6.NS.7: Order Rational Numbers and Absolute Value
Also written as 6.NS.C.7 and CCSS.MATH.CONTENT.6.NS.C.7 · Cluster: Apply and extend previous understandings of numbers to the system of rational numbers.
The Official Wording
Understand ordering and absolute value of rational numbers.
Common Core State Standards, Grade 6, The Number System · Read it at the source · Checked October 14, 2026
What 6.NS.7 Means in Plain English
Sixth graders compare negative numbers by position: -2 > -9 because -2 is farther right on the number line, so -2 °C is warmer than -9 °C. Absolute value is distance from 0: |-45| = 45, so a balance of -45 dollars is a debt of 45 dollars.
The last part is the subtle one: a balance below -45 dollars is a bigger debt, so “less than” for the number means “more than” for the size. Students keep the two comparisons apart. In 7th grade, 7.NS.1 uses absolute value as distance when adding and subtracting.
6.NS.7 I Can Statements
- I can order positive and negative numbers on a number line.
- I can write an inequality for a real situation, like -2 > -9.
- I can find an absolute value and say what it measures.
6.NS.7 Worked Example
Three bank balances that have to be put in order twice: once by the number, once by the size of the debt.
Three accounts show balances of -45, 20 and -80 dollars. Order the balances from least to greatest, then order the accounts by how much they owe.
- Place each number on a number line. Negatives go left of 0, and the farther from 0, the farther left.-80 ... -45 ... 0 ... 20
- Least to greatest is left to right. -80 is the smallest balance because it is farthest left.-80 < -45 < 20
- Debt is the size of a negative balance, which is absolute value: distance from 0.|-80| = 80 and |-45| = 45; the 20-dollar account owes nothing
- Now compare the debts. The account with the smaller balance has the bigger debt.-80 < -45, but the debt 80 > the debt 45
Check it: Say both sentences about one account: -80 is less than -45, and a debt of 80 is more than a debt of 45. Both are true, because one is about position and the other about size.
Common Mistakes with 6.NS.7
Bigger digits, bigger number
-80 > -45 “because 80 is more than 45”
Try this: Put both on a number line. -80 is farther left, so it is less. Ask which temperature is colder, -80 or -45.
Absolute value as “make it positive” with no meaning
|-30| = 30, but “a balance of -30 means you have 30 dollars”
Try this: Attach the context every time: |-30| = 30 is the size of the debt, 30 dollars owed, not 30 dollars owned.
Mixing order with magnitude
“A balance less than -30 is a debt less than 30”
Try this: Test with a number: -50 is less than -30, and a 50-dollar debt is more than a 30-dollar debt. Lower balance, bigger debt.
Where 6.NS.7 Fits
Practice 6.NS.7
Quick Check
- Which is greater, -12 or -4? Write it as an inequality.
- Write a statement comparing a morning low of -6 °C with an afternoon high of 3 °C.
- An account balance is -75 dollars. What is |-75|, and what does it tell you?