6.NS.C.6b 6th Grade The Number System

The Coordinate Plane

Understand signs of numbers in ordered pairs as indicating locations in the four quadrants of the coordinate plane.

How to explain it

Students read the signs of an ordered pair to name the quadrant a point falls in, plot signed ordered pairs on the four-quadrant coordinate plane, and recognize that two points whose coordinates differ only in sign are reflections of each other across the x-axis, the y-axis, or both axes.

The anchor students hold onto: Signs name the quadrant: (+,+) = I, (−,+) = II, (−,−) = III, (+,−) = IV. Flip one sign → reflect across the axis that controls it.

Naming quadrants and reflecting across axes prepares students for coordinate-plane distances (6.NS.C.8), polygon vertices (6.G.A.3), and four-quadrant graphing throughout grades 7–8.

Worked examples

Example 1

Which quadrant holds (−3, 5)?

Step 1x = −3 (negative), y = 5 (positive)

Step 2Signs: (−, +)

Step 3Match to quadrant map → Quadrant II

AnswerQuadrant II

Example 2

Reflect (4, 2) across x-axis.

Step 1Reflecting over x-axis flips the sign of y

Step 2(4, 2): keep x = 4; flip y: 2 → −2

Step 3Image = (4, −2)

Answer(4, −2)

Common mistakes

What students write Reading (x, y) as (y, x) — placing the point at the reversed location

The fix x is always first: move horizontally (left/right) for x, then vertically (up/down) for y.

Try this A student reflected (−3, 6) across the y-axis and wrote (−3, −6) as the image. The student flipped the sign of y instead of x. Find the correct image and explain the error.

What students write Thinking any point with negative coordinates is in Quadrant III

The fix The quadrant depends on BOTH signs: (−, +) → Quadrant II; (−, −) → Quadrant III.

Teacher tip

Head off the two predictable errors before they happen. First: x is always first: move horizontally (left/right) for x, then vertically (up/down) for y. Second: The quadrant depends on BOTH signs: (−, +) → Quadrant II; (−, −) → Quadrant III.