Negative Numbers, Absolute Value and the Coordinate Plane: Grade 6 Study Guide
Numbers continue below zero. Grade 6 introduces the full number line and the four-quadrant plane.
Positive and negative numbers describe opposite directions or values: temperatures above and below zero, elevations above and below sea level, deposits and withdrawals. The opposite of a number is the same distance from zero on the other side: the opposite of 5 is −5. Zero is its own opposite.
The absolute value of a number is its distance from zero, always non-negative: |−7| = 7 and |7| = 7. The absolute value shows magnitude, such as how large a debt is, without its direction.
Ordering and comparing
On a horizontal number line, numbers increase to the right. −2 > −5 because −2 is farther right. A debt of $50 (−50) is worse than a debt of $20 (−20), even though 50 > 20 in absolute value. Compare real-world values by thinking of the situation.
The four quadrants
The coordinate plane has an x-axis and y-axis meeting at the origin (0, 0). The axes split the plane into four quadrants. Points are written (x, y).
| Quadrant | Sign of x | Sign of y | Example |
|---|---|---|---|
| I | + | + | (3, 2) |
| II | − | + | (−3, 2) |
| III | − | − | (−3, −2) |
| IV | + | − | (3, −2) |
Reflections and distance
Reflecting a point across the x-axis changes the sign of y: (3, 2) becomes (3, −2). Across the y-axis it changes the sign of x. When two points share a coordinate, the distance between them is found using absolute value: from (−4, 3) to (2, 3) the distance is |−4| + |2| = 6 units.
Mark them on the grid.
Same y means horizontal.
Add if on opposite sides of zero.
6 units.
Worked examples and common mistakes
Example: A diver at −12 m rises 5 m: −12 + 5 = −7 m. Common mistakes: thinking −8 > −3, mixing up the order of x and y and confusing absolute value with the opposite. Draw a number line for every comparison.
Check your understanding: model answers
1. −4. 2. 15. 3. Quadrant II.
✨ Key Takeaways
- Opposites are on opposite sides of zero.
- Absolute value is distance from zero.
- The plane has four quadrants.
- Reflections change the sign of one coordinate.
💬 Questions for Discussion & Reflection
- Which is greater: −9 or −4?
- Find |−15|.
- In which quadrant is (−2, 5)?
Print coordinate plane grids →