Learning goal: I can tell the difference between comparing absolute values (size/distance from 0) and comparing the actual order of two numbers.
Language goal: I can explain the difference between 'greater' and 'bigger absolute value' using an example.
📚 Vocabulary
Absolute value: The distance of a number from 0, written |x|. Always zero or positive.
Magnitude: The size of a number ignoring its sign — its absolute value.
Order: Which number is actually greater or less, signs included.
💡 Learn it
Absolute value asks how far from 0. Order asks which is greater on the line. They are not the same for negatives.
Example: −30 < −5 (order: −30 is less). But |−30| = 30 and |−5| = 5, so |−30| > |−5| (size: −30 is farther from 0).
Real meaning: a balance of −$30 is less than −$5, yet it is a bigger debt because its absolute value is larger.
Worked example. Compare −7 and −2 two ways.
Order: −7 is left of −2, so −7 < −2.
Absolute value: |−7| = 7 and |−2| = 2, so |−7| > |−2|.
So −7 is the lesser number but has the greater magnitude.
✏️ Practice
Score: 0 / 5
1. Evaluate: |−7| =
💡 Absolute value is distance from 0 — drop the sign.
2. Which number is GREATER: −7 or −2 ?
💡 Greater = farther right on the line.
3. Which number has the GREATER ABSOLUTE VALUE: −7 or −2 ?
💡 |−7| = 7, |−2| = 2.
4. A debt of $45 (−45) vs a debt of $20 (−20): who OWES more?
💡 Owing more = greater absolute value, even though −45 < −20.
5. True or False: If a < b then |a| < |b| is always true.
💡 Counterexample: −5 < 2 but |−5| = 5 > 2 = |2|.
🗣️ Sentence frames (ESOL support)
I know ___ because ___.
First, I ___. Then, I ___.
The answer is ___, so ___.
🎟️ Exit ticket
Diver A is at −40 ft and Diver B is at −25 ft. Write one sentence comparing their positions (order) and one sentence comparing their depths (absolute value).