Year 6 Mathematics · AC9M6N01

Integers on Number Lines and the Cartesian Plane

Use zero as a reference point to interpret positive and negative integers in finance, position, coordinates, movement and temperature

Ready to project and teach

Learning goalsSay it simply

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)
I
(+x,+y)
III
(−x,−y)
IV
(+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.

Key conceptTeach from the board

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)
I
(+x,+y)
III
(−x,−y)
IV
(+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.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6N01 - Integers on Number Lines and the Cartesian Plane
Example 1

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.

Example 2

Negative integers extend the number line to the left of zero. For example, −2 &lt; 0 &lt; +2. Values farther right are greater.

Example 3

Equal distances from zero can have opposite signs: −4 and +4.

Example 4

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.

Curriculum examplesCopied content

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.

Teacher Slides

Open Classroom View

Homework / Homework

Open printable sheet

Interactive

Practice
Test

Australian Curriculum v9.0 • NSW Curriculum • Victorian Curriculum F–10

Questions and answersWith answers
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.
Practice and reviewReady for practice

Compare integers

Farther right = greater. Among negative numbers, the value closer to zero is greater.

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.

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.

Teacher Slides

Open Classroom View

Homework / Homework

Open printable sheet

Interactive

Practice
Test

Australian Curriculum v9.0 • NSW Curriculum • Victorian Curriculum F–10

Curriculum alignmentStart here

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)
I
(+x,+y)
III
(−x,−y)
IV
(+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.

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.

Teacher Slides

Open Classroom View

Homework / Homework

Open printable sheet

Interactive

Practice
Test

Australian Curriculum v9.0 • NSW Curriculum • Victorian Curriculum F–10

Related resourcesKeep teaching
Teach & ExplainTeaching slides and samples

Teach this topic step by step

Explore optional teaching slide packs for classroom lessons and explanations at home.

Browse Teach & Explain · Browse Print & Go

Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.

Request a free sample

After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.