Transformation: Year 5: Planning tool

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 two-dimensional 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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