Integers on the Number Line
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Learning Objectives
- 1Identify integers as positive whole numbers, negative whole numbers, and zero
- 2Place positive and negative integers at their correct tick on a number line
- 3Recognize opposite integers as mirror values across zero
- 4Describe absolute value as the distance from zero on the number line
Mini Lesson
Integers are the whole numbers together with their opposites. They include the counting numbers 1, 2, 3, the negatives -1, -2, -3, and the special integer zero. Integers show up in temperatures, elevations, money, scores, and any situation that has a clear "above and below" or "forward and backward" direction.
What Counts as an Integer?
- Positive integers: +1, +2, +3, +4, ... (often written without the plus sign)
- Negative integers: -1, -2, -3, -4, ...
- Zero: 0 — the boundary integer, neither positive nor negative.
- Integers do NOT include fractions or decimals like 1/2 or 3.7.
The Number Line Orders Every Integer
- Draw a horizontal line and mark zero in the middle.
- Positive integers sit to the right of zero, growing larger as you move right.
- Negative integers sit to the left of zero, growing more negative as you move left.
- Each step left or right is the same size, so every integer has its own tick.
- A number on the LEFT is always less than a number on the RIGHT.
Opposites — Mirror Integers Across Zero
Two integers are opposites if they sit the same distance from zero but on different sides. +3 and -3 are opposites. +7 and -7 are opposites. The opposite of zero is zero itself. Opposites always add to zero: +3 + (-3) = 0.
Absolute Value (Light Intro)
The absolute value of an integer is its distance from zero on the number line. Distance is never negative, so absolute values are always positive (or zero). We write absolute value with two vertical bars: |-3| = 3 and |+3| = 3 — both integers are 3 steps from zero. Opposites always share the same absolute value.
- |+5| = 5 — five is five steps from zero.
- |-5| = 5 — negative five is also five steps from zero.
- |0| = 0 — zero is zero steps from itself.
- |-12| = 12 — drop the sign and you are left with the distance.
Tip: when you compare two negatives, the one closer to zero is greater. -2 is greater than -8, even though 8 is bigger than 2. Think of temperature: -2 degrees is warmer than -8 degrees.
Guided Practice
Exercises
Click the correct tick on each number line.
Click the tick that shows -7 on this number line from -10 to +10.
Click the tick that shows +3 on this number line.
Which tick shows zero — the boundary between positive and negative integers?
Click the tick that shows -4 — the opposite of +4.
Which tick shows the greatest integer on this number line?
Which tick shows the integer with absolute value 6 on the negative side?
Sort each integer into the correct bucket: Positive, Negative, or Zero.
Positive
Negative
Zero
Pick the best answer for each question.
1. Which of these is NOT an integer?
2. On a horizontal number line, where do negative integers sit?
3. Which integer is GREATER: -2 or -9?
4. What is the OPPOSITE of +7?
5. Which integer has the SAME absolute value as -8?
6. Which list of integers is in order from LEAST to GREATEST?
7. Is zero a positive integer, a negative integer, or neither?
8. Which real-life situation is BEST described with a negative integer?
Assessment
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