CCSS.Math.Content.6.NS.C.6
The Standard
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 for Mathematics · The Number System
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students place positive and negative rational numbers on horizontal and vertical number lines. They plot ordered pairs in all four quadrants and connect opposite signs with reflected locations.
What Mastery Looks Like
- Students accurately plot integers, fractions, decimals, and ordered pairs on scaled axes. They identify opposites, use signs to choose directions, and describe reflections across either axis.
Common Misconceptions
- Students often reverse the x-coordinate and y-coordinate when plotting points. They may think any negative coordinate means move left, even when it is the y-coordinate. Some think the opposite of a negative number is still negative.
How to Assess It
- Exit ticket: Plot -3/2, 0, and the opposite of -3/2 on a number line. Then plot P(-2, 3) and give its reflections across each axis.
Lesson moves
Ways to Teach It
Make a floor number line with tape, then have students stand at fraction cards and move to each number's opposite.
Ask, "How do the signs in (3, -2) tell you where to move?" Students sketch and explain.
Play coordinate bingo by calling rational ordered pairs while students cover matching points on four-quadrant grid cards.
Graph morning temperatures and town locations relative to school, using negative values for below zero, west, or south.
Free download
Printable 6.NS.C.6 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.6.NS.C.6, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
See the whole path on the The Number System progression map.
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.5.G.A.1
Students extend ordered pairs, axes, and distance from the origin to include rational and negative coordinates.
- CCSS.Math.Content.6.NS.C.5
Interpreting positive and negative quantities and zero supports placing negative rational numbers on number lines and coordinate axes.
- CCSS.Math.Content.4.NF.B.4a
Seeing a/b as a copies of 1/b supports locating fractional rational numbers by unit intervals before adding negatives.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.6.NS.C.6a
Students need rational numbers as number line points to interpret negative signs and opposites as locations relative to zero.
- CCSS.Math.Content.7.NS.A.1b
Adding rational numbers as movement from p requires placing positive and negative rational numbers accurately on the number line.
- CCSS.Math.Content.8.G.A.3
Coordinate transformations require locating and tracking points across all quadrants using signed x and y coordinates.
- CCSS.Math.Content.6.NS.C.7a
Interpreting inequalities by left and right position requires seeing positive and negative rational numbers as points on the number line.
- CCSS.Math.Content.6.NS.C.7
Ordering and absolute value use rational numbers’ locations on the number line, especially distance and direction from zero.
- CCSS.Math.Content.7.NS.A.1
Students must locate positive and negative rational numbers on number lines before representing rational addition and subtraction as movements.
Keep exploring
Related Standards
- CCSS.Math.Content.6.NS.C.7c
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative q...
- CCSS.Math.Content.6.NS.C.6c
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational nu...
- CCSS.Math.Content.6.NS.C
Apply and extend previous understandings of numbers to the system of rational numbers.
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