Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M6SP03
Numeracy Progression: Understanding geometric properties: P5
At this level, students continue to develop their understanding and skills in transformations including reflections (flips), translations (slides) and rotations (turns).
Use explicit teaching strategies to assist students’ understanding of transformations. Revise transformations by modelling and questioning. Model how to perform:
- translation (slide) – a movement in a straight line without rotation, reflection or change of size
- reflection (flip) – a mirror image of the shape where the shape and image face opposite directions in relation to the line of reflective symmetry (mirror line)
- rotation (turn) – a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.
Tessellations provide a useful example when looking at patterns of transformations on simple and composite shapes. Explore using combinations of transformations to create tessellations and other geometric patterns.
Explore transformations in geometric design. Set a design project that incorporates transformations of at least one shape.
Use digital tools to create geometric patterns including geometric software such as GeoGebra.
Teaching and learning summary:
- Model and describe the effects of transformations by manually flipping, sliding and turning 2D shapes and by using digital technologies.
- Use questioning to prompt students to justify their thinking when describing the properties of shapes that do not change when shapes are translated, reflected or rotated.
- Use engaging contexts such as tessellations.
Students:
- perform and describe positions and orientation of shapes under combinations of transformations
- describe transformations on a cartesian plane
- create tessellations using a combination of transformations.
Some students may:
- believe that when 2D shapes are transformed, their initial properties change. To address this, expose students to a range of experiences to aid conceptual development of transformation. Gauge whether students can generalise that when 2D shapes are transformed they still retain their initial properties.
- have difficulty reflecting an object when the mirror line is at an angle (other than horizontal or vertical). Support students with a visual aid such as a plane mirror to show where the reflected object is mapped.
- use the incorrect fixed point when rotating a shape. Support students by providing them with the original diagram on a sheet of paper as well as a transparent sheet with the same display. The transparent sheet covers the original paper and a pin is placed through both sheets on the point of rotation. The original sheet remains in the original position, while the transparent sheet is rotated displaying the various positions of rotation.
- have difficulty when plotting a shape on Cartesian plane if unfamiliar with negative numbers, particularly in quadrants other than the first. Link learning about transformation with learning about the Cartesian plane.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
Learning intention
- We are learning how to model and describe the effects of transformations by flipping, sliding and turning 2D shapes.
- We are developing our understanding and skills in transformations including reflections (flips), translations (slides)
and rotations (turns).
Why are we learning about this?
- Transformation is a way of organising space. Tessellations can be found in quilts, tiling and architecture.
What to do
Today I am going to show you how to make a simple tessellation pattern.
- Create this rectangular shape called a ‘tromino’ on a sheet of paper or copy into a new document.
If you are making the shape on a sheet of paper you will need to cut out 16 to make the tessellation.
- Start the pattern with the first shape, then slide the shape along.
- Do two more slides of the shape
- Now rotate the shape one half turn (180˚) and slide down
- Slide this shape along 3 times. Yours won’t have gaps. This is just to make it easier to see the transformations.
- The tessellation will look like this:
Success criteria
I can:
- perform and describe positions and orientation of shapes
- create tessellations using a combination of transformations.
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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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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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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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Culturally responsive pedagogies
Culturally responsive pedagogy is a form of teaching that incorporates learners’ cultural background and histories into classroom practice.
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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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Reptiles
Students apply the properties of transformations, including enlargement, to find how four copies of the shape form a larger version of itself.
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One good turn
Students use pattern blocks to create geometric designs and describe the rotational symmetry of their shapes.
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Starry-eyed
Students explore symmetry in geometric patterns by joining points around the circumferences of circles.
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Synchronised swim shapes
Students apply their understanding of geometry to design and describe shapes and formations as well as the transformations that map one formation onto another.
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Change course
Students explore transformations, symmetry and tessellations using geoboards, centimetre dot paper, tracing paper, Mira mirrors and worksheets.
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Types of transformations study guide
This guide outlines the different types of transformations of a 2D shape.
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Rigid transformations
This resource helps students learn to recognise different transformations of rigid shapes.
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