3D shapes worksheet for identifying vertices.

The image you've uploaded is a worksheet titled "3-dimensional shapes" from *Coloring Katerina Limited (2014)*, designed to help students understand and identify the vertices (corners) of various 3D shapes.

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🔍 Task Description:

> "Draw a small circle around each vertex in these shapes."

A vertex (plural: vertices) is a point where two or more edges meet in a 3D shape. For example:
- A cube has 8 vertices.
- A pyramid has 4 or 5 vertices depending on its base.

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✔ Step-by-Step Solution:

Let’s go through each shape one by one and determine how many vertices it has, then explain where to place the small circles.

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#### 1. Cube
- Shape: A box with six square faces.
- Number of vertices: 8
- Where to draw circles: At each corner where three edges meet.
- ✔ Draw a small circle at all 8 corners.

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#### 2. Square Pyramid
- Shape: A pyramid with a square base and four triangular faces meeting at a single top point.
- Number of vertices: 5
- 4 at the base (square corners)
- 1 at the top (apex)
- ✔ Draw a small circle at each of the 5 corners.

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#### 3. Cylinder
- Shape: A tube-like shape with two circular bases and a curved surface.
- Number of vertices: 0
- Why? A cylinder has no sharp corners — it's smooth along the sides and circular at the ends.
- ✔ Do not draw any circles. Cylinders have no vertices.

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#### 4. Triangular Prism
- Shape: Two triangular bases connected by three rectangular faces.
- Number of vertices: 6
- 3 on the top triangle
- 3 on the bottom triangle
- ✔ Draw a small circle at all 6 corners.

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#### 5. Sphere
- Shape: A perfectly round object like a ball.
- Number of vertices: 0
- Why? A sphere has no flat surfaces or edges — it's completely curved.
- ✔ Do not draw any circles. Spheres have no vertices.

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#### 6. Tetrahedron (Triangular Pyramid)
- Shape: A pyramid with a triangular base and three triangular faces meeting at a point.
- Number of vertices: 4
- 3 at the base
- 1 at the apex
- ✔ Draw a small circle at all 4 corners.

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🧩 Summary Table:

| Shape | Number of Vertices | Draw Circles? |
|---------------------|--------------------|---------------|
| Cube | 8 | ✔ Yes |
| Square Pyramid | 5 | ✔ Yes |
| Cylinder | 0 | ✘ No |
| Triangular Prism | 6 | ✔ Yes |
| Sphere | 0 | ✘ No |
| Tetrahedron | 4 | ✔ Yes |

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✔ Final Answer:

On the worksheet, you should:
- Place small circles at every corner of the cube, square pyramid, triangular prism, and tetrahedron.
- Leave the cylinder and sphere without any circles because they have no vertices.

This helps reinforce understanding that only polyhedra (shapes with flat faces and straight edges) have vertices.

Let me know if you'd like a visual guide or printable version!