CBSE · Class 8 · Mathematics · Chapter 11

Exploring Some Geometric Themes

Investigate geometric structures, transformations and spatial reasoning through visual problems and models.

13 lessons 55 min
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Lessons in this chapter

  1. 1Fractals and the Sierpinski CarpetDiscover self-similarity by constructing a square pattern and explaining how its pieces and holes grow.
  2. 2The Sierpinski Triangle and Fractal AreaBuild a repeating triangular pattern and discover why more pieces can occupy less area.
  3. 3The Koch Snowflake and Fractals in ArtConstruct a growing boundary, calculate its perimeter, and recognise repeated shapes in art and architecture.
  4. 4Imagining Solids and Reading Their ProfilesUse mental cutting, paper models, and different viewpoints to connect flat outlines with solid shapes.
  5. 5Making Solids and Counting Their PartsRecognise prisms and pyramids and derive their face, edge, and vertex counts from their structure.
  6. 6Cube and Cuboid NetsUnfold boxes, test which flat arrangements close correctly, and design nets with matching face dimensions.
  7. 7Nets of Other SolidsConnect polygon faces and unrolled curved surfaces to the nets of prisms, pyramids, cylinders, and cones.
  8. 8Shortest Paths on a Cube and CuboidUnfold a box surface to find straight routes, check their validity, and compare their lengths.
  9. 9Foundations of ProjectionProject points, segments, and shapes onto a plane and identify which information a view preserves or loses.
  10. 10Front, Top, and Side Views; ShadowsCoordinate three perpendicular views and distinguish measured projections from shadows made by different light sources.
  11. 11Cube Arrangements from Multiple ViewsRead cube stacks, reconstruct possible models, and explain why the same views can conceal different totals.
  12. 12Isometric Projections and GridsDraw cubes and combined blocks on an isometric grid while preserving the three edge directions and equal unit steps.
  13. 13Drawing Complex Solids and Testing Impossible FiguresBuild varied four-cube models, check drawings for spatial consistency, and connect the chapter’s geometric ideas.
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