Rotational Symmetry worksheet for Grade 5-6 students, focusing on identifying the order of rotation in shapes and patterns.

You're working on a Rotational Symmetry worksheet designed for Grade 5–6, focusing on the Order of Rotation.

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## ✔ What is Rotational Symmetry?

A shape has rotational symmetry if it looks the same after being rotated (turned) around its center by a certain angle less than 360°.

The order of rotational symmetry is the number of times the shape looks exactly the same during a full 360° rotation.

> 📌 Formula:
> Order = 360° ÷ smallest angle of rotation that maps the shape onto itself

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## 🧩 Let’s Solve “ROTATIONAL SYMMETRY 1” (Left Worksheet)

We’ll go row by row, shape by shape.

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🔹 Row 1:

1. Arrow (→)
- Rotating 180°: points left → doesn’t match original.
- Only looks same at 360° → Order = 1

2. Trapezoid (non-isosceles)
- No rotational symmetry — rotating it never matches original until 360° → Order = 1

3. Square
- Looks same at 90°, 180°, 270°, 360° → Order = 4

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🔹 Row 2:

4. Double Arrow (↔)
- Looks same at 180° and 360° → Order = 2

5. Left-pointing arrow (←)
- Same as right-pointing arrow — only matches at 360° → Order = 1

6. Regular Hexagon
- Regular polygons have order = number of sides → Order = 6

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🔹 Row 3:

7. Right Triangle (not isosceles)
- No rotational symmetry → Order = 1

8. Regular Octagon
- Order = number of sides → Order = 8

9. Rhombus (diamond shape)
- Rotates 180° to look same → Order = 2

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## ✍️ Answers for “ROTATIONAL SYMMETRY 1”:

| Shape | Order |
|-------------------|-------|
| Right Arrow | 1 |
| Trapezoid | 1 |
| Square | 4 |
| Double Arrow | 2 |
| Left Arrow | 1 |
| Regular Hexagon | 6 |
| Right Triangle | 1 |
| Regular Octagon | 8 |
| Rhombus | 2 |

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## 🌀 Now, “ROTATING PATTERNS 1” (Right Worksheet)

This section asks you to find the order of rotation for repeating patterns.

Patterns with rotational symmetry will look the same after being rotated around their center.

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🔹 Top Row:

1. Empty square (placeholder) → Not a pattern → Order = 1 (or N/A — but likely 1)

2. Checkerboard/Diamond Grid Pattern
- Rotates 90°, 180°, 270°, 360° → looks same → Order = 4

3. Concentric Squares Spiral
- Rotates 90°, 180°, 270°, 360° → symmetric → Order = 4

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🔹 Middle Row:

4. Empty square → Order = 1

5. Interlocking Diamond/Chain Pattern
- Rotates 180° → looks same → Order = 2

6. Hexagonal Mesh Pattern
- Like honeycomb — rotates 60°, 120°, 180°, 240°, 300°, 360° → Order = 6

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🔹 Bottom Row:

7. Empty square → Order = 1

8. Zigzag/Wavy Line Pattern
- Rotates 180° → looks same → Order = 2

9. Honeycomb/Hexagon Tiling
- Same as above → Order = 6

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## ✍️ Answers for “ROTATING PATTERNS 1”:

| Pattern | Order |
|-----------------------------|-------|
| Empty | 1 |
| Checkerboard Grid | 4 |
| Concentric Squares | 4 |
| Empty | 1 |
| Interlocking Diamonds | 2 |
| Hexagonal Mesh | 6 |
| Empty | 1 |
| Zigzag Lines | 2 |
| Honeycomb Tiling | 6 |

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## 🎯 Final Tip:

- If a shape or pattern looks the same only once per full turn (at 360°), its order is 1.
- If it repeats every 90°, order = 4.
- If every 60°, order = 6.
- Always count how many *distinct positions* look identical during one full rotation.

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✔ You’ve now mastered identifying the order of rotational symmetry for both shapes and patterns!

Let me know if you want a printable answer key or visual explanations! 🖍️📐