Two Different Questions: "How Big?" vs. "Which Is Greater?"
I can tell the difference between absolute value (distance from 0) and order (which number is greater).
📘 Word Bank + Sentence Frames
absolute value | x | distance from 0 size of a debt order (> / <)
Two questions, two answers:
- Order: "Which is greater?" → the number farther right on the number line.
- Absolute value: "How far from 0 / how big?" → ignore the sign. |−30| = 30.
- "−30 < −5 (order), but |−30| > |−5| because −30 is farther from 0."
👀 See It: A Worked Example
Which is greater? (order)
−30 vs. −5 → −5 > −30
(−5 is farther right, less debt is "better")
Which debt is bigger? (absolute value)
|−30| = 30, |−5| = 5 → $30 debt is bigger
(farther from 0)
Same two numbers — opposite answers, because the questions are different!
✏️ Your Turn — Check Your Thinking
0 of 3 checks complete
1. Which is the greater number (order): −20 or −9?
2. Which has the larger absolute value (farther from 0): −20 or −9?
3. Ana owes $15 and Leo owes $6. Who has the bigger debt?
💬 Explain Your Thinking
Explain why a number can be "less" but still be "bigger" in size:
"−15 is blank than −6 in order, but |−15| is blank than |−6| because blank."