Step 1
Absolute value is distance
Absolute value tells how far a number is from zero. It does not tell direction.
👀 |-12| = 12 and |12| = 12
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Grade 6 · Maths · Lesson 2.2
Absolute Value and Integer Inequalities
Use absolute value to compare distance from zero and inequalities to compare signed numbers.
CCSS.MATH.CONTENT.6.NS.C.7
Lesson Mission
How can a number be less than another number but still farther from zero?
🧭 MATH-G6-N02 · Integers, Absolute Value, and Navigating the 4-Quadrant Grid
✅ I can interpret absolute value as distance from zero.
✅ I can compare negative numbers using inequalities.
✅ I can explain why distance cannot be negative.
✅ I can solve real-world absolute value problems.
AI Learning Helper
Grade 6 Teacher
Helping with: Absolute Value and Integer Inequalities
MATH-G6-N02 · The Subterranean Compass
Teacher Welcome
I am your Subterranean Compass math teacher. I will help you use signed numbers, absolute value, and coordinate grids like a navigator.
Teacher Response
Guided Hint
Is the situation above zero or below zero?
Ask for a Specific Hint
Teacher Tip
Always label the direction first: above, below, left, right, up, or down. Then decide whether the number should be positive or negative.
Common Mistake Alert
Remember: absolute value is distance from zero. Distance cannot be negative.
Student Question Box
Helper Suggestion
Type a question above. The helper will guide the student toward the first step without giving away the answer immediately.
Challenge Prompt
Can you create your own coordinate grid problem using a drone, robot, or underground tunnel?
Warm-Up
Think First
Which is farther from zero: -8 or +5? How do you know?
Show expected answer
-8 is farther from zero because |-8| = 8 and |+5| = 5.
Vocabulary
Key Words
Integer
A whole number, zero, or the opposite of a whole number, such as -3, 0, or 7.
Opposite numbers
Numbers that are the same distance from zero but on opposite sides of the number line.
Absolute value
The distance a number is from zero on the number line.
Coordinate plane
A two-dimensional grid formed by the x-axis and y-axis.
Quadrant
One of the four regions created by the x-axis and y-axis.
Real-World Connection
Why This Matters
Absolute value is used to measure distance from sea level, temperature change, account balance distance from zero, and grid distance.
Mini Lesson
Learn the Concept
Step 2
Distance cannot be negative
A location can be negative, but the distance from zero is always zero or positive.
👀 Distance scanner removes direction.
Step 3
Negative number comparisons can feel backward
-4 is greater than -18 because -4 is closer to zero on the number line.
👀 -18 < -4
Interactive Practice
Practice, Build, Simulate, Explain
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Activity 1 · scenario-challenge
Problem 6: The Polar Bear vs. Deep Sea Trench
A polar bear hunts at -5 meters relative to sea level. A deep-sea crab crawls at -25 meters. Write an inequality comparing their depths, and determine who is deeper.
10 ptsNot checked
💡 Use the visual model first. Then write the signed integer, inequality, coordinate, or distance.
Absolute Value and Inequalities
A polar bear is at -5 meters. A deep-sea crab is at -25 meters.
Interactive Visual Model
[Sea Level 0] ➔ Bear (-5) ➔ Crab (-25) ➔ -5 > -25
Activity 2 · scenario-challenge
Problem 7: Scuba Diver Distance Tracking
Diver A is at -40 feet. Diver B is at -15 feet. Use absolute value to calculate who is a greater physical distance away from the surface boat at 0 feet.
10 ptsNot checked
💡 Use the visual model first. Then write the signed integer, inequality, coordinate, or distance.
Absolute Value and Inequalities
Diver A is at -40 feet and Diver B is at -15 feet.
Interactive Visual Model
|-40| = 40 feet away | |-15| = 15 feet away
Activity 3 · scenario-challenge
Problem 8: Checking Warehouse Balances
Store A has a stock balance of -12 items. Store B has a stock balance of -20 items. Write an inequality showing which store has a higher, healthier inventory balance.
10 ptsNot checked
💡 Use the visual model first. Then write the signed integer, inequality, coordinate, or distance.
Absolute Value and Inequalities
Store A has -12 items backordered. Store B has -20 items backordered.
Interactive Visual Model
◀──[ -20 Store B ]───────[ -12 Store A ]───────[ 0 ]──▶
Activity 4 · scenario-challenge
Problem 9: The Drone Altitude Comparison
A weather drone flies at +80 meters. A submarine dives at -80 meters. Use absolute value to show if one vehicle is further from sea level than the other.
10 ptsNot checked
💡 Use the visual model first. Then write the signed integer, inequality, coordinate, or distance.
Absolute Value and Inequalities
A drone is at +80 meters and a submarine is at -80 meters.
Interactive Visual Model
Drone: |+80| = 80 | Submarine: |-80| = 80
Activity 5 · scenario-challenge
Problem 10: Winter Temperature Swings
In Alaska, the temperature on Tuesday was -18°F. On Wednesday, it was -4°F. Write an inequality using < or > to show which day was colder.
10 ptsNot checked
💡 Use the visual model first. Then write the signed integer, inequality, coordinate, or distance.
Absolute Value and Inequalities
Tuesday was -18°F and Wednesday was -4°F.
Interactive Visual Model
Tuesday [-18°F] ◄═══ Colder ═══ Wednesday [-4°F]