Year 6 Mathematics · AC9M6SP03

Transformations and Tessellations

Combine translations, rotations and reflections without gaps or overlaps

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students analyse how repeated congruent shapes cover a plane, describe the transformation sequence and use angle relationships to test whether vertices fit around a point.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: recognise and use combinations of transformations to create tessellations and patterns, using digital tools where appropriate
Key conceptTeach from the board

Build a repeating tessellation

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

A repeated shape covers the plane without gaps or overlaps

A tessellation preserves congruence under rigid transformations. Around each vertex, the meeting angles total 360°.

Use transformations to explain the pattern

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

movedescriptiontranslationslide motif by a fixed vectorrotationturn motif about a vertexreflectionflip motif across a lineglide reflectionreflect, then translate along the linevertex testmeeting angles total 360°

Digital tools can repeat precise transformations, but students should identify the generating motif and transformation rule.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6SP03 - Transformations and Tessellations
Example 1

move description translation slide motif by a fixed vector rotation turn motif about a vertex reflection flip motif across a line glide reflection reflect, then translate along the line vertex test meeting angles total 360°

Example 2

: understanding that the Cartesian plane provides a graphical or visual way of describing location with respect to a fixed origin

Example 3

: understanding that the axes are number lines that can have different scales, including fractions and decimals, depending on purpose

Example 4

: understanding that the horizontal coordinate is written first and is changed if there is a move to the left or right, whereas a move up or down will change the vertical coordinate

Curriculum examplesCopied content

AC9M6SP03: recognise and use combinations of transformations to create tessellations and other geometric patterns, using dynamic geometric software where appropriate

  • E1: understanding that the Cartesian plane provides a graphical or visual way of describing location with respect to a fixed origin
  • E2: understanding that the axes are number lines that can have different scales, including fractions and decimals, depending on purpose
  • E3: understanding that the horizontal coordinate is written first and is changed if there is a move to the left or right, whereas a move up or down will change the vertical coordinate
  • E4: using the Cartesian plane to draw lines and polygons, listing co-ordinates in the correct order to complete a polygon
  • E5: exploring how coordinates can be used to input positional data for artificial intelligence systems to locate positions in an image or other two-dimensional space
  • E6: investigating and connecting land or star maps used by First Nations Australians with the Cartesian plane through a graphical or visual way of describing location

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Identify a tessellation.
  • Name the motif.
  • Describe a translation.
  • Use a vertex-angle test.
  • Combine transformations.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Pattern with gaps called tessellationThe plane must be covered continuously.
Shape resized during repetitionRigid transformations preserve congruence.
Transformation described vaguely as moveName direction, distance, centre, angle or line.
Vertex angle condition ignoredUse 360° to test feasibility.
Curriculum alignmentStart here

Learning goal

Students analyse how repeated congruent shapes cover a plane, describe the transformation sequence and use angle relationships to test whether vertices fit around a point.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: recognise and use combinations of transformations to create tessellations and patterns, using digital tools where appropriate
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