Tessellation Worksheet - Key Stage 2 - Free Printable

Problem Analysis:

The task involves determining whether each given shape can be tessellated. Tessellation refers to the ability of a shape to cover a plane completely without gaps or overlaps when repeated in a pattern.

Key Points for Tessellation:

1. Regular Tessellation: Only three regular polygons can tessellate the plane: equilateral triangles, squares, and regular hexagons.
2. Irregular Shapes: Some irregular shapes can also tessellate if their edges fit together perfectly.
3. Curved Shapes: Shapes with curved edges (like circles) generally cannot tessellate because they leave gaps when placed side by side.

Step-by-Step Solution:

#### 1. Equilateral Triangle (Top Left):
- An equilateral triangle can tessellate because six triangles can meet at a single vertex without gaps.
- Answer: Yes

#### 2. Circle (Second from Left, Top Row):
- Circles cannot tessellate because there will always be gaps between them when placed side by side.
- Answer: No

#### 3. Isosceles Trapezoid (Third from Left, Top Row):
- An isosceles trapezoid can tessellate because its sides can fit together seamlessly.
- Answer: Yes

#### 4. Ellipse (Fourth from Left, Top Row):
- Ellipses cannot tessellate because they have curved edges, which will leave gaps when placed side by side.
- Answer: No

#### 5. Rectangle (Rightmost, Top Row):
- Rectangles can tessellate because their edges align perfectly when placed side by side.
- Answer: Yes

#### 6. Arrowhead (Leftmost, Middle Row):
- The arrowhead shape can tessellate because its edges can fit together without gaps.
- Answer: Yes

#### 7. Cross (Second from Left, Middle Row):
- The cross shape can tessellate because its arms can fit together seamlessly.
- Answer: Yes

#### 8. Square (Third from Left, Middle Row):
- Squares can tessellate because four squares can meet at a single vertex without gaps.
- Answer: Yes

#### 9. Oval (Fourth from Left, Middle Row):
- Ovals cannot tessellate because they have curved edges, which will leave gaps when placed side by side.
- Answer: No

#### 10. Downward Arrow (Rightmost, Middle Row):
- The downward arrow shape can tessellate because its edges can fit together without gaps.
- Answer: Yes

Final Answers:

- Equilateral Triangle: Yes
- Circle: No
- Isosceles Trapezoid: Yes
- Ellipse: No
- Rectangle: Yes
- Arrowhead: Yes
- Cross: Yes
- Square: Yes
- Oval: No
- Downward Arrow: Yes

Boxed Answer:

\[
\boxed{
\begin{array}{c|c|c|c|c}
\text{Shape} & \text{Equilateral Triangle} & \text{Circle} & \text{Isosceles Trapezoid} & \text{Ellipse} \\
\hline
\text{Tessellates?} & \text{Yes} & \text{No} & \text{Yes} & \text{No} \\
\end{array}
}
\]
\[
\boxed{
\begin{array}{c|c|c|c|c}
\text{Shape} & \text{Rectangle} & \text{Arrowhead} & \text{Cross} & \text{Square} \\
\hline
\text{Tessellates?} & \text{Yes} & \text{Yes} & \text{Yes} & \text{Yes} \\
\end{array}
}
\]
\[
\boxed{
\begin{array}{c|c|c}
\text{Shape} & \text{Oval} & \text{Downward Arrow} \\
\hline
\text{Tessellates?} & \text{No} & \text{Yes} \\
\end{array}
}
\]