Year 6 Mathematics · AC9M6SP02

Coordinates in Four Quadrants

Locate, transform and reason about points across the Cartesian plane

Ready to project and teach

Learning goalsSay it simply

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 conceptTeach from the board

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 (+,+), (−,+), (−,−), (+,−).

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.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6SP02 - Coordinates in Four Quadrants
Example 1

movement coordinate rule 4 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)

Example 2

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

Example 3

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

Example 4

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

Curriculum examplesCopied content

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.

    Questions and answersWith answers

    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.

    Practice and reviewReady for practice
    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.
    Curriculum alignmentStart here

    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
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