math class 678 4-in-1 skill sheets
6.NS.C.7 6th Grade The Number System

Comparing/Ordering Rationals & Absolute Value

Understand ordering and absolute value of rational numbers, and interpret absolute value as distance from zero.

How to explain it

At this standard, students compare and order rational numbers on a number line, write and interpret inequalities in real-world contexts, compute absolute value as distance from 0, and distinguish absolute-value comparisons from order comparisons.

The anchor students hold onto: On a number line, the number farther to the RIGHT is always the GREATER number. Absolute value = distance from 0; it never depends on the sign.

Comparing and ordering rational numbers and using absolute value closes the Rational Numbers strand; the Expressions and Equations strand opens next with exponents.

Worked examples

Example 1
Compare −4 and −1. Use < or >.
Step 1Plot: −4 is to the LEFT of −1 on the number line
Step 2Number farther RIGHT is greater → −1 is right of −4
Step 3−4 < −1
Answer−4 < −1
Example 2
Find |−5|. Explain on the NL.
Step 1|−5| = distance from 0 to −5 on the number line
Step 2Count: −5 is 5 units away from 0
Step 3|−5| = 5
Answer|−5| = 5

Common mistakes

What students write Comparing digits of negatives — writing −8 > −3 because 8 > 3
The fix Ignore digits alone. Place both on a number line: −3 is farther RIGHT than −8, so −3 > −8.
Try this A student compares −8 and −3. She writes −8 > −3 because 8 > 3. The student compared the absolute values, ignoring the negative signs. Identify the error and write the correct inequality.
What students write Assuming order and absolute value always agree: if −9 < −5 then |−9| < |−5|
The fix Order and absolute value can point opposite ways for negatives. −9 < −5 in order, but |−9| = 9 > |−5| = 5.
Try this A student correctly writes −9 < −5 in order, then concludes |−9| < |−5| for the same reason. Identify the error and give the correct absolute value comparison.

Teacher tip

Head off the two predictable errors before they happen. First: Ignore digits alone. Place both on a number line: −3 is farther RIGHT than −8, so −3 > −8. Second: Order and absolute value can point opposite ways for negatives. −9 < −5 in order, but |−9| = 9 > |−5| = 5.