## Lesson: Comparing and Ordering Integers and Decimals Introducing the Concept

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 Learning Tool 5 in the Learning Tools Folder.

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.