Numeracy: Lines | Worksheet | PrimaryLeap.co.uk - Free Printable

Problem Overview:

The task involves analyzing six squares and counting the number of vertical, horizontal, and diagonal lines in each square. The goal is to carefully identify and count all lines, including those that form the boundary of the square.

Solution Approach:

1. Understand the Definitions:
- Vertical Lines: Lines that run up and down (parallel to the sides of the square).
- Horizontal Lines: Lines that run left to right (perpendicular to the vertical lines).
- Diagonal Lines: Lines that run at an angle (neither vertical nor horizontal).

2. Analyze Each Square:
For each square, systematically count the vertical, horizontal, and diagonal lines. Make sure to include the lines that form the outer boundary of the square.

3. Counting Strategy:
- Vertical Lines: Count all lines parallel to the sides of the square.
- Horizontal Lines: Count all lines perpendicular to the sides of the square.
- Diagonal Lines: Count all lines that are neither vertical nor horizontal.

Step-by-Step Analysis:

#### Square 1:
- Vertical Lines: There are 3 vertical lines (including the outer boundary).
- Horizontal Lines: There are 3 horizontal lines (including the outer boundary).
- Diagonal Lines: There are 4 diagonal lines (two sets of intersecting diagonals).

Counts:
- Vertical = 3
- Horizontal = 3
- Diagonal = 4

#### Square 2:
- Vertical Lines: There are 3 vertical lines (including the outer boundary).
- Horizontal Lines: There are 3 horizontal lines (including the outer boundary).
- Diagonal Lines: There are 0 diagonal lines.

Counts:
- Vertical = 3
- Horizontal = 3
- Diagonal = 0

#### Square 3:
- Vertical Lines: There are 3 vertical lines (including the outer boundary).
- Horizontal Lines: There are 2 horizontal lines (including the outer boundary).
- Diagonal Lines: There are 5 diagonal lines (a series of diagonal lines forming a staircase pattern).

Counts:
- Vertical = 3
- Horizontal = 2
- Diagonal = 5

#### Square 4:
- Vertical Lines: There are 4 vertical lines (including the outer boundary).
- Horizontal Lines: There are 3 horizontal lines (including the outer boundary).
- Diagonal Lines: There are 1 diagonal line.

Counts:
- Vertical = 4
- Horizontal = 3
- Diagonal = 1

#### Square 5:
- Vertical Lines: There are 3 vertical lines (including the outer boundary).
- Horizontal Lines: There are 3 horizontal lines (including the outer boundary).
- Diagonal Lines: There are 6 diagonal lines (multiple intersecting diagonals).

Counts:
- Vertical = 3
- Horizontal = 3
- Diagonal = 6

#### Square 6:
- Vertical Lines: There are 4 vertical lines (including the outer boundary).
- Horizontal Lines: There are 4 horizontal lines (including the outer boundary).
- Diagonal Lines: There are 0 diagonal lines.

Counts:
- Vertical = 4
- Horizontal = 4
- Diagonal = 0

Final Answer:

\[
\boxed{
\begin{array}{ccc}
\text{Square 1:} & \text{Vertical = 3, Horizontal = 3, Diagonal = 4} \\
\text{Square 2:} & \text{Vertical = 3, Horizontal = 3, Diagonal = 0} \\
\text{Square 3:} & \text{Vertical = 3, Horizontal = 2, Diagonal = 5} \\
\text{Square 4:} & \text{Vertical = 4, Horizontal = 3, Diagonal = 1} \\
\text{Square 5:} & \text{Vertical = 3, Horizontal = 3, Diagonal = 6} \\
\text{Square 6:} & \text{Vertical = 4, Horizontal = 4, Diagonal = 0} \\
\end{array}
}
\]