🔢 MathGrade 6Lesson 1
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Integers on the Number Line

  1. 1Print it first. Read it once together and talk it through.
  2. 2Exercises on paper, then correct together with the answer key.
  3. 3Next day: a 10-minute review here on screen saves progress.

What you will learn

  • 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
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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.

Words to know

integer

A whole number, its negative, or zero — no fractions or decimals.

positive

A number greater than zero, sitting to the right of zero on the number line.

negative

A number less than zero, sitting to the left of zero and written with a minus sign.

opposite

Two integers the same distance from zero but on different sides, like +4 and -4.

absolute value

The distance an integer is from zero on the number line; always zero or positive.

number line

A straight line that orders numbers from least on the left to greatest on the right.

Integers on the Number LineA horizontal number line from -10 to +10 with negative, zero, and positive regions labeled, and highlighted callouts for -7, -3, 0, and +5.Integers on the Number LineNegativeZeroPositive-10-9-8-7-6-5-4-3-2-10+1+2+3+4+5+6+7+8+9+10-7-30+5Numbers grow larger to the right, smaller to the left.Zero is neither positive nor negative.
Integers stretch from negatives on the left to positives on the right.
Opposites and Absolute ValueA number line from -8 to +8 showing -3 and +3 as opposites, both 3 steps from zero, illustrating absolute value as distance from zero.Opposites and Absolute Value-8-7-6-5-4-3-2-10+1+2+3+4+5+6+7+83 steps3 stepsOpposites are mirror integers across zero.-3 and +3 are opposites-6 and +6 are oppositesAbsolute value = distance from zero|-3| = 3 and |+3| = 3 — both sit 3 steps from zero.An integer and its oppositeshare the same absolute value.
Distance from zero is always positive — that is absolute value.
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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.

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Guided Practice

Write 3-4 sentences explaining what you have learned. Use at least 3 of the vocabulary words below.
integerpositivenegativeopposite
📝 Words: 0 / 30🔤 Vocabulary used: 0 / 3
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Exercises

Click the correct tick on each number line.

Click the tick that shows -7 on this number line from -10 to +10.

-10
?
-5
0
+5
+10

Click the tick that shows +3 on this number line.

-5
-3
0
?
+5
+8

Which tick shows zero — the boundary between positive and negative integers?

-4
-2
?
+2
+4

Click the tick that shows -4 — the opposite of +4.

-6
?
-2
0
+4

Which tick shows the greatest integer on this number line?

-9
-3
0
+4
+8

Which tick shows the integer with absolute value 6 on the negative side?

-8
?
-2
0
+6

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?

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Parent Checklist

For the parent: after correcting together, check off what your child has really understood

Lesson 2: Add and Subtract Integers →
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