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Common Core Math6th GradeThe Number System

6.NS.6: Rational Numbers on the Number Line and Coordinate Plane

Also written as 6.NS.C.6 and CCSS.MATH.CONTENT.6.NS.C.6 · Cluster: Apply and extend previous understandings of numbers to the system of rational numbers.

Make 6.NS.6 Graph PaperAll 29 6th Grade Math Standards

The Official Wording

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Common Core State Standards, Grade 6, The Number System · Read it at the source · Checked October 14, 2026

What 6.NS.6 Means in Plain English

Sixth graders extend the number line past 0 and the grid into all four quadrants. They place -3, -1/2 and 2.5 on a horizontal or vertical line, know that -3 and 3 sit the same distance from 0 on opposite sides, and that -(-3) = 3.

On the plane, the signs of an ordered pair tell the quadrant: (3, -2) is below the x-axis, and (-3, -2) is its mirror image across the y-axis. This sets up distances in 6.NS.8 and, in 7th grade, adding and subtracting on the number line in 7.NS.1.

6.NS.6 I Can Statements

  • I can place integers, fractions and decimals on a number line, including negatives.
  • I can explain why the opposite of -3 is 3.
  • I can tell a point’s quadrant from the signs of its coordinates.

6.NS.6 Worked Example

One point and its three reflections on the grid: a decimal coordinate, a quadrant for each, and the sign changes that move it.

Problem

Plot the point (-4, 2.5) and name its quadrant. Then plot the points you get by changing the sign of one coordinate, and of both.

Plotting (-4, 2.5) and its reflections
  1. Read the pair: x is -4, y is 2.5. Negative x means go left of 0; positive y means go up. Left and up is quadrant II.(-4, 2.5): 4 left, 2.5 up, quadrant II
  2. 2.5 is halfway between 2 and 3 on the y-axis, so the point sits between gridlines. Fraction and decimal coordinates are allowed.y = 2.5 lies between y = 2 and y = 3
  3. Change the sign of x only: (4, 2.5). Same height, flipped to the right side. That is a reflection across the y-axis.(4, 2.5) in quadrant I, mirror across the y-axis
  4. Change the sign of y only: (-4, -2.5). Same left-right position, flipped below the x-axis.(-4, -2.5) in quadrant III, mirror across the x-axis
  5. Change both signs: (4, -2.5). Reflected across both axes, which lands in the opposite quadrant.(4, -2.5) in quadrant IV
Answer(-4, 2.5) is in quadrant II; its reflections are (4, 2.5), (-4, -2.5) and (4, -2.5)

Check it: Fold the paper along the y-axis and (-4, 2.5) lands on (4, 2.5). Fold along the x-axis and it lands on (-4, -2.5). Each reflected point is the same distance from the axis as the original.

Common Mistakes with 6.NS.6

Reading -(-3) as -3

“The opposite of -3 is -3, it already has a minus sign”

Try this: Read each sign as a flip. Start at 3, flip to -3, flip again to 3. The two flips undo each other.

Placing negatives in the wrong order

-1/2 placed to the right of 0, or -7 placed closer to 0 than -3

Try this: Fold the number line at 0. Each negative sits where its positive partner lands, so -7 is as far left as 7 is right.

Swapping x and y in an ordered pair

(-4, 2.5) plotted 2.5 to the left and 4 up

Try this: Say “over, then up” every time. The first number always moves along the x-axis, and its sign says which way.

Where 6.NS.6 Fits

Comes Before5.G.1Plot points in the first quadrant and name the x- and y-coordinates.3.NF.2Place fractions on a number line.6.NS.5Use positive and negative numbers for opposite directions in real contexts.
Alongside6.NS.7Order rational numbers and read absolute value as distance from 0.6.G.3Draw polygons from vertex coordinates in the coordinate plane.
Comes Next6.NS.8Find the distance between two points that share a coordinate.7.NS.1Add and subtract on the number line, where p + q is |q| away from p.8.G.3Describe reflections, rotations and dilations with coordinates.

Practice 6.NS.6

Graph Paper GeneratorFree ToolFour-quadrant grids with the axes drawn and 0 at the center, so plotting (-4, 2.5) and its reflections takes no setup.Four quadrants1 cm squaresOne page
Make Graph Paper
Number Line GeneratorFree ToolNumber lines from -10 to 10 with half or quarter steps, for placing -1/2, 2.5 and their opposites side by side.-10 to 10Half stepsBlank
Make a Number Line

Quick Check

  1. What is -(-8)? Where is it on the number line compared with -8?
  2. In which quadrant is (-6, -1.5)? What point is its reflection across the x-axis?
  3. Put these in order on a number line from left to right: 1/2, -2, 0, -1/2.

6.NS.6: Other Names

6.NS.66.NS.C.6CCSS.MATH.CONTENT.6.NS.C.6

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.