Comparing and Ordering Integers and Decimals

You will want to give your students some real-life applications of comparing and ordering decimals through thousandths. Spend some time brainstorming for examples in which decimals are used, such as in batting averages, stock values, distances between cities, government budgets, bank-account balances, or points scored in Olympic competition. This discussion will help your students better understand the concept of the magnitude of numbers. Using a number line to compare and order numbers will help students visualize the concept of the magnitude of numbers.

Materials: large model of a number line from 0 to 5; blank number line with write-on lines, for each student (see below)

Preparation: Construct a large number line and post it where students can see it. Prepare student number lines with write-on lines. Use Teaching Tool 25 in the Teacher Resource Book.

Prerequisite Skills and Concepts: Your students will have worked with number lines before. They should be able to tell you where 1.5 is on a number line. They should be able to tell that any number to the left of 1.5 is less than 1.5, and any number to the right of 1.5 is greater than 1.5. They should also be able to compare and order decimals in tenths and hundredths by using a number line or a place-value chart.

Show students the number line from 0 to 5 that you have made. Point to the section of the number line between 1 and 2. Tell students that there are decimal numbers to the left of 1, between 1 and 2, and to the right of 2.

• Ask: (pointing to the mark for 1.5) Does anyone know what this number is called?
  If students do not come up with the correct answer, tell them it is 1.5.

• Ask: (pointing to each of the marks between 1 and 2) What is the name for this number?
  Students should identify each number as you point to its mark on the number line. Write the appropriate number on the number line as you proceed.

• Ask: Where would I find 1.45 on the number line? 1.67? 1.82?
  Students should answer halfway between 1.4 and 1.5; between 1.6 and 1.7 but closer to 1.7 than 1.6; and between 1.8 and 1.9 but closer to 1.8 than 1.9, respectively.
  Indicate the position of each number. Then state that 1.45 is less than 1.67 and also less than 1.8, and that 1.67 is less than 1.82.

• Ask: What is the same about the numbers 1.45 and 1.456?
  Students should reply that both have 1.45 in them. Point out that both numbers have the same ones, tenths, and hundredths digits, and both numbers are between 1.4 and 1.5 on the number line.

• Ask: What is different about the two numbers?
  Students should say that 1.456 has a 6 and 1.45 does not. Point out that since 1.456 has a digit in the thousandths place, and 1.45 does not, 1.456 is to the right of 1.45 on the number line. Therefore, 1.456 is greater than 1.45. Label both numbers on your number line.

• Ask: Tell me something that is the same about the numbers 1.753 and 1.768. Tell me something that is different about the two numbers.
  Students should reply that both begin with 1.7 and each has three digits after the decimal. Point out on the number line that both numbers are between 1.7 and 1.8. Students should also say that what is different about the numbers is that 1.743 ends with 43 and 1.768 ends with 68. Point out that 1.743 is to the left of 1.768 on the number line. Therefore, 1.743 is less than 1.768. Label both numbers on the number line.

  On the board, draw a number line beginning with 152, with marks at 152 and 153 and nine marks between them.

• Ask: Is this number line part of the number line from 0 to 5?
  Students should say it is. Be sure to explain that the number line continues indefinitely in both directions. Point out that the decimal numbers 152.5 and 1.5 are both located on the fifth mark past their whole-number place values. Repeat questions similar to those above for decimal numbers beginning with 152, such as 152.5, 152.45, and so on.

• Ask: In which part of the number line from 0 to 5 would I find 0.5?
  Students should be able to point out the section from 0 to 1. Repeat questions similar to those above for decimal numbers such as 0.8, 0.45, and so on.

• Say: Now that you have a good idea of how to locate a decimal number in tenths, hundredths, and thousandths on a number line, each of you will label a number line from 0 to 5, using the strip of paper I will pass out to you.
  Ask students to write neatly and to carefully place the numbers on the number line so that it looks like the number line from 0 to 5 that you have modeled.