math class 678 4-in-1 skill sheets
6.NS.C.6c 6th Grade The Number System

Rationals on Number Line & Coord Plane

Find and position integers and other rational numbers on a horizontal or vertical number line and in the coordinate plane.

How to explain it

At this standard, students read the scale of a number line, plot rational numbers (fractions and decimals) on a horizontal number line, and plot and read ordered pairs with integer and rational coordinates on a coordinate plane.

The anchor students hold onto: To plot a rational: find the tick value (span ÷ equal parts), then count ticks from 0. For ordered pairs: move x (horizontal) first, then y (vertical).

Plotting rationals (6.NS.C.6c) leads directly into comparing and ordering rational numbers and absolute value in Sheet #15.

Worked examples

Example 1 Plot on Number Line
Plot 3/4. Axis: 0 to 1, 4 parts.
Step 1Tick value: 1 ÷ 4 = 1/4 per tick
Step 2Count 3 ticks RIGHT of 0
Step 3Plot dot at 3/4
Answer3/4 (between 0 and 1)
Example 2 Plot Ordered Pair
Plot (−3, 2) on the CP.
Step 1x = −3: move 3 units LEFT from origin
Step 2y = 2: from there, move 2 units UP
Step 3Plot at (−3, 2) — Quadrant II
Answer(−3, 2) — Quadrant II

Common mistakes

What students write Student counts tick marks instead of intervals when plotting 3/4 on a 4-part axis, placing the dot at 1 (the 4th tick) instead of the 3rd tick.
The fix The denominator tells how many equal PARTS (intervals), not how many ticks. 3/4 means 3 of 4 parts — place the dot at the 3rd tick, not the 4th.
Try this A student plots 3/4 on a number line divided into 4 equal parts from 0 to 1. The student counts 4 tick marks and places the dot at 1. Find the error and write the correct position. The student wrote: "The denominator is 4, so I count 4 ticks and land at the 4th tick = 1."
What students write Student plots (3, −2) by moving DOWN 2 first, then RIGHT 3, reversing the x-y movement order.
The fix Always move HORIZONTAL (x) first, then VERTICAL (y). For (3, −2): move RIGHT 3 from the origin, then DOWN 2.
Try this A student plots (3, −2) by moving DOWN 2 first, then RIGHT 3. Is this method correct? If not, identify the error and describe the correct approach. The student wrote: "I moved y = −2 first (down 2), then x = 3 (right 3). The point is at (3, −2)."

Teacher tip

Head off the two predictable errors before they happen. First: The denominator tells how many equal PARTS (intervals), not how many ticks. 3/4 means 3 of 4 parts — place the dot at the 3rd tick, not the 4th. Second: Always move HORIZONTAL (x) first, then VERTICAL (y). For (3, −2): move RIGHT 3 from the origin, then DOWN 2.