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Geometry & spatial reasoning


Geometry originates from Greek  ge or gaia meaning earth or land and metria meaning measuring, or measurement of earth or land. Today geometry’s big ideas include the study of spatial properties and relations of points, lines, surfaces, solids, and higher dimensional quantities. Their shapes, variables or invariables, definitions, & proofs.

Analytic geometry is the combination of geometry and algebra.

Relative position is used to locate objects in space with distance and directions.


Knowledge base & tools for mathematical literacy

Knowledge base

Mathematical knowledge base with concepts necessary for learners to conceptualize to become mathemtically literate and misconceptions that must be over come. Particularly important for geometry and spatial reasoning are:


Tools to facilitate literacy in geometry & spatial reasoning & tools to achieve it

Background information for learning and teaching.


Activities to facilitate geometry & visual spatial literacy

Puzzles & challenges, with work sheets

  • Pythagoras theorem - Explanation sheet to justify a2 + b2 = c with 1. Area model & 2. lengths of sides model
  • Relative position & topology - Work sheet to identify: in, on, out, for 3d & 2d pictures, & draw the 5 shapes. Age: preschool - first grade
  • Tessellation - Work sheet: How to make a tessellation
  • Triangles - properties, kinds, angles, sides, and relationships
  • Ruler and compass constructions
  • Cross sections

Tangram puzzle sets and tables

Tangram puzzle sets
fancy Tangrams and case image
Tangram tables
tangram tables image




Geometry is the science of correct reasoning on incorrect figures. George Polya


Two or Three dimension figure


Never repating shape

Shape with sides in a pattern that never repeats!