Week+7+-+3-dimensional+shapes

The mathematical name of the toblerone is a triangular prism.
 * Learning Activity 7.1: Munching mathematics again

'Geometric Solids' - virtual manipulatives: ** **
 * Learning Activity 7.2: Exploring 3-dimensional objects
 * **POLYHEDRON** || **Number of edges** || **Name of each face** || **Number of sides on each face** || **Number of faces** || **Number of v**ertices ||
 * **Tetrahedron** || 6 || Triangle || 3 || 4 || 4 ||
 * **Cube** || 12 || Square || 4 || 6 || 8 ||
 * **Octahedron** || 12 || Triangle || 3 || 8 || 6 ||
 * **Dodecahedron** || 30 || Pentagon || 5 || 12 || 20 ||
 * **Icosahedron** || 30 || Triangle || 3 || 20 || 12 ||
 * **Irregular Polyhedron** || 20 || Rhombus || 4 || 10 || 12 ||

QUESTIONS:
 * Explore the six polyhedron listed below. For each shape, determine the number of faces, edges, and vertices (corners). Record your results below.**
 * 1) **Look at the first shape in the table above. Find the sum of the number of faces and the number of vertices. How does this sum compare with the number of edges?**
 * 2) **Do you think this may be a rule for the other shapes?**
 * 3) **Add the number of faces and the number of corners for the other shapes in the table. Compare the sum of faces and corners to the number of edges. What did you find out? Is there a rule for all of the shapes?**

**
 * ANSWERS:
 * 1) Tetrahedron: 4 faces + 4 vertices = 6 edges

THINKING HEAD NOTES:
 * Not knowng what they meant by 'sides of face,' got confused between edges.
 * Didn't realise how many different properties a single 3 dimensional shape could have
 * The ease of virtual manipulatives. Was actually easier than using, blocks/models, as I could highlight properties (vertices, edges etc.)
 * Completing table helped me to really comprehend polyhedrons
 * The table was easy to fill in, once I started, I realised that the edges/vertices/faces was never an odd number. This helped me to know whether my counting was likely to be correct or not.

**What ideas and examples did your group gain this week about supporting children's learning of 3D Shapes?**
 * GROUP SUMMARY:**


 * The relevance of 3d objects in everyday life - 'We live in a three-dimensional world that can be represented and described geometerically' (Reys et al, 2009).
 * Early introduction to mathematics should begin with physical manipulation of already familiar objects; tennis balls, dice etc. (Reys et al 2009). This allows students to link what they already know (the everyday objects) to progress to new ideas such as the names of shapes, edges, vertices, nets etc.
 * Teachers need to work towards students developing an ability to transfer between visualisations of 2D and 3D shapes (Booker et al, 2009). This can be achieved by using nets (flat versions of 3D shapes), which shares similar properties with 2D shapes (number and shape of faces, edges and vertices)
 * In order to develop conceptual understanding of three dimensional shapes, language is to be considered as having an important role. Part of assisting this development is the introduction of mathematical terms; spheres (balls), cylinders (cans), prisms (boxes) and the like (Reys et al, 2009). Distinctions must be made, for instance, between A 2D square and 3D cube. A similar consideration exists for the use of more than one name for a property (vertices/vertex/corner). This encompasses the conceptual and language development, and familiarity of mathematical language in order to better understand maths. 