Stage 2 – Maths - Space and Geometry - 3D Space
Term
Week
Outcome: SGS2.1
Makes, compares, describes and names threedimensional objects including pyramids, and
represents them in drawings
Key Ideas:
Name, describe, sort, make and sketch prisms,
pyramids, cylinders, cones and spheres
Create nets from everyday packages
Describe cross-sections of three-dimensional
objects
WORKING MATHEMATICALLY OUTCOME/S
Questioning
Asks questions that could be explored using mathematics in relation to Stage 2 content
Applying Strategies
Selects and uses appropriate mental or written strategies, or technology to solve a given problem
Communicating
Uses some mathematical terminology to describe or represent mathematical ideas
Reasoning
Checks the accuracy of a statement and explains the reasoning used
Reflecting
Links mathematical ideas and makes connections with existing knowledge and understanding in relation to Stage 2
content.
Knowledge and Skills
Working Mathematically
Students learn about
Students learn to
 comparing and describing features of prisms, pyramids,
cylinders, cones and spheres
 identifying and naming three-dimensional objects as
prisms, pyramids, cylinders, cones and spheres
 recognising similarities and differences between prisms,
pyramids, cylinders, cones and spheres
 identifying three-dimensional objects in the environment
and from drawings, photographs or descriptions
 making models of prisms, pyramids, cylinders, cones and
spheres given a three-dimensional object, picture or
photograph to view
 sketching prisms, pyramids, cylinders and cones,
attempting to show depth
 creating nets from everyday packages eg a cereal box
 sketching three-dimensional objects from different views
including top, front and side views
 making and visualising the resulting cut face (plane
section) when a three-dimensional object receives a
straight cut
 recognising that prisms have a uniform cross-section when
the section is parallel to the base
 recognising that pyramids do not have a uniform crosssection
 describe three-dimensional objects using everyday language
and mathematical terminology (Communicating)
 recognise and describe the use of three-dimensional objects
in a variety of contexts eg buildings, packaging (Reflecting,
Communicating)
 compare features of three-dimensional objects and twodimensional shapes
(Applying Strategies, Reflecting)
 compare own drawings of three-dimensional objects with
other drawings and photographs of three-dimensional
objects (Reflecting)
 explore, make and describe the variety of nets that can be
used to create particular three-dimensional objects
(Applying Strategies, Reasoning, Communicating)
 draw three-dimensional objects using a computer drawing
package, attempting to show depth
(Applying Strategies)
LEARNING ACTIVITIES (3D7)
CONSTRUCTING PRISMS AND CYLINDERS
Students build and stack attribute blocks, books or pattern
blocks
to develop the idea of a prism as an object having a constant
crosssection.
Students could build prisms using Base 10 naterial, Cuisenaire
rods, Multilink, Centicubes, Lego bricks, Duplo bricks, pattern
blocks or Unifix.
BLINDFOLD
Students handle and discuss geometric models or everyday
examples of various prisms and cylinders whilst blindfolded. They
count the faces, edges and corners and describe the shape of the
faces. Then they take off the blindfold and repeat the activity,
comparing results.
Students could use a “feely bag” instead of being blindfolded.
INVESTIGATING PRISMS AND CYLINDERS
Students make prints of the faces and bases of prisms. A chart
may
be built up to illustrate the prints obtained from various prisms
and
cylinders.
SORTING PRISMS
Students sort collections of everyday objects into “objects which
are prisms” and “objects which are not prisms”. Students could
further sort their prisms into categories of their own choosing.
PRISMS IN THE ENVIRONMENT
Students go on a prism hunt, finding and drawing examples of
prisms in their environment. Students could collect photographs
of
prisms from magazines and make a prisms book.
LEARNING ACTIVITIES (3D8)
PLAYING WITH PYRAMIDS
Provide students with a variety of pyramids, eg having square,
triangular, hexagonal or rectangular bases. Students discuss the
faces, edges, corners and bases, noting the similarities and
differences.
Students stack sets of seriated shapes to form “pyramids”.
Although such stacks are not strictly pyramids, they allow
students
to explore the idea that the cross-sections parallel to the base
become progressively smaller the further away from the base
they
are taken.
Ask students to sort the collection of pyramids according to some
attribute related to size, eg height.
PRINTING WITH PYRAMIDS
Students make prints using the faces and bases of a variety of
pyramids and construct a chart of results.
BLINDFOLD
Students handle models of different pyramids with their eyes
closed, describing and counting the faces, edges and corners. The
activity may then be repeated with the students having their eyes
open and noting any differences in their descriptions.
Similar activities could be arranged with pyramids being included
with other objects in a “feely bag”.
PYRAMID PAINT
Students choose a model of a pyramid and paint each of its faces
a
different colour.
Students investigate how many faces they can touch at once, how
many faces meet at any one corner, etc.
Students could list the colours that meet at each corner and
comment on the possible combinations.
PRYAMID HUNT
Students find examples of pyramids in the real world and make
collections of objects and photographs, eg the Egyptian Pyramids,
glasshouses, drink cartons.
CLASSIFICATION
Students sort models into prisms, pyramids and those that are
neither.
