6th Grade Integers: An Introduction to Integers for 6th Grade Students

Intro to Integers

Integers include all whole numbers (0, 1, 2, 3…) and the negatives of the natural numbers (-1, -2, -3…). Up until 6th grade, you've probably just studied positive integers, but now you'll learn to work with negative integers as well.

Comparing Integers

You may already know how to compare whole numbers using the greater than and less than signs. For instance, 5 > 3 and 8 < 10. You can use these signs with negative integers, too. Just remember the integer that's farther to the right on the number line is greater. That means if you're comparing a negative integer with a positive one, the positive integer will always be greater because it's farther to the right. If you're comparing two negative integers, the one that's closer to zero is greater. Here are a few examples:

• -2 > -9
• -10 < 2
• 0 > -1

Ordering Integers

When we compare more than two integers, this is called ordering. To put a set of integers in order, follow the same rules that you use for comparing, and pay close attention to whether you're listing the integers from greatest to least or least to greatest. Here's a sample list of integers ordered from least to greatest:

-12 < -4 < 0 < 4 < 12

Absolute Value

An integer's absolute value is its physical distance from zero on a number line. Absolute values are always stated as positive integers. Since 14 and -14 are both the same physical distance from zero - just in opposite directions - their absolute values are both 14. Absolute value is indicated by placing vertical bars on either side of a number. For example, |-14| = 14 is read, 'The absolute value of -14 equals 14.' Here are a few more examples:

• |-3| = 3
• |5| = 5
• |-9| = 9

Once you've mastered absolute values, you might be asked to compare them like you did with integers. Remember that you're comparing the absolute values, not the integers themselves. For instance, |-7| > 6 because |-7| = 7 and 7 > 6.

Integers in Real Life

Positive and negative integers are used in lots of real-life situations to show amounts relative to zero. For example, when the temperature drops below zero, we say that it is negative. School might be canceled if it is -30 degrees outside. Positive and negative integers are also used with money. If you spend more money than you have in your bank account, your balance will be negative, which means you owe the bank money. For instance, if you had $50 in your account, and you spent $75, your balance would be -$25.