Polyhedra

LEARNING EXPERIENCES: For all these activities you will need as many boxes of 3D solids as you can.
  • (S1) Polywhat? – Teacher’s Guide – (1 period. You need as many boxes of 3D solids as you can find) Classification/sorting challenges to arrive at a common definition of polyhedra and the properties their properties. Good opportunity to introduce/revise the vocabulary of 3D shape (face, edge, vertices) as students describe their classification. eg. These all have flat sides (instead of faces); These have sharp corners (instead of vertices). If you would like to link to the challenges, use the Polywhat? – Student Challenges post.
  • (S2) Discovering Euler’s Theorem – (1-2 periods) A split task lesson to try and discover Euler’s Theorem. One group works on the computer, the other builds polyhedra using Polydron materials.
  • (S3) Regular and irregular polyhedra – Classify different polyhedra to define regular and irregular.
  • (S4) Constructing regular polyhedra – How many nets are there for the different polyhedra? Use the Platonic Solids (regular polyhedra) guide to help you construct each of the solids.
ASSESSMENT TASKS:
NB: Both these assessment need a tetrahedron and a hexagonal prism.
Students can choose to demonstrate proficient or highly proficient understanding for this unit by choosing one of the following:
  • Polyhedra-Assessment_P– Students use a given polyhedra to classify and number the faces, edges, vertices and match terms with definitions.
  • Polyhedra assessment – HP – Students use a given polyhedra to classify and number the faces, edges, vertices and write their own definitions.

Aligning the Benchmarks with Learning Activities:

  • MAT.MS.5.1: 1.  investigate how 2D representations of 3D objects can be used to visualize and solve problems.
  • MAT.MS.5.3: 3.  analyse, describe, classify and visualize 2D (including triangles and quadrilaterals) and 3D shapes, using geometric vocabulary.  Identifying Objects  Polygons  Triangles  Features of Pyramids
  • MAT.MS.5.4: 4.  use geometric vocabulary when describing shape and space in mathematical situations and beyond.
  • MAT.MS.5.5: 5.  identify the properties of regular and irregular polyhedra.

(S3) Regular and irregular polyhedra – Classify different polyhedra to define regular and irregular.

  • MAT.MS.5.6: 6.  use 2D representations of 3D objects to visualize and solve problems, for example using drawings or models.

Build the Best Doghouse

  • MAT.MS.5.12: 12.  create and model how a 2D net converts into a 3D shape and vice versa.

(S4) Constructing regular polyhedra – How many nets are there for the different polyhedra? Use the Platonic Solids (regular polyhedra) guide to help you construct each of the solids.

Meet My Shape for net and review practice

NZ Book Level 4 Book 1: pages – 264 – 271
Mathletics Resources:
Level F – Nets
Level G –


RESOURCES:

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