LEARNING ACTIVITIES (3D9)
LEARNING ACTIVITIES (3D10)
NETS
CONSTRUCTING PYRAMIDS
Students collect boxes, then cut and fold them to form nets. The
nets of various prisms may be compared and discussed. The nets
can be refolded and the shape made inside out.
Students could consider whether the same figure can have more
than one net, eg consider which hexominoes can be folded to form
a cube.
Students could be given cut-out nets and asked to fold and glue to
form the three dimensional shape. Alternatively, drawings of nets
could be given to students, who then copy the nets using
interlocking plastic squares, triangles and pentagons (Polydrons).
The copied net can then be folded and clipped together to form
the
3D shape.
Cardboard shapes are available which can be joined by elastic
bands to form 3D shapes. Students could investigate these
shapes.
• Students construct pyramid models using clay, plasticine or
playdough. Using wire or a knife, students can slice models
parallel to the base and investigate the cross-sections. The
truncated solids could then be investigated. Students could
predict the results obtained from taking slices at an oblique
angle to the base and check their predictions
• The teacher provides nets of pyramids which students fold and
stick together. The various forms of the net which fold to give
the same 3D solid could be investigated.
• Students build pyramids using interlocking plastic shapes such
as Polydrons. With different coloured squares, the task of
counting the faces, edges and corners is simplified.
• Students use cardboard shapes and elastic bands to build
pyramids.
Students construct prisms from clay, plasticine or playdough.
RESEARCH
CLAY MODELS
SKELETONS
Students make skeletal models of pyramids using toothpicks, pipe
cleaners or straws.
Students compare and discuss their results.
CONSTRUCTING NETS BY TRACING
Students may trace templates of regular polygons onto cardboard
or paper to form given nets. These may then be folded into their
3D forms, painted and labelled.
MAKING SKELETAL MODELS
Skeletons may be made using such materials as toothpicks, straws
and pipe cleaners.
Students could study the rigidity of the various models.
INVESTIGATING CROSS-SECTIONS
Students make prisms from clay, plasticine or playdough. By
carefully cutting the models with a piece of wire or a knife, the
cross-sections may be studied. Students make various sections at
right angles to the axis and note the results. They then predict
the
shapes resulting from cutting at an oblique angle or cutting with a
curved blade and perform the section to check their predictions.
• Students research the building of the Egyptian Pyramids. A
wall chart could be produced, showing the number of workers
involved, construction techniques, dimensions, time taken, etc.
• Students find other examples of pyramidal structures, such as
the glasshouse in the Royal Botanic Gardens, Sydney. Research
the reasons for a pyramidal shape being chosen, its advantages
and disadvantages, construction difficulties, etc. Drawings and
photographs could illustrate the research in a wall chart.
UNIQUENESS OF BASE
Students handle a variety of models of pyramids and decide
whether the base is unique or whether any face could be the base.
Models of tetrahedrons should be included.
LEARNING ACTIVITIES (3D11)
BUILDING MODELS
• Students collect photographs or pictures of everyday objects from magazines. Students find objects in the photographs which are
based on prisms and model them. Material used may be papier-mache, blocks, Lego bricks, etc.
• Students build Lego and other models according to instructions and plans.
SPATIAL VISUALISATION
• Students draw classroom objects from different viewpoints, eg side, top, front. Grid paper may be used. Repeat for everyday objects
chosen by the students.
• Students are given photographs or various objects and are asked to draw one of the objects from a different view.
FIND IT
Students are given cards prepared by the teacher showing various everyday objects as seen from different viewpoints.
Students have to name the object using as few of the teacher’s cards as they can.
SOLIDS
Students study drawings of solids from various viewpoints, eg top, sides, and identify the solid by choosing from a range of models.
DRAW IT
• The teacher shows the students a box or packet and asks them to draw what they think it looks like from some particular
viewpoint.
• The students draw their prediction for the net of the box or packet. The teacher then cuts and unfolds the box or packet to form
the net and this is compared with the students’ drawings.
SHAPE IN THE ENVIRONMENT
Ask students to draw pictures of everyday objects as they imagine they would look from various viewpoints, eg a car from directly
above.
UNSEEN FACES
The teacher gives students drawings of various rectangular prisms made from interlocking cubes. The students have to say how many
of the cubes would have three faces, two faces, one face and no faces visible in the actual model. Have students check by building
the model. 3 faces - 8 cubes
2 faces - 16 cubes
1 face - 6 cubes
Links
Resources
Blocks, cups, glasses, geometric models, Lego bricks,
models, construction kits, dolls’ house furniture, grip
paper, photographs.
Technology
Relevant positional language is used to describe and label plan views
and drawings (Position)
Links to other key learning areas
Visual Arts – Selects and explores different aspects of subject
matter in particular ways in their making of artworks eg
construction techniques in sculpture and ceramics
Language
prism, pyramid, cylinder, cone, sphere, cube, cross-section, solid,
hollow, inside out, skeleton, angle, face, surface, edge, base, corner,
complete, completion, description, direction, represent,
representation, view, viewpoint
Assessment
Ask students to
• look at a drawing or photograph and make a reasonable
model of the object using various materials
• draw different views of a given object
• identify an object, given drawings taken from various
viewpoints
• match drawings with objects.
Evaluation
• Did I give students time to discuss their findings amongst themselves?
• Were classroom activities adequate in addressing the unit objectives?