AC9M6SP02 • Year 6 Mathematics

Coordinates in Four Quadrants

Locate, transform and reason about points across the Cartesian plane

Topic GuideClassroom ViewHomeworkPracticeTest
Learning goals

Learning goal

Students plot ordered pairs with positive and negative coordinates, identify quadrants and explain coordinate changes under horizontal, vertical and symmetric movement.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position
Key concept

Plot one point in each quadrant

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

BACD

x first, then y

Quadrants are numbered anticlockwise from the upper right. The signs follow (+,+), (−,+), (−,−), (+,−).

Worked examples

Describe coordinate changes and symmetry

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

movementcoordinate rule4 right(x,y) → (x+4,y)3 down(x,y) → (x,y−3)reflect in y-axis(x,y) → (−x,y)reflect in x-axis(x,y) → (x,−y)half-turn about origin(x,y) → (−x,−y)

State the transformation or displacement, then verify distance and orientation on the grid.

Curriculum elaborations explicitly taught

AC9M6SP02: locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the plane

    Use the central and application models above to connect each elaboration to the same underlying concept.

    Common misconceptions
    Coordinate order reversedRead x then y.
    Negative direction ignoredLeft and down are negative on a standard plane.
    Point on an axis assigned a quadrantAxis points are not inside a quadrant.
    Reflection rule guessedIdentify which coordinate changes sign.
    Classroom activities

    Build and annotate the model

    Represent coordinates in four quadrants and label the important parts, quantities or choices.

    Compare and reason

    Use the application model to compare two cases, explain the relationship and identify a likely error.

    Transfer and verify

    Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.

    Revision Notes and quick mastery check

    Check understanding

    • Plot (−3,2).
    • Name Quadrant IV.
    • Translate a point.
    • Reflect in y-axis.
    • Identify an axis point.

    Evidence of mastery

    • Represent or identify the concept
    • Explain the underlying relationship
    • Select an appropriate strategy or feature
    • Apply it in a new context
    • Justify and verify the response

    Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

    Curriculum wording and references

    Australian Curriculum v9.0

    AC9M6SP02: locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position

    The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.

    Resources and next steps

    Homework

    Use the printable activity for written practice.

    Open Homework
    🎥 Optional Video Lesson

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    Back to the lesson

    Before you watch:

    • Pause after each worked example.
    • Try the examples yourself.
    • Return to the SkillrHub lesson before continuing.
    Recommended: Graphing on the Coordinate Plane

    Math Antics — Locate ordered pairs in all four quadrants of the Cartesian plane.

    As you watch: How do the signs of the coordinates identify the quadrant?

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    Try it: Plot A(-3,2), B(3,2), C(3,-2) and D(-3,-2). Describe the changes from A to B and B to C.

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    Curriculum equivalents: Victoria, NSW and international

    Curriculum equivalents for Locate points in the 4 quadrants of a Cartesian plane...

    Mapped skill: locate points in the 4 quadrants of a Cartesian plane; describe changes to the coordinates when a point is moved to a different position in the 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.

    RegionCurriculum frameworkClosest level or code
    AustraliaAustralian Curriculum v9.0AC9M6SP02 · Year 6
    VictoriaVictorian Curriculum F–10 Version 2.0 — MathematicsVC2M6SP02 · Level 6
    New South WalesNSW Mathematics K–10 Syllabus (2022)MA3-GM-01 · Stage 3
    United States (USA)Common Core State Standards for MathematicsGrade 6
    Canada (Ontario)Ontario Curriculum — MathematicsGrade 6
    United Kingdom (England)National Curriculum in England — MathematicsYear 7, Key Stage 3
    IndiaNCERT / CBSE — MathematicsClass 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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