How to teach transformation in mathematics

Transformations can be found everywhere. You don’t have to go far to find one, which makes teaching kids about transforming 2D shapes relevant, and a lot of fun!

Transformations are movements through space. We see them as a repeating pattern. Transformations are part of our everyday lives and we don’t even know it!

There are so many examples of transformation processes, and the range is so diverse:

• walking, skipping and running
• a factory machine that makes thousands of bottles
• the movement of a robotic Mars Rover
• strumming a guitar
• the twists and turns of a roller-coaster
• mosaics, art & graphic design

So many professions use transformation skills, including Architects, Artists, and Designers. They use transformation understanding to create and design patterns which can be used in so many different areas, including:

• textiles
• buildings
• models
• flooring
• gaming
• films
• interior design
• graphics
• furniture

I like to start a unit on transformations by encouraging students to find examples of flip, slide & turns around the classroom, school & environment.

Teaching Transforming 2D Shapes

Teaching Transforming 2D Shapes is a Measurement & Geometry topic, and it’s part of the Location & Transformation sub-strand area.

Teaching Flip, Slides, Turns, Dilations & Symmetry is taught from Year 2 onwards. Notice that not ALL areas are covered in all year levels.

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The essence of Teaching Transformations  is to enable students to develop their ability to identify the properties of shapes and objects and how they can be combined. This is an important range of spatial reasoning skills that are used to solve problems in a range of real life situations and occupations. .

Knowledge of how certain shapes will tessellate allows tilers, paving companies and architects to design spaces efficiently and creatively. Symmetry is a fundamental aspect of geometry both in the environment and in design.

Here’s some basic definitions about transformation geometry:

Transformation

A transformation is where 2D shapes are repeated using flips, slides and turns. When you transform a shape, it stays the same shape and size but it can change direction.

Flip

Flips are also know as reflections. To make a flip pattern, take an exact copy of your shapes and reflect it across an axis of symmetry or mirror line.

A flip creates a MIRROR Image of the original shape and can be in any direction. Some shapes look exactly the same when they have been reflected, which can confuse your students into thinking all shapes will look the same when they are reflected!

Slide

Slides are also known as Translations. A slide pattern is created by moving your original shape without turning or flipping it. You can move up, down, forwards and back. You can even overlap shapes in a slide transformation.

Just make sure that each shape in the pattern is still facing the same direction as the first shape.

Turn

Turns are also know as rotations. To make a rotation pattern, turn shapes around a point and copy them into the new position. Turns can be made clockwise and anticlockwise.

The rotation can be an infinite number of degrees. Introduce students to quarter turns, 90° and half turns, 180°

Dilation

Dilation are enlargements or reductions. They are transformations that produce an image that is the same shape but a different size. 

Dilations that produce bigger sized images are Enlargements and dilations that create smaller images are known as reductions.

Symmetry

A shape, object or image has symmetry or is symmetrical when one half of the shape can fit exactly over the other half.

Some shapes can have more than one line of symmetry.

Line Symmetry

A shape, drawing or image has line symmetry if one half is a reflection of the other half. The ‘mirror line’ line cuts the shape into 2 mirror images. 

Rotational symmetry

A shape or image has rotational symmetry when it looks the same after it has been rotated by less that 360°

Teaching Transforming 2D Shapes By Year Level

Here’s the continuum of learning for formally teaching Transformations from Year 2 – Year 6. Click each arrow to see the details:

Year 2

Investigate the effect of one-step slides and flips with and without digital technologies (ACMMG044)

• Understand that objects can be moved but changing position does not alter an object’s size or features

Achievement Standard -‘C’ Grade – Satisfactory

• Students explain the effects of one-step transformations

Key Teaching Points For Year 2:

• Identify slides
• Identify flips
• Identify turns  
• Flip or slide transformations do not change size, and shape or features of objects
• Slide transformations can be done in any direction but without turning the shape
• Flip transformations is performed around a mirror line, which may or may not be drawn in.
• In some Flip or Slide transformations, the shape stays the same
• Mirror symmetry and Line symmetry are not the same

Year 3

Identify symmetry in the environment (ACMMG066)

• identify symmetry in Aboriginal rock carvings or art
• identify symmetry in the natural and built environment

Achievement Standard -‘C’ Grade – Satisfactory

• Students identify symmetry in the environment

Key Teaching Points For Year 3:

• Identify lines of symmetry in artwork
• Identify lines symmetry in man-made environments
• Identify lines symmetry in natural environments
• Identify more than one line of symmetry where appropriate
• Identify no lines of symmetry in shapes or say they are asymmetrical
• Use folding and cutting & or pattern blocks etc. as a means to determine reflectional symmetry
•  Use transparent mirrors to identify symmetry

Year 4

Create symmetrical patterns, pictures and shapes with and without digital technologies(ACMMG091)

• Use stimulus materials such as the motifs in Central Asian textiles, Tibetan artefacts, Indian lotus designs and symmetry in Yolngu or Central and Western Desert art

Achievement Standard -‘C’ Grade – Satisfactory

• Students create symmetrical shapes and patterns

Key Teaching Points For Year 4:

