Space & Geometry - Properties of Solids
Syllabus Reference Content Page: 147
Outcome: SGS 4.1
Key Ideas:
Describes and sketches three-dimensional solids
including polyhedra, and classifies them in terms of
their properties.
Determine properties of three-dimensional objects
Investigate Platonic solids
Investigate Euler’s relationship for convex polyhedra
Make isometric drawings
Prior Outcome: SGS 3.1
Post Outcome:
Identifies 3D objects, including particular prisms and
pyramids, on the basis of their properties, and
visualises, sketches and constructs them given drawings
of different views
Working Mathematically Outcomes
Questioning
Applying Strategies
Asks questions that
could be explored
using mathematics in
relation to Stage 4
content
Analyses a mathematical or
Real-life situation, solving
problems using technology
where appropriate
Communicating
Reasoning
Reflecting
Uses mathematical
terminology and
notation, algebraic
symbols, diagrams,
text and tables to
communicate
mathematical ideas
Identifies
relationships and the
strengths and
weaknesses of
different strategies
and solutions, giving
reasons
Links mathematical
ideas and makes
connections with,
and generalisations
about, existing
knowledge and
understanding in
relation to Stage 4
content
Knowledge and Skills
Working Mathematically
Students learn about
Students learn to
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describing solids in terms of geometric properties
number of faces
shape of faces
number and type of congruent faces
number of vertices
number of edges
convex or non-convex
identifying any pairs of parallel flat faces of a solid
determining if two straight edges of a solid are
intersecting, parallel or skew
determining if a solid has a uniform cross-section
classifying solids on the basis of their properties
A polyhedron is a solid whose faces are all flat
A prism has a uniform polygonal cross-section
A cylinder has a uniform circular cross-section
A pyramid has a polygonal base and one further vertex
(the apex)
A cone has a circular base and an apex
All points on the surface of a sphere area fixed
distance from its centre
identifying right prisms and cylinders and oblique prisms
Pendle Hill HS Stage 4 mathematics program
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interpret and make models from isometric drawings
(Communicating)
recognise solids with uniform and non-uniform crosssections (Communicating)
analyse three-dimensional structures in the environment
to explain why they may be particular shapes eg
buildings, packaging (Reasoning)
visualise and name a common solid given its net
(Communicating)
identify parallel, perpendicular and skew lines in the
environment (Communicating, Reflecting)
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and cylinders
identifying right pyramids and cones and oblique pyramids
and cones
sketching on isometric grid paper shapes built with cubes
representing three-dimensional objects in two dimensions
from different views
confirming, for various convex polyhedra, Euler’s formula
F+V=E+2
relating the number of faces (F), the number of vertices
(V) and the number of edges (E)
exploring the history of Platonic solids and how to make
them
making models of polyhedra
Technology
Links
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Resources
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3D solid models, centicubes, multilinks
straws, plasticine, scissors, glue, sticky tape
card match activity
card for vortex, trihexaflexagon, stellated
icosahedra models
geodesic dome
Pendle Hill HS Stage 4 mathematics program
measurement-surface area, volume
trigonometry
Language
Many terms need to be defined: prism, pyramid, face,
edge, vertex, parallel, skew
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Learning Experiences and Assessment Opportunities
Assessment for learning
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Students complete cardmatch activity to match a solid with its net and name
Students brainstorm in small groups all they know about solids. Posters are displayed in class. Teacher
observes product and listens to class discussion
At Stage 2 students are expected to be able to:
 Name, describe, sort make and sketch prisms, pyramids, cylinders, cones and spheres.
 Create nets from everyday packages.
 Describe cross-sections of 3-dimensional objects.
At Stage 3 students are expected to be able to:
 Identify 3-dimensional objects, including particular prisms and pyramids, on the basis of their properties.
 Construct 3-dimensional models given drawings of different views.
Investigating 3D Solids
It is important that students use, make and describe 3D solids in a variety of situations. They should have access
to various building materials.
Students could:
 build 3D models using multilinks, centicubes, . . . .
 investigate packaging of everyday items
 explore and make nets to create 3D solids
 use 3D models to describe solids in terms of the number of faces, shapes of faces, number and type of
congruent faces, number of vertices, number of edges
 use skeletal solids to define parallel intersecting and skewlines
 use solids to develop Euler’s formula
 draw diagrams of solids on isometric dot paper or some form of grid with perspective
 draw diagrams to show 2D views of solids.
 Use the geometry unit from Teaching Literacy in Mathematics in Year 7 to build and share knowledge about t
solids and develop skills in both group work and literacy
 use barrier activities to promote speaking and listening skills using appropriate mathematical language.
eg one student with a picture of a solid made from blocks describes it to a second student, who attempts to
build the solid. Students reverse roles and repeat process for another shape.
 use card matching activities to develop language skills and clarify understanding eg in small groups, students
match one set of cards containing the nets of various solids to a second set of cards containing the picture of
the solids.
 Use the geodesic dome to build the platonic solids and the dome itself
 use cooperative logic activities - Point of View 1, 2, 3, 4
Extension Activities
Students could:
 make the vortex
 make the trihexaflexagon
 make the stellated icosahedron
Pendle Hill HS Stage 4 mathematics program
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