This worksheet features ten numbered geometric figures and symbols, challenging students to determine the order of rotational symmetry for each.

To determine the order of rotational symmetry for each shape, we need to identify how many times the shape looks exactly the same as it rotates through 360 degrees. The order of rotational symmetry is the number of positions in which the shape appears identical during a full rotation.

Let's analyze each shape step by step:

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1. Circle

- A circle looks the same at any angle of rotation.
- It has infinite rotational symmetry.
- Order of rotational symmetry: ∞

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2. Letter "S"

- The letter "S" does not look the same at any rotation other than 360 degrees.
- It has no rotational symmetry.
- Order of rotational symmetry: 1

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3. Starfish-like Shape

- This shape has 5 arms and looks the same after rotating by \( \frac{360^\circ}{5} = 72^\circ \).
- It repeats its appearance 5 times in a full rotation.
- Order of rotational symmetry: 5

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4. Diamond (Rhombus)

- A diamond (rhombus) looks the same after rotating by \( \frac{360^\circ}{2} = 180^\circ \).
- It repeats its appearance 2 times in a full rotation.
- Order of rotational symmetry: 2

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5. Letter "Y"

- The letter "Y" does not look the same at any rotation other than 360 degrees.
- It has no rotational symmetry.
- Order of rotational symmetry: 1

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6. Letter "W"

- The letter "W" looks the same after rotating by \( \frac{360^\circ}{2} = 180^\circ \).
- It repeats its appearance 2 times in a full rotation.
- Order of rotational symmetry: 2

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7. Swastika-like Symbol

- This symbol looks the same after rotating by \( \frac{360^\circ}{4} = 90^\circ \).
- It repeats its appearance 4 times in a full rotation.
- Order of rotational symmetry: 4

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8. Square

- A square looks the same after rotating by \( \frac{360^\circ}{4} = 90^\circ \).
- It repeats its appearance 4 times in a full rotation.
- Order of rotational symmetry: 4

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9. Irregular Shape

- This shape does not look the same at any rotation other than 360 degrees.
- It has no rotational symmetry.
- Order of rotational symmetry: 1

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10. Sun-like Shape

- This shape has 10 triangular rays and looks the same after rotating by \( \frac{360^\circ}{10} = 36^\circ \).
- It repeats its appearance 10 times in a full rotation.
- Order of rotational symmetry: 10

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Final Answers

1. ∞
2. 1
3. 5
4. 2
5. 1
6. 2
7. 4
8. 4
9. 1
10. 10

\boxed{∞, 1, 5, 2, 1, 2, 4, 4, 1, 10}