Compare integers
Farther right = greater. Among negative numbers, the value closer to zero is greater.
Topic Guide
Key concept
Integers are whole numbers below zero, zero and above zero. Their position tells their size; their sign often tells direction relative to a chosen zero reference.
E1 — Number lines and zero
Negative integers extend the number line to the left of zero. For example, −2 < 0 < +2. Values farther right are greater.
Essential diagram 1 — number line
−6−30+3+6
Equal distances from zero can have opposite signs: −4 and +4.
E2 — Financial contexts
Use positive integers for profit or gains, negative integers for loss or amounts below a zero balance, and 0 for break-even. Example: income $450 and costs $520 gives a net result of −$70.
E3 — Everyday position and Cartesian coordinates
Integers model floors above/below ground, heights above/below sea level and coordinates. Read ordered pairs as (x, y): horizontal first, vertical second.
Essential diagram 2 — Cartesian plane
II
(−x,+y)
(−x,+y)
I
(+x,+y)
(+x,+y)
III
(−x,−y)
(−x,−y)
IV
(+x,−y)
(+x,−y)
Points on an axis are not in a quadrant: (3,0) lies on the x-axis and (0,−5) lies on the y-axis.
E4 — Sign shows direction
Choose the positive direction first. On a horizontal line, right can be positive and left negative. On a vertical line, up can be positive and down negative. A robot should move on one number line at a time.
E5 — Temperature
A thermometer is a vertical number line. Temperatures below zero are negative; temperatures above zero are positive. The colder temperature is the smaller integer.
20 Must Questions with Worked Solutions
1. Order −7, 4, −1, 0 from least to greatest.
Solution: −7 < −1 < 0 < 4.
2. Place −5, −2 and 3 on a number line.
Solution: from left to right: −5, −2, 3.
3. Which is greater: −9 or −3?
Solution: −3, because it lies farther right and closer to zero.
4. Which integers are 4 units from zero?
Solution: −4 and +4.
5. Explain why −2 < 0.
Solution: −2 lies two units to the left of zero.
6. A stall earns $60 and spends $85. What is the net integer?
Solution: 60 − 85 = −25, so the result is −$25.
7. A student earns $12 and spends $9.
Solution: 12 − 9 = +3.
8. What integer represents break-even?
Solution: 0.
9. Write an integer for a loss of $40.
Solution: −40.
10. Write an integer for a profit of $75.
Solution: +75.
11. An elevator is 6 floors below ground.
Solution: −6.
12. A diver is 45 m below sea level.
Solution: −45 m.
13. Which quadrant contains (−4,3)?
Solution: Quadrant II: x is negative and y is positive.
14. Does (0,−7) lie on the x-axis or y-axis?
Solution: y-axis because x = 0.
15. Plot (3,−5). Where is it?
Solution: move 3 right and 5 down; it is in Quadrant IV.
16. If right is positive, what does −30 m mean?
Solution: 30 m left of the reference point.
17. On a vertical line, a robot moves +18 units.
Solution: 18 units up if up is defined as positive.
18. Write an integer for 22 m left of a reference point.
Solution: −22.
19. Write an integer for 14 units down.
Solution: −14 if up is positive.
20. A robot starts at 0, moves 9 left then 4 right. Final position?
Solution: 0 → −9 → −5, so final position = −5.
Revision Notes
Interpret signs
+ and − depend on the context: gain/loss, above/below, right/left, up/down.
Coordinates
Read x first, y second. Use the signs to identify the quadrant.
Check reasonableness
Return to zero as the reference. Ask whether the sign and direction match the story.
Common mistakes
- Thinking −8 is greater than −3 because 8 > 3.
- Treating negative values as impossible instead of relative to a reference.
- Reading coordinates as y then x.
- Calling a point on an axis a quadrant point.
- Assuming “negative” always means left; the meaning depends on the chosen axis and context.
Curriculum Coverage & Resources
AC9M6N01: recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane.
- E1: extend the number line into negative integers and compare positions around zero.
- E2: represent financial quantities including profit and loss.
- E3: solve everyday position/order problems and distinguish the four Cartesian quadrants.
- E4: use signs to indicate direction and program movement on one horizontal or vertical number line.
- E5: represent planetary temperatures using a thermometer as a vertical number line.
Australian Curriculum v9.0 • NSW Curriculum • Victorian Curriculum F–10
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Recommended: Negative Numbers
Math Antics — Locate positive and negative integers on a number line. Coordinate plotting is covered in the written lesson.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Situations, including financial contexts, that use integers; locate and represent...
Mapped skill: recognise situations, including financial contexts, that use integers; locate and represent integers on a number line and as coordinates on the Cartesian plane
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6N01 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6N01 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-RN-01 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M6N01 — Integers on Number Lines and the Cartesian Plane
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