Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M5SP03
Numeracy Progression: Understanding geometric properties: P5
At this level, students develop their understanding and skills in transformations including reflections (flips), translations (slides) and rotations (turns). Students investigate reflection symmetry.
Use explicit teaching strategies to assist students’ understanding of transformations.
Use a 2D shape to demonstrate and model:
 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.
Provide relevant contexts that engage student interest to create transformations using practical activities of folding and cutting shapes manually or by using digital technologies. Students develop their understanding that a rotation is a shape turned about a point, that a reflection is achieved when the shape is flipped over creating a ‘mirror image’ of the shape, and that a translation is a shape slid along a line.
Provide opportunities for students to develop their understanding of how the line of symmetry defines the two aspects of a ‘mirror’ image of the figure into two congruent halves. They explore rotational symmetry using familiar 2D shapes, letters or numbers.
Make explicit through relevant examples, modelling and investigation that a figure can have one line of symmetry, several lines of symmetry, or no lines of symmetry.
Teaching and learning summary:
 Model and describe the effects of transformations by manually flipping, sliding and turning 2D shapes and by using digital tools.
 Use questioning to prompt students to justify their thinking when describing the properties of shapes (size and shape) that do not change when shapes are translated, reflected or rotated.
 Use engaging contexts such as geometric design.
 Use practical activities to explore symmetry.
 Consider opportunities to incorporate cultural connections through traditional art and design using tessellations as the context.
Students:
 create transformations of folding and cutting shapes manually or by using digital tools
 describe objects as those with one line of symmetry, several lines of symmetry, or no lines of symmetry
 explain why some figures have no line of symmetry.
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.
 may 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.
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 describe the transformations of a twodimensional shape.
 We use flip, slide and turns to change the position of a shape.
Why are we learning about this?
 We are using spatial reasoning skills that can be used to solve problems in a range of real life situations. Knowing how certain shapes tessellate helps tilers, paving companies and architects to design spaces.
What to do
 Find either a 50 cent, 20 cent, 10 cent or a 5 cent coin.
 Draw the position of the coin on a piece of paper. This is the starting position.
 Next flip the coin in a horizontal direction. Draw the coin on your sheet of paper and add the label flip.
 Now turn the coin a half turn. Draw the coin on your sheet of paper and add the label turn.
 Slide the coin vertically then flip. Draw the coin on your sheet of paper and add the label slide and flip.
 What transformations do you need to do to return to the original position?
 List the steps on your drawing .
Success criteria
I can:
 describe the effects of transformations by manually flipping, sliding and turning 2D shapes
 identify the effects of transformations by flipping, sliding and turning.
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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.

Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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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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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.

Shipping container space
This game draws on students’ knowledge of translations, reflections, and rotations of plane shapes.
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Friezes
Students create a repeating pattern using geometric transformations.
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Attractive rotations
Students create attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees.
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Quilts
In this unit, students use patchwork quilting to explore translations, reflections and rotations of plane shapes.
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Tessellating art
Students describe the reflection or rotational symmetry of a shape or tessellation.
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Tessellation, transformation and art
In this unit, students learn about transformations and tessellations, then apply this knowledge to create a piece of artwork.
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Symmetry and tessellations study guide
This guide provides a basic overview of symmetry.
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Reflection symmetry principles: basic
A student tutorial with interactive activities to learn about symmetry.
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Shady symmetry
Students work out how many different symmetrical shapes they can make by shading triangles or squares.
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Logo licenses
This unit examines the use of reflective, rotational and translational symmetry in the design of logos.
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Fold and cut 2
This unit involves folding and cutting paper to produce and perceive number patterns and geometric shapes.
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Getting in line
This is a level 2 geometry activity from the Figure It Out series. A PDF of the student activity is included.
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Assessment
By the end of Year 5, students are performing and describing the results of transformations and identifying any symmetries.

Mathematics: ACARA work sample portfolio summary – Year 5
Refer to ACARA work sample 8, 'Geometry: Location and transformation', and the related task for guidance in assessing students’ understanding of transformations.
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A case for a new phone
The purpose of this activity is to engage the student in using a description of transformations to solve a problem.
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