Numeracy: Symmetrical patterns | Worksheet | PrimaryLeap.co.uk - Free Printable

Problem Overview:

The task involves completing symmetrical patterns on a grid. Each pattern must have one or two lines of symmetry. The goal is to fill in the missing squares so that the completed pattern is symmetrical.

Key Concepts:

1. Line of Symmetry: A line where one side of the pattern is a mirror image of the other side.
2. One Line of Symmetry: The pattern is symmetrical along one axis (either vertical, horizontal, or diagonal).
3. Two Lines of Symmetry: The pattern is symmetrical along two axes (e.g., both vertical and horizontal).

Solution Approach:

For each grid, we will:
1. Identify the existing squares and their positions.
2. Determine the line(s) of symmetry based on the given squares.
3. Reflect the existing squares across the identified line(s) of symmetry to complete the pattern.

---

Step-by-Step Solutions:

#### Pattern 1:
- Existing Squares: Top-left and top-right squares are filled.
- Symmetry: Vertical line of symmetry.
- Completion: Mirror the top-left square to the top-right and vice versa. Similarly, mirror the bottom-left and bottom-right squares.

Completed Pattern:
```
X X
X X
X X
X X
```

#### Pattern 2:
- Existing Squares: Top-middle, middle-left, and middle-right squares are filled.
- Symmetry: Horizontal line of symmetry.
- Completion: Mirror the top row to the bottom row.

Completed Pattern:
```
X X X
X X
X X X
```

#### Pattern 3:
- Existing Squares: Top-right, middle-left, and bottom-left squares are filled.
- Symmetry: Diagonal line of symmetry (top-left to bottom-right).
- Completion: Reflect the squares across the diagonal.

Completed Pattern:
```
X X
X
X X
```

#### Pattern 4:
- Existing Squares: Top-left, middle-left, and bottom-middle squares are filled.
- Symmetry: Vertical line of symmetry.
- Completion: Mirror the left side to the right side.

Completed Pattern:
```
X X
X X
X
```

#### Pattern 5:
- Existing Squares: Top-middle, middle-left, and bottom-middle squares are filled.
- Symmetry: Horizontal line of symmetry.
- Completion: Mirror the top row to the bottom row.

Completed Pattern:
```
X X X
X X
X X X
```

#### Pattern 6:
- Existing Squares: Top-middle, middle-right, and bottom-middle squares are filled.
- Symmetry: Vertical line of symmetry.
- Completion: Mirror the right side to the left side.

Completed Pattern:
```
X X X
X X
X X X
```

#### Pattern 7:
- Existing Squares: Top-left, middle-left, and bottom-left squares are filled.
- Symmetry: Vertical line of symmetry.
- Completion: Mirror the left side to the right side.

Completed Pattern:
```
X X
X X
X X
```

#### Pattern 8:
- Existing Squares: Top-middle, middle-middle, and bottom-middle squares are filled.
- Symmetry: Vertical and horizontal lines of symmetry.
- Completion: Mirror the pattern both vertically and horizontally.

Completed Pattern:
```
X X X
X X X
X X X
```

#### Pattern 9:
- Existing Squares: Top-middle, middle-middle, and bottom-middle squares are filled.
- Symmetry: Vertical and horizontal lines of symmetry.
- Completion: Mirror the pattern both vertically and horizontally.

Completed Pattern:
```
X X X
X X X
X X X
```

---

Final Answer:

The completed patterns are as follows:

1.
```
X X
X X
X X
X X
```

2.
```
X X X
X X
X X X
```

3.
```
X X
X
X X
```

4.
```
X X
X X
X
```

5.
```
X X X
X X
X X X
```

6.
```
X X X
X X
X X X
```

7.
```
X X
X X
X X
```

8.
```
X X X
X X X
X X X
```

9.
```
X X X
X X X
X X X
```

Final Answer:
\boxed{
\begin{array}{c}
\text{Patterns completed as shown above.}
\end{array}
}