to point out where +1.5 is. They may be able to tell you where −1.5 is on your number line. If they don't, tell them that −1.5 is between −1 and −2. Then help them determine exactly where −1.5 is on your number line.
  • Say: The numbers +1.5 and −1.5 are called opposites. This means that they are both the same distance from 0 on the number line.
    Help students count the number of units from 0 for each number.

    Ask several other questions in which students locate numbers on the number line and identify and then locate the opposites of those numbers.

  • Ask: Which is greater, +1.5 or −1.5?
    Students should say that positive numbers are always greater than negative numbers; therefore +1.5 is greater than −1.5. Remind them that numbers to the right are always greater than the numbers to their left. Write +1.5 > −1.5 on the board.
  • Ask: Which is greater, −2.1 or −1.7?
    Students may incorrectly say that −2.1 is greater than −1.7. If they do, have them locate −2.1 and −1.7 on the number line. Then remind them that numbers to the right are always greater than the numbers to their left.

    Write −1.7 > −2.1 on the board.

    Ask several other questions in which students locate two numbers on the number line and then identify which of the numbers is the greater or lesser of the two.

  • Say: Now that you have a good idea of how you can find and compare integers on a number line, each of you will extend your number line to include negative numbers, using the number line I will pass out to you.

    Ask students to write neatly and to carefully place the numbers on the number line.
    Have the students join the two number lines so that they have one number line that looks like the number line from −5 to +5 that you have modeled.

Wrap-Up and Assessment Hints
Create several true-or-false statements and have students use their number lines to tell you whether a statement is true or false. If the statement is false, have students rewrite it to make a true statement.

+2.3 > −2.3 (True)
−1.8 > +0.9 (False; +0.9 > −1.8 or −1.8 < +0.9)
Zero is an integer. (True)
The number −8 is to the left of 150 on a number line. (True)
Negative 3 can be written as 3 or −3. (False; negative 3 can only be written as −3; positive 3 can be written as 3 or +3.)
The numbers −2.4 and +2.4 are opposites of each other. (True)
All positive numbers are to the left of zero on a number line. (False; all positive numbers are to the right of zero on a number line; all negative numbers are to the left of zero on a number line.)

Houghton Mifflin Math Grade 5