Expected level of development
Australian Curriculum Mathematics V9: AC9M8SP03
Numeracy Progression: n/a
At this level, students work with 3D objects that can be located on the x, y, z planes, allowing students to extend their thinking away from flat objects on a 2D plane, to objects with volume that have a position in space with (x, y, z) coordinates. Students can explore various ways to view 3D objects, such as drawing 3D cubes and rectangles on the x, y, z planes, but digital technologies affords the means to explore the 3D world by building an object in space, defining an object and recording objects.
Show students how to transform objects, recognising patterns, exploring reflections and rotations. Dynamic geometric software programs, such as GeoGebra, have several interactive activities to explore this topic. Such activities can be found in the Teaching Resources section.
Connections to the world around us help students comprehend meaning. An object does not have to be just a shape, it could be a country on a global map, a house on a street in your area, or the position of the moon or sun in relation to Earth at a particular point in time.
Making cross-connections with Science, Engineering and Design builds engagement and consolidates learning on this topic.
Teaching and learning summary:
- Revise transformations of shapes, as well as area and volume.
- Revise the Cartesian plane and introduce the third dimension.
- Compare and contrast the 2D and 3D coordinate systems.
- Investigate the x, y, z coordinates and manipulate them to recognise patterns of change.
- Model the 3D world using digital technologies and various spatial software programs.
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Teaching strategies
A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
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Mathematics investigation
By giving students meaningful problems to solve they are engaged and can apply their learning, thereby deepening their understanding.
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Differentiated teaching
Differentiation involves teachers creating lessons that are accessible and challenging for all students.
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Collaborative learning
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
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Plotting points in 3D: dynamic illustrator
This interactive activity using dynamic geometric software allows students to play with x, y, z coordinates and see how they move in first quadrant of the x, y, z planes.
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Plotting points in 3 space
Using dynamic geometric software, students move the coordinates in the 3D plane to observe the changes.
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Coordinate Patterns
This is an explorative task involving three-patterned scenarios asking students to consider various transformations of shapes and emerging patterns. The activity encourages questioning, discussion and reasoning.
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