Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M7SP03
Numeracy Progression: Interpreting and representing data: P7
At this level, students will describe translations, reflections and rotations and identify line (mirror) and rotational symmetries. They will extend their understanding of transformations through exploring transformations on a Cartesian plane.
Demonstrate transformations individually before showing students how they can be combined.
When introducing the Cartesian plane, show students that they should focus on one point of the shape and how that point will move under the transformation. Then extend that to other points on the shape. Students understand that a reflection will flip the shape along the axis of symmetry whereas a translation will move the shape left, right, up or down but will not flip it.
The use of mirrors and other concrete materials will allow students to develop the necessary visual and spatial skills for this topic.
This topic links to plotting coordinates on the Cartesian plane, equations of a line (for symmetry and mirror lines).
Teaching and learning summary:
 Build on students’ previous knowledge of transformation – translation, rotation, reflection.
 Translations (moving left, right, up or down).
 Reflections (flipping over the x and/or yaxis).
 Rotations (turning an object in 90° multiples clockwise or anticlockwise).
 Identify line (mirror) and rotational symmetries.
 Revise the vocabulary of transformations and how to describe them.
 Describe twostep transformations.
 Apply transformation to a Cartesian plane and look at the effect of transformations on coordinates.
 Use transformations to create patterns.
 Identify symmetry in shapes and patterns – both line and rotational.
Students:
 identify symmetry (line and rotational) in a shape or pattern
 describe a transformation or series of transformations, using the correct vocabulary
 recognise that a twostep transformation can be equivalent to a different onestep transformation
 transform a shape in a Cartesian plane and identify the corresponding coordinates.
Some students may:
 confuse the term 'translation' for 'transformation' as translations, rotations, enlargement and reflections all come under the umbrella term of 'transformation'.
 have more difficulty understanding transformation than performing it.
 mistakenly believe that the lines of reflection must be horizontal or vertical, or adjacent to a side of the image.
 mistakenly believe that the centre of rotation must be at a vertex or on the midpoint of one of the sides of the image.
 mistakenly believe that a transformation moves only some points in the plane.
 have trouble reflecting shapes over the x or yaxis.
 be able to translate the shape onto the other side of the required axis but struggle to draw the mirror image. Use mirrors, cutout shapes and other concrete materials to support students as they work through these concepts.
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 describing translations, reflections and rotation, identifying line and rotational symmetries.
 We are expanding our understanding of transformations.
Why are we learning about this?
When you understand twostep transformations, you can then create patterns and identify symmetry in these shapes. You will build on knowledge of translation, rotation and reflection.
What to do
Read this statement:
If you reflect a shape twice in two different lines of reflection, then you can map the object onto the image with one transformation.
 Try combining transformations to return to the original location.
 Record your transformations as steps with the type of transformation:
translation (slide), reflection (flip), rotation (turn).  Do you agree with the statement above? Explain your answer.
 Record your transformations as steps with the type of transformation:
 Now use a different shape and try combining transformations to return to the original location.
Success criteria
 I can successfully complete reflection and rotation of a given shape or object.
 I can describe twostep transformations and recognise that a twostep transformation can be equivalent to a different twostep transformation.
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Teaching strategies
A collection of evidencebased 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.

Concrete, Representational, Abstract (CRA)
The CRA model is a threephased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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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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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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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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Worked examples
A worked example is not just a preworked question that is given to the students. There are several types of worked examples and ways of using them.
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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.

Practical numbers: Part 1
In this lesson, students explore standardised measuring systems.
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Syllabus BITES
Syllabus BITES contains a series of modules that introduce transformations in the Cartesian plane. Each module focuses on a different transformation – translation, rotation, reflection and combinations.
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Transformations of the plane
This resource, focusing on transformations of the plane, gives detailed explanations for teachers and students of the curriculum content, worked examples and assessment questions.
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Transformations and congruence
In this unit, students learn to understand and use the terms ‘reflection’, ‘rotation’ and ‘translation’, recognising what determines each type of transformation.
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Rotations in the Cartesian plane
An interactive tool to investigate anticlockwise rotations of a triangle in the Cartesian plane.
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Transformations
This resource allows students to see the effect of different types of transformations on a triangle on a Cartesian plane.
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Transformations – rotation
This resource allows students to see the effect of rotation on a triangle on a Cartesian plane. You can adjust the position of the centre of rotation.
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