Module 4 - Exploring Geometry
Typical Progression
Common Difficulties
Pedagogy/Strategies for Teaching & Assessment
Mathematical Representation
Manipulatives, Games and Technology
Jigsaws, Construction Material (lego, Duplo, K-nex) - Free & Directed Play
Young children perception of world is very diff from adult
Spatial knowledge developed as students investigate shapes
Geometric properties - exploring patterns and reflecting on the situation
Language - 2D Shape (Curriculum) and Figure (Conventional)
3D Object (Curriculum) and Solid (Conventionally)
Child experiences world in 3D, so best to make sure there is a solid connection of 2D to the 3D
Playdough - Models of 2D and 3D
2D shapes are 'surfaces'
Why teach 2d? 2D Properties are part of our environment and we freq need to use associated language "square window", "Circular saw"
Teaching 2D spatial awareness for future mathematical ideas
Triangle
Interior angles = 180
Polygons
Pattern Blocks
Regular and Irregular
"Junk Models" - finding shapes in real life objects
Pentominos - Geometric figure consisting of 5 unit squares, each square having at least one side in common with another square
Polyhedra
Solids which have many plane faces
Verticies - Points where three or more edges meet
Prism
Polyhedron with two congruent parallel faces joined by rectangles
Pyramid
Has a polygonal base with triangular faces which meet at a common vertex
Geoshapes or Polydrons - Making Nets out of 3d shapes
Tangrams - Chinese shape puzzle
Lamington Drive (Ways of packing shapes)
"Kit Homes" - Different ways to make a house with the cubes
Interior Angles
Location & Transformation
Rosies Walk, Outline of classroom
Escher Type Drawings - identical changes made to opposite pair of sides
Symmetry stages - 1) Informal activities that form symmetrical patterns 2) Testing shapes and objects for symmetry 3) Investigating and applying properties of symmetry
Line Symmetry - Blob Paintings, Cutting Shapes, Folding Shapes, Mira Mira, Complete the shape, Master Shape
Angles
90 - Right angle, <90 acute, <90 obtuse, reflex angle 180>360, 180 is straight angle, 45 is half 90, 270 is 3/4 turn, 360 is full turn
Geometric reasoning - Network tracing/traceability
Geoboard
VAN HIELE MODEL
Level 1 - Figures are judged by appearance ie. viewing holistically without analysing properties
Level 2A - Classified on basis of one property -
Level 2B - Classified on basis of more than one property
Level 3 - Focus on relationship between properties and figures ie. rectangle and rhombus are linked because they both have opposite sides equal and opposite sides parallel
Level 4 (Secondary) - Use relationships between properties and figures to solve duductive problems
Congruence (Shape and size stay same) & Similarity
Equilateral (3 sides equal), Isoceles (2 sides equal), Scalene (no sides equal)
Volume = a(base) x height
Volume = 1/3 x a(base) x height
Cylinder
volume = pie r^2 x height
Cone Volume = 1/3 x pie r^2 x height
Platonic Solids - Convex regular polyhedra ie. octahedron, dodecahedron, icosahedron
Geogebra