Rotational symmetryThe order of rotational symmetry
Name: Date:
Write how many times each shape lands on itself in one full turn.
1
2
3
4
5
6
7
8
Rotational symmetry worksheets
A shape has rotational symmetry when turning it about its centre lands it back on itself before the turn is complete. These free printable worksheets draw twelve shapes at three different tilts and ask how many times each one lands on itself in a full turn.
If they get stuck
Rotational symmetry
The answer key prints on a separate page.
What's on this sheet
Line symmetry and rotational symmetry are two different questions and children routinely answer the first when asked the second. The parallelogram is the shape that separates them: it has no line of symmetry at all — there is no way to fold it in half — and a half turn lands it exactly back on itself, so its order is 2. A page that puts it next to a rectangle, which has both kinds, is the page where the two ideas stop being one idea.
Why this sheet works
Every shape is drawn upright and at two tilts, because a square turned 45° is a diamond and a child who learned "a square has order 4" from one picture has learned the picture. The answer key draws what the number means: a dot at the centre of rotation and an arc through the smallest turn that works. A shape with no rotational symmetry gets the dot alone, which says the honest thing — there is a centre, and nothing short of a whole turn brings it back.
How this one works
How many times does it land on itself?
regular octagon
lands on itself8 times in a full turn
360°÷8=45°
8
- The shape is a regular octagon. Rotational symmetry asks how it looks while you turn it about its centre — not how it folds.
- It is a regular octagon: eight equal sides and eight equal angles, so turning it until one corner reaches the next lands it on itself.
- Those 8 positions share the full turn equally, so each step is 360 ÷ 8 = 45°.
- The question asks for the order, so the answer is 8.