The idea, step by step
Build from a stated rule
Choose a mirror line or a centre of rotation first. For a reflection, match each tile on one side with a tile the same distance on the other side. A square next to the line reflects to the square next to the line on the opposite side, not onto the line itself.
Check every feature
After drawing the design, check the outline, colours and positions. A design that looks balanced is not automatically symmetrical. You can use tracing paper, a fold or a careful count of grid spaces to test the rule. Keep your original construction rule so another person can recreate the design.
A common trap
Copying a pattern the same way round instead of reflecting it.
Instead: Reflection reverses left and right across the mirror line. Count equal distances from the line.
See the thinking
Matching a tile
On a six-column grid, a tile in the far-left column reflects across the central vertical line. Which column receives its copy?
- The central line separates columns 3 and 4.
- The far-left tile is three columns out from that boundary.
- Its copy goes in the far-right column.
A rotating decoration
A rectangle has a blue dot near its top-left corner. Add one dot so the design has half-turn symmetry.
- A half turn swaps top-left with bottom-right.
- Keep the new dot the same distance from the nearby edges.
Check your understanding
Which row does a reflected tile stay in when reflecting across a vertical line?
Show answer
The same row.
A vertical mirror swaps left and right but not up and down.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- A six-column grid is reflected across the middle vertical line. Which column matches column 2?1 mark
- On that grid, which column matches column 3?1 mark
- Copy the supplied half-design and complete its reflection.2 marks
- A red dot is near the top-right corner of a rectangle. Where is its half-turn matching dot?2 marks
- Create a square-tile design with a vertical mirror line. Explain how you checked it.2 marks
- Why might a shape outline be symmetrical while its coloured design is not?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A six-column grid is reflected across the middle vertical line. Which column matches column 2?1 mark
The pairs are 1 with 6, 2 with 5, and 3 with 4.
Column 5. - On that grid, which column matches column 3?1 mark
These columns sit immediately beside the mirror line.
Column 4. - Copy the supplied half-design and complete its reflection.2 marks
Match each given tile in the same row and the opposite column.
Add shaded tiles at (column 6, row 1), (5, 2), (4, 2) and (5, 3), counting rows from the top. - A red dot is near the top-right corner of a rectangle. Where is its half-turn matching dot?2 marks
A half turn swaps opposite corners.
Near the bottom-left corner, at matching distances from the edges. - Create a square-tile design with a vertical mirror line. Explain how you checked it.2 marks
Check every row and colour, not just the outside outline.
Many answers are valid: each shaded tile must have a matching tile at equal distance on the other side. - Why might a shape outline be symmetrical while its coloured design is not?2 marks
Symmetry applies to the whole design.
The colours or decorations may fail to match across the line or after the turn.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Composite shapes/objects; angle names; reflection/rotational symmetry; creating designs.
Official curriculum source ↗