Understand the idea.
Build from a stated rule
Choose the symmetry rule before placing the parts of a design: a mirror line for reflection or a fixed centre and turn for rotation. To reflect a tile, place its matching tile on the opposite side at the same distance from the mirror line.
On a six-column grid, the central vertical line runs between columns 3 and 4. The nearest columns pair together, then the next pair and the outer pair. Keep each reflected tile in the same row and match its colour.
Check every feature
Check every feature after constructing the design. Matching outlines are not enough if colours or dots fail to match. Use a fold, tracing paper or equal grid distances to test the rule, rather than judging whether the picture looks balanced.
For a half-turn design, turn through half a full circle about the centre. A dot near one corner must have an identical dot near the opposite corner, at matching distances from the edges, so each moves into the other’s place.
See the method in action.
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?
Worked solution
- 1
Locate the mirror line.
The central vertical line lies between columns 3 and 4, separating the grid into two three-column halves.
- 2
Pair columns at equal distances from the line.
Each pair occupies matching positions on opposite sides; columns are not all shifted by the same amount.
- 3
Place the far-left tile’s copy.
Column 1 pairs with column 6, and reflection in a vertical line keeps the tile in the same row.
Column 6, 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.
Worked solution
- 1
Find where a half turn sends the corner.
Turning the rectangle halfway around its centre swaps the top-left corner with the bottom-right corner.
- 2
Match the dot’s position and appearance.
Place an identical blue dot near the bottom-right, as far from the bottom and right edges as the original is from the top and left edges.
- 3
Check both dots under the turn.
Each blue dot moves onto the other, while the rectangle outline also matches, so the whole design has half-turn symmetry.
Add a matching blue dot near the bottom-right corner.
Try it yourself.
Check your understanding
Which row does a reflected tile stay in when reflecting across a vertical line?
Show answer & reasoning
The same row.
The tile stays in the same row. Reflection in a vertical line changes its left-to-right position at an equal distance across the line, but does not move it up or down.
Keep practising
6 worksheet questions · 10 marks
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), , and , 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 ↗