6.NS.8: Graph Points in All Four Quadrants
Also written as 6.NS.C.8 and CCSS.MATH.CONTENT.6.NS.C.8 · Cluster: Apply and extend previous understandings of numbers to the system of rational numbers.
The Official Wording
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
Common Core State Standards, Grade 6, The Number System · Read it at the source · Checked October 14, 2026
What 6.NS.8 Means in Plain English
Sixth graders map a situation onto all four quadrants: a library at (-3, 4), a school at (5, 4), a park at (5, -2). Distances between points that share a coordinate come from absolute values: library to school is |-3| + |5| = 8 units.
Only horizontal and vertical distances are in play. Same side of an axis, subtract the absolute values. Opposite sides, add them. Diagonal distances need the Pythagorean theorem in 8th grade (8.G.8). Along the way, 6.G.3 uses the same idea for the side lengths of polygons drawn from their vertices.
6.NS.8 I Can Statements
- I can plot points with negative coordinates in all four quadrants.
- I can find the distance between points that share a coordinate.
- I can use absolute value to find a distance that crosses an axis.
6.NS.8 Worked Example
A neighborhood map with the school at the corner: two distances, one crossing an axis and one not, so students see when to add and when to subtract.
On a map where 1 unit is 1 block, the library is at (-3, 4), the school at (5, 4) and the park at (5, -2). How far is it from the library to the school, and from the school to the park?
- Plot all three. The library is left of the y-axis and up, the school is right and up, the park is right and down.(-3, 4) in quadrant II, (5, 4) in quadrant I, (5, -2) in quadrant IV
- Library and school share y = 4, so they sit on one horizontal line. The distance runs along x from -3 to 5 and crosses the y-axis.|-3| + |5| = 3 + 5 = 8 blocks
- School and park share x = 5, a vertical line. From y = 4 down to y = -2 crosses the x-axis, so add the absolute values again.|4| + |-2| = 4 + 2 = 6 blocks
- Compare with two points on the same side, say (5, 4) and (5, 1): no axis is crossed, so subtract.|4| - |1| = 3 blocks
Check it: Count the grid squares between the points on the graph: 8 across along y = 4 and 6 down along x = 5.
Common Mistakes with 6.NS.8
Subtracting coordinates with opposite signs
From (-3, 4) to (5, 4): 5 - 3 = 2 blocks
Try this: Draw the segment and notice it crosses the y-axis. Two legs, 3 on the left and 5 on the right, add to 8.
A negative distance
From (5, 4) to (5, -2): -2 - 4 = -6 blocks
Try this: Remind students that distance is never negative. Take the absolute value of each coordinate and add: 4 + 2 = 6.
Adding when both points are on the same side
From (5, 4) to (5, 1): 4 + 1 = 5 blocks
Try this: Check whether the segment crosses an axis. Both y-values are positive, so no crossing: subtract, 4 - 1 = 3.
Where 6.NS.8 Fits
Practice 6.NS.8
Quick Check
- What is the distance between (-7, 2) and (4, 2)?
- What is the distance between (3, -5) and (3, -1)?
- A rectangle has corners at (-2, 3), (6, 3), (6, -1) and (-2, -1). What is its perimeter?