This worksheet introduces rotational symmetry with examples and asks students to find the order for six different shapes.

Problem Overview:

The task is to determine the order of rotational symmetry for each of the given shapes. The order of rotational symmetry is defined as the number of times a shape looks exactly the same during a full rotation (360°). If a shape looks the same after being rotated by an angle \( \theta \), then the order of rotational symmetry is given by:

\[
\text{Order} = \frac{360^\circ}{\theta}
\]

Step-by-Step Solution:

#### Shape 1: Smiley Face
- The smiley face is a circle with two eyes and a mouth.
- A circle has infinite rotational symmetry because it looks the same at any angle.
- However, the specific features (eyes and mouth) limit the symmetry.
- The smiley face looks the same only when rotated by 360°.
- Therefore, the order of rotational symmetry is 1.

#### Shape 2: Cross
- The cross is symmetrical along both horizontal and vertical axes.
- It looks the same after a rotation of 90°, 180°, 270°, and 360°.
- The smallest angle of rotation that makes the shape look the same is 90°.
- The order of rotational symmetry is:

\[
\text{Order} = \frac{360^\circ}{90^\circ} = 4
\]

#### Shape 3: Heart
- The heart shape is not symmetrical under rotation.
- It does not look the same after any rotation other than 360°.
- Therefore, the order of rotational symmetry is 1.

#### Shape 4: Trapezoid
- The trapezoid is not symmetrical under rotation.
- It does not look the same after any rotation other than 360°.
- Therefore, the order of rotational symmetry is 1.

#### Shape 5: Star
- The star is a five-pointed star.
- It looks the same after rotations of 72°, 144°, 216°, 288°, and 360°.
- The smallest angle of rotation that makes the shape look the same is 72°.
- The order of rotational symmetry is:

\[
\text{Order} = \frac{360^\circ}{72^\circ} = 5
\]

#### Shape 6: Plus Sign
- The plus sign is symmetrical along both horizontal and vertical axes.
- It looks the same after rotations of 90°, 180°, 270°, and 360°.
- The smallest angle of rotation that makes the shape look the same is 90°.
- The order of rotational symmetry is:

\[
\text{Order} = \frac{360^\circ}{90^\circ} = 4
\]

Final Answers:

1. Smiley Face: 1
2. Cross: 4
3. Heart: 1
4. Trapezoid: 1
5. Star: 5
6. Plus Sign: 4

\[
\boxed{1, 4, 1, 1, 5, 4}
\]