Answer key for a 2nd-grade math worksheet on counting faces, edges, and vertices of 3D shapes.

The task involves counting the number of faces, edges, and vertices for each 3D shape provided in the image. Below is a detailed explanation of how to solve this problem:

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Definitions:

1. Faces: The flat surfaces of a 3D shape.
2. Edges: The line segments where two faces meet.
3. Vertices: The corners or points where edges meet.

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Step-by-Step Solution:

#### Shape 1: Triangular Prism
- Faces: A triangular prism has 2 triangular faces and 3 rectangular faces, totaling 5 faces.
- Edges: There are 3 edges on the top triangle, 3 edges on the bottom triangle, and 3 vertical edges connecting the triangles, totaling 9 edges.
- Vertices: There are 3 vertices on the top triangle and 3 vertices on the bottom triangle, totaling 6 vertices.

#### Shape 2: Cube
- Faces: A cube has 6 square faces.
- Edges: Each face of the cube is a square, and there are 12 edges in total.
- Vertices: A cube has 8 vertices.

#### Shape 3: Square Pyramid
- Faces: A square pyramid has 1 square base and 4 triangular faces, totaling 5 faces.
- Edges: There are 4 edges on the square base and 4 edges connecting the apex to the base, totaling 8 edges.
- Vertices: There are 4 vertices on the square base and 1 vertex at the apex, totaling 5 vertices.

#### Shape 4: Octagonal Prism
- Faces: An octagonal prism has 2 octagonal faces and 8 rectangular faces, totaling 10 faces.
- Edges: There are 8 edges on the top octagon, 8 edges on the bottom octagon, and 8 vertical edges connecting the octagons, totaling 24 edges.
- Vertices: There are 8 vertices on the top octagon and 8 vertices on the bottom octagon, totaling 16 vertices.

#### Shape 5: Rectangular Prism (Cuboid)
- Faces: A rectangular prism has 6 rectangular faces.
- Edges: There are 12 edges in total.
- Vertices: A rectangular prism has 8 vertices.

#### Shape 6: Octahedron
- Faces: An octahedron has 8 equilateral triangular faces.
- Edges: Each face is a triangle, and there are 12 edges in total.
- Vertices: An octahedron has 6 vertices.

#### Shape 7: Pentagonal Pyramid
- Faces: A pentagonal pyramid has 1 pentagonal base and 5 triangular faces, totaling 6 faces.
- Edges: There are 5 edges on the pentagonal base and 5 edges connecting the apex to the base, totaling 10 edges.
- Vertices: There are 5 vertices on the pentagonal base and 1 vertex at the apex, totaling 6 vertices.

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Final Answer:

The completed table with the correct counts is as follows:

| Shape | Faces | Edges | Vertices |
|-------|-------|-------|----------|
| 1 | 5 | 9 | 6 |
| 2 | 6 | 12 | 8 |
| 3 | 5 | 8 | 5 |
| 4 | 10 | 24 | 16 |
| 5 | 6 | 12 | 8 |
| 6 | 8 | 12 | 6 |
| 7 | 6 | 10 | 6 |

Thus, the final answer is:
\[
\boxed{
\begin{array}{|c|c|c|c|}
\hline
\text{Shape} & \text{Faces} & \text{Edges} & \text{Vertices} \\
\hline
1 & 5 & 9 & 6 \\
2 & 6 & 12 & 8 \\
3 & 5 & 8 & 5 \\
4 & 10 & 24 & 16 \\
5 & 6 & 12 & 8 \\
6 & 8 & 12 & 6 \\
7 & 6 & 10 & 6 \\
\hline
\end{array}
}
\]