What Is an Integer?

An integer is any whole number - positive, negative, or zero.

The set of integers includes:

... -4, -3, -2, -1, 0, 1, 2, 3, 4 ...

Integers continue infinitely in both directions on the number line.

Integers include:

Positive whole numbers: 1, 2, 3, 100, 1,000
Negative whole numbers: -1, -2, -3, -100
Zero: 0

Integers do NOT include:

Fractions: 1/2, 3/4
Decimals: 0.5, 3.7, -2.5

Integers on the Number Line

A number line is the clearest way to visualize integers. Zero sits in the middle. Positive integers extend to the right, negative integers extend to the left.

← -4 -3 -2 -1 0 1 2 3 4 →

Key relationships:

Every positive integer has a negative counterpart called its opposite: the opposite of 3 is -3
The absolute value of an integer is its distance from zero, regardless of sign: |−5| = 5 and |5| = 5
As you move left on the number line, numbers get smaller: -5 < -2 < 0 < 3

Comparing Integers

When comparing two integers, the one farther to the right on the number line is greater.

-3 < -1 (because -1 is to the right of -3) 0 > -5 (because 0 is to the right of -5) -10 < 2 (because 2 is to the right of -10)

Common mistake: students often think -10 is greater than -2 because 10 is greater than 2. Remind them to think about the number line - -10 is farther from zero in the negative direction.

Real-World Contexts for Integers

Integers make sense in the context of:

Temperature: 5°F above zero = +5; 12°F below zero = -12
Elevation: 200 feet above sea level = +200; 282 feet below sea level = -282
Money: earning $20 = +20; owing $15 = -15
Football: a 7-yard gain = +7; a 3-yard loss = -3
Floors in a building: floor 3 = +3; basement level 2 = -2

Practice Activities

Draw a large number line on the floor with tape. Give students integer cards and have them stand in the correct position. Quiz: who is standing closest to zero? Farthest left?
"Real-world integers" - give students scenarios (temperature, elevation, money) and have them write the integer that represents each situation.
Compare integers using <, >, =. Mix positive and negative comparisons to address the common misconception.
Plot integers on a number line and use them to answer questions: "What integer is 3 to the right of -2?" "What is the opposite of -7?"

Frequently Asked Questions

What is an integer?

An integer is any whole number - either positive, negative, or zero. The set of integers includes: ...,-3, -2, -1, 0, 1, 2, 3,... and so on in both directions. Integers do not include fractions (like 1/2) or decimals (like 3.7). Every whole number you count with is a positive integer; the mirror image below zero is a negative integer.

What is the difference between an integer and a whole number?

Whole numbers include only 0, 1, 2, 3, 4... (zero and the positive whole numbers). Integers include whole numbers AND their negative counterparts: ...-3, -2, -1, 0, 1, 2, 3... So all whole numbers are integers, but not all integers are whole numbers (negative integers like -5 are not whole numbers).

Where do students encounter integers in real life?

Integers appear in many real-world contexts: temperatures below zero (-12°F), floors below ground level in a building (floor -1, floor -2), debt (owing $15 is like having -15 dollars), elevation below sea level (Death Valley is at -282 feet), and football yardage (a 5-yard loss is -5 yards). These contexts help students understand why negative numbers are useful.