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Mathable Smart Lab

GRADE 8 • GEOMETRY Strand: Fractals, Solids, Nets and Visualisation

Exploring Some Geometric Themes Smart Lab

Explore self-similar fractals, Sierpinski patterns, Koch snowflakes, solid profiles, nets, prisms, pyramids, and shortest paths on cuboids.

What are Geometric Themes?

This chapter explores two big ideas: fractals, which repeat similar patterns at smaller scales, and ways to visualise solids using profiles, faces, edges, vertices, nets and projections.

Fractals: Self-similar shapes such as ferns, trees, the Sierpinski Carpet, Sierpinski Triangle and Koch Snowflake.
Solids: Three-dimensional objects can be understood through faces, edges, vertices, profiles and viewpoints.
Nets: A net is a flat shape that can be folded to form a solid such as a cube, cuboid, prism, pyramid, cylinder or cone.

Choose a fractal and step number to see how repetition creates complex shapes.

Rules Hub

Sierpinski Carpet

Each remaining square creates 8 smaller squares.

\(R_n=8^n\)

Sierpinski Triangle

Each remaining triangle creates 3 smaller triangles.

Remaining area after \(n\) steps: \((3/4)^n\)

Koch Snowflake

Each side is replaced by 4 smaller sides.

Sides at step \(n\): \(3\cdot4^n\)

Faces, Edges, Vertices

Cube/cuboid: 6 faces, 12 edges, 8 vertices.

Prism with n-sided Base

Faces \(=n+2\), edges \(=3n\), vertices \(=2n\).

Pyramid with n-sided Base

Faces \(=n+1\), edges \(=2n\), vertices \(=n+1\).

Guided Solve Lab

Score: 0Current Streak: 🔥 0Badge: Geometry Explorer


Activity Zone

🎛️ Fractal Counter

Choose a fractal and step. Count remaining pieces, holes or sides.

🧊 Prism and Pyramid Counter

Enter the number of sides in the base polygon.

📦 Cube Net Checker

Can this pattern fold into a cube? Try visualising first.

🧩 Shape/Profile Identifier

A cylinder viewed from the top can have this profile.

Worksheet Generator

Generate printable practice on fractal patterns, counts, faces-edges-vertices, nets, and visualising solids.



Real-Life Lab

Teacher Tools

Learning Outcomes

  • Recognise self-similarity and construct early steps of fractals.
  • Find formulas for remaining pieces in Sierpinski fractals and sides/perimeter in Koch Snowflake.
  • Identify faces, edges and vertices of prisms and pyramids.
  • Visualise solid profiles from different viewpoints.
  • Understand and test nets of cubes, cuboids, prisms, pyramids, cylinders and cones.
  • Use nets to reason about shortest paths on cuboids.

Exit Ticket Prompts

  • How many squares remain in Step 3 of the Sierpinski Carpet?
  • What are faces, edges and vertices?
  • How many faces does a prism with a pentagonal base have?