6.NS.C.8
6th Grade
The Number System
Real-World Problems on Coordinate Plane
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.
How to explain it
At this standard, students solve real-world problems using points on a coordinate plane.
The anchor students hold onto: Same y → |x₁ − x₂| · Same x → |y₁ − y₂|
Variables in an ordered pair (x, y) represent two related quantities — the basis for 6.EE.C.9, where the coordinate plane shows how one variable changes as another changes.
Worked examples
Example 1
Park: (−3, 2); Library: (4, 2)
Step 1Both at y = 2 — share y-coordinate
Step 2Distance = |−3 − 4| = |−7| = 7
Step 37 units
Answer7 units
Example 2
A(−2, 5); B(−2, −3)
Step 1Both at x = −2 — share x-coordinate
Step 2Distance = |5 − (−3)| = |8| = 8
Step 38 units
Answer8 units
Common mistakes
What students write
Student subtracts coordinates without absolute value and reports a negative distance.
The fix
Distance is always positive. Use absolute value: |x₁ − x₂| or |y₁ − y₂|.
Try this
A student found the distance between A(5, −3) and B(5, 8). Her work: distance = 8 − (−3) = 8 − 3 = 5. What error did she make? Give the correct distance.
What students write
Student applies the shared-coordinate formula to points that do NOT share a coordinate.
The fix
The shared-coordinate shortcut only works when both points share the same x OR the same y value.
Teacher tip
Head off the two predictable errors before they happen. First: Distance is always positive. Use absolute value: |x₁ − x₂| or |y₁ − y₂|. Second: The shared-coordinate shortcut only works when both points share the same x OR the same y value.