Let's solve the problem step by step.
---
🔷 Understanding Rotational Symmetry
Rotational symmetry refers to how many times a shape looks exactly the same as it rotates through 360°. The
order of rotational symmetry is the number of times the shape matches its original appearance during a full rotation (360°).
- If a shape looks the same only when rotated 360°, its order is
1.
- If it looks the same after 180°, then again at 360°, that’s
order 2.
- For example: A square has rotational symmetry of order 4 because it looks the same every 90°.
---
Now let's analyze each shape:
---
1. Smiley Face
```
😊
```
- It has two eyes and a curved mouth.
- If you rotate it by
180°, the eyes and mouth will be upside down — it
doesn’t look the same.
- Only after
360° does it return to original position.
- So, it only matches once per full turn.
✔ Order of rotational symmetry = 1
---
2. Green "X" Shape (Cross-like)
```
X
```
- This shape is made of four arms at right angles.
- Rotate it by
90°: it looks the same.
- Rotate again by 90° (total 180°): still looks the same.
- Again at 270°: same.
- At 360°: back to start.
So it matches
4 times in 360°.
✔ Order of rotational symmetry = 4
---
3. Heart Shape (with concentric hearts)
```
❤️
```
- A heart is not symmetric under rotation.
- Rotate it by 180°: the top becomes the bottom, but the pointy tip goes up → it looks different.
- Only matches at 360°.
✔ Order of rotational symmetry = 1
---
4. Trapezium (Isosceles Trapezoid)
```
▄▄▄▄
▄ ▄
▄ ▄
▄▄▄▄▄▄▄▄▄▄
```
- It's symmetrical along the vertical axis, but not rotationally.
- Rotate by 180°: the top base becomes the bottom, but since they are different lengths, it won't match.
- Only matches at 360°.
✔ Order of rotational symmetry = 1
---
5. Four-pointed Star (like a diamond star)
```
▲
◆◆
▼
```
- This is a regular four-pointed star (rotated square with points).
- It looks the same every
90° rotation.
- After 90°, 180°, 270°, and 360°, it matches.
So, it matches
4 times.
✔ Order of rotational symmetry = 4
---
6. Cross Shape (Plus sign)
```
□
□□□
□
```
- This is a cross with equal arms.
- Rotate by 90°: it looks the same.
- Rotate by 180°: same.
- Rotate by 270°: same.
- Rotate by 360°: back to start.
It matches
every 90°, so
4 times.
✔ Order of rotational symmetry = 4
---
✔ Final Answers:
| Shape | Order of Rotational Symmetry |
|-------|-------------------------------|
| 1. Smiley Face |
1 |
| 2. Green X |
4 |
| 3. Heart |
1 |
| 4. Trapezium |
1 |
| 5. Four-pointed Star |
4 |
| 6. Cross |
4 |
---
📝 Summary:
- Shapes that are
not symmetric under rotation (like smiley face, heart, trapezium) have
order 1.
- Shapes with
equal arms or points around a center (like X, star, cross) often have
higher orders, especially
4 if they repeat every 90°.
Let me know if you'd like visual explanations or diagrams!
Parent Tip: Review the logic above to help your child master the concept of printable shapes for rotational symmetry.
