Comparing Integers: >, <, =

Lesson Plan - Get It!

Audio:

The "Integer Shuffle" is an activity where you use your WHOLE body, especially your brain!

To do the "Integer Shuffle," you need to make a number line on the floor. You don't need to do it now. I just wanted to let you know in the beginning. Your number line needs to include both positive and negative numbers and zero.

What are integers? Simply put, integers are whole numbers and their opposites. Examples would be 1 and -1, and 1001 and -1001.

We see integers in our lives on a regular basis. If you have a bank account, when you deposit money, that is considered a positive integer. If you withdraw money, that is a negative integer. The temperature outside can be expressed in integers. Very hot days are positive integers, and any temperature below 0 is a negative integer.

Those are only two of many examples of integers in our daily lives. Because we deal with integers so much, it is important for us to know how to compare them and put them in order.

Before you can even think about setting up for the "Integer Shuffle," make sure you understand the vocabulary associated with ordering integers, and how to order them.

Vocabulary Copy the following vocabulary words and their definitions on a piece of paper. Then, draw a picture of each word next to it to help you remember the meaning (All definitions taken from www.mathematicsdictionary.com):

• less than To indicate one number is smaller than another

• greater than A symbol used to indicate one number is bigger than another

• equal The same in size, value, or amount

• ordering To arrange according to numerical value

• number line A straight line on which each point represents a real number

• positive A number that is greater than zero

• negative A number that is less than zero

Remember, integers include the counting numbers (1, 2, 3, 4, …), their opposites, or negative numbers (-1, -2, -3, -4, …), and zero. One way to learn how to put integers in order is through the use of a number line like this one:

Because integers include positive numbers, negative numbers, and zero, you need to make sure you include them when you draw your number line.

An important point to remember about using a number line when ordering integers is that the farther the number is to the right on the line, the greater or higher the number. So, numbers to the left are lower or less than numbers to the right. (See the Number Line Template in Downloadable Resources in the right-hand sidebar.)

When we are showing the order of two integers without the number line, we have symbols that we use. Look at the symbols below and their descriptions:

< Less than

> Greater than

= Equal

There are a couple ways to help you remember which symbol is which:

• The equal sign is a symbol we are already familiar with (=).
• One way to remember which sign is the greater or less than sign is to look at the point. The number that the point is facing is the smaller number. For example, 1 < 2.
• The other way to help you remember is to look at the opening of each sign. Some people refer to the signs as the head of an alligator, and the open end as the mouth. Whatever number the open end is facing is the higher number and the alligator is going to eat it.
• Use whatever way helps you remember which sign is which.

Go back to your number line with some integers and put them in order.

Here is a group of random numbers:

-9, 7, 0, -5, 6, -2, 10, 5, -3

Look at your number line and place a dot where each of these numbers falls on the number line, like this:
Now, the integers are in order. You can even write them in order off the number line:

(-9, -5, -3, -2, 0, 5, 6, 7, 10)

Great job! Looking at the number line, you can see that -9 is the number we plotted farthest to the left, so that is the lowest number in our group of integers. We also see that the number 10 is farthest to the right. This means 10 is the highest number in the our group of integers.

Continue on to the Got It? section to practice a little more before the Shuffle!