Construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement

Students perform rigid transformations, describe direction, distance, axis or centre and angle, and explain which properties remain invariant.

Translation, reflection and rotation preserve length, angle size, area and shape while changing position or orientation.

A complete description names the transformation and its parameters. The image remains congruent to the original.

Dynamic software can test and animate transformations, but students should predict coordinates and properties before using it.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Construct or represent accurately
• Use correct vocabulary and notation
• Interpret relationships
• Apply to a new example
• Justify and evaluate

Content description: construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement.

• E1: understanding how the numbers on the axes on a grid coordinate system are numbers on a number line and are used to pinpoint locations
• E2: discussing the conventions of indicating a point in a grid coordinate system; for example, writing the horizontal axis number first and the vertical axis number second, using brackets and commas
• E3: comparing a grid reference system to a grid coordinate system (first quadrant only) by using both to play strategy games involving location; for example, “Quadrant Commander”, deducing that in a grid coordinate system the lines are numbered (starting from zero), not the spaces
• E4: placing a coordinate grid over a contour line, drawing and listing the coordinates of each point in the picture, asking a peer to re-create the drawing using only the list of coordinates, and discussing the reasons for the potential similarities and differences between the 2 drawings
• E5: investigating how autonomous vehicles use mapping, GPS systems, communication systems and path planning to navigate within a space

Core idea: Translation, reflection and rotation preserve length, angle size, area and shape while changing position or orientation.

Remember

• Construct or represent accurately
• Use correct vocabulary and notation
• Interpret relationships
• Apply to a new example
• Justify and evaluate

Important questions

• Translate a point. Explain using the model or evidence above.
• Reflect across an axis. Explain using the model or evidence above.
• Describe a 90° rotation. Explain using the model or evidence above.
• Name invariant properties. Explain using the model or evidence above.
• Predict before using software. Explain using the model or evidence above.

• Reflection described as rotation — A reflection reverses orientation across a line.
• Different points moved different distances in a translation — Every point follows the same vector.
• Rotation centre omitted — The same angle around different centres gives different images.
• Image resized — Rigid transformations preserve size.

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

Students perform rigid transformations, describe direction, distance, axis or centre and angle, and explain which properties remain invariant.

Translation, reflection and rotation preserve length, angle size, area and shape while changing position or orientation.

A complete description names the transformation and its parameters. The image remains congruent to the original.

Dynamic software can test and animate transformations, but students should predict coordinates and properties before using it.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

• Construct or represent accurately
• Use correct vocabulary and notation
• Interpret relationships
• Apply to a new example
• Justify and evaluate

Australian Curriculum Version 9.0

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