• Identify & create lines of symmetry in artwork
• Identify & create lines symmetry in man-made environments
• Identify & create lines symmetry in natural environments
• Identify & create shapes and patterns with one or more line of symmetry where appropriate
• Identify no lines of symmetry in shapes or say they are asymmetrical
• Use folding and cutting & or pattern blocks etc. as a means to create symmetrical patterns
•  Use transparent mirrors to create symmetry

Year 5

Describe translations, reflections and rotations of two dimensional shapes. Identify line and rotational symmetries (ACMMG114)

• Identify and describe the line and rotational symmetry of a range of two-dimensional shapes, by manually cutting, folding and turning shapes and by using digital technologies
• Identify the effects of transformations by manually flipping, sliding and turning two-dimensional shapes and by using digital technologies

Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (ACMMG115)

• Use digital technologies to enlarge shapes
• Use a grid system to enlarge a favourite image or cartoon

Achievement Standard -‘C’ Grade – Satisfactory

• Students describe transformations of two-dimensional shapes and identify line and rotational symmetry

Key Teaching Points For Year 5:

• Translate, reflect & rotate 2D shapes
• Identify line symmetry
• Identify rotational symmetry
•  Size & shape of a shape does not change after it has been translated
• Symmetry can be man-made and found in nature, art, design and cultural art works
• There is an infinite number of degrees of turn that can be produced in a rotation
• A 360° turn takes the shape back to where it started
• A 180° turn results in an upside-down image
• 90° clockwise and 90° anti-clockwise create very different results

Year 6

Investigate combinations of translations, reflections and rotations, with and without the use of digital technologies (ACMMG142)

• Design a school or brand logo using transformation of one or more shapes
• Understand that translations, rotations and reflections can change the position and orientation but not shape or size

Achievement Standard -‘C’ Grade – Satisfactory

• Students describe combinations of transformations

Key Teaching Points For Year 6:

• Translates, reflects & rotates shapes
• Combines translations
• Identifies combined transformations
• Understands tessellation
• Size, shape & features of a shape do not change when it is translated, reflected or rotated
• Translations can be done in any direction, but without rotating the shape or object
• Tessellations are created on the basis of transformations
• Reflections are performed on a mirror line
• Rotations are performed on a point
• Transparent mirrors can be used for identifying line symmetry, but not rotational symmetry

Flip, Slide, Turns, Dilation Geometry Teacher Resources

To help students build their visualisation skills we hacked a K-Mart Mini Lazy Susan! It really helped the students learn how to visualise the rotations in their head! You could also use paper-plates or card and split pins too!

Check out our video and make your own Transformation Rotation Wheel!

Download our teacher resources for teaching Transformations. There’s math activities for the classroom and versions for distance learning too. Please note our resources cannot be used on Outschool.

Click to Junp To Resources...

Flip Slide Turn Interactive Activities

Transforming 2D Shapes Vocabulary Thinkboards

Frayer Model Thinkboards are perfect for warm-ups and topic introductions, Reviews & KWL’s. They can be teacher-led or used in group activities and will help your students build mathematical vocabulary. Use as single sheets or print in a student booklet.

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Flip, Slide, Turn, 2 Piece Puzzles

Fun 2 piece puzzles to help students identify flip, slides and turns. Perfect for Year 2 ACMMG044

Download

Reflect, Translate, Rotate, 2 Piece Puzzles

Fun 2 piece puzzles to help students identify Reflect, Translate, Rotate transformation. Perfect for Year 5 ACMMG114

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Flip, Slide, Turn, Transformations Name Activity 

A fun engaging activity with pattern blocks. Students make their name using pattern blocks and describe any transformations they made. Incudes 2 versions: flip, slide, turn & Rotate, Translate, Reflect versions.

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Flip, Slide, Turn Interactive Games

Year 5 – A Set of 19 spinner games for students to practise the transformation of shapes. Spin the spinner and complete a task. Continue until all tasks are completed. Or play in pairs where 3 in a row wins! Connects the language of flip-reflect, slide-translate, turn -rotate.

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Flip, Slide, Turn, Google Slides/PowerPoint

Year 5- DISTANCE LEARNING Version- PNG & Powerpoint to change, delete, share-online or send home. A Set of 19 spinner games for students to practise the transformation of shapes. Spin the spinner and complete a task. Continue until all tasks are completed. Or play in pairs where 3 in a row wins!

Download

Flip, Slide, Turn, Pattern Block Numbers

Year 5 – This set of pattern block number activities has been created to help your students identify transformations in their designs. Students use real pattern blocks or the cut outs provided to build number 0-9. They complete the task by identifying which 2D shapes have been used in their design and how shapes have been trnslated, rotated and reflected. There’s 3 versions and 3 levels of the activity in this file.

Download

Pattern Block Numbers Powerpoint & Google Slides

DISTANCE Learning Version of our Pattern Block Numbers For Teaching transformations- Includes Powerpoint with drag & Drop pieces for loading onto Google Slides, Interactive Whiteboards, Seesaw etc. Also includes JPEG version too.

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