Mathematics – 3D Space
Strand: Space & Geometry
Stage: 3
Term: 4
Stage 3
Term 4
Week 4
Substrand: 3D Space
Week: 4
Language: face, edge, vertex, vertices, triangular prism, square prism, cube,
rectangular prism, pentagonal prism, triangular pyramid, square pyramid, rectangular
pyramid, cross-section, perspective, surface, net, curved, view points, polyhedron.
Outcome
SGS3.1 – Recognises 3D objects, including
particular prisms and pyramids, on the basis of
their properties, and visualises, sketches and
constructs them given drawings of different
views.
Maintenance
Times Tables
Mentals
Gp 3- tables
practise /using your
tables
Key Ideas:
1. Identify 3D objects, including particular prisms and pyramids, on the basis of their
properties.
2. Construct 3D models given drawings of different views.
Working Mathematically
Questioning:
Applying Strategies:
Communicating:
Reasoning:
Reflecting:
WMS3.1 - Asks questions
that could be explored
using mathematics in
relation to Stage 3 content.
WMS3.2 - Selects and applies
appropriate problem-solving
strategies, including technological
applications, in undertaking
investigations.
WMS3.3 - Describes and
represents a
Mathematical situation in a
variety of ways using
mathematical terminology and
some conventions.
WMS3.4 - Gives a
valid reason for
supporting one
possible solution over
another.
WMS3.5 - Links mathematical ideas
and makes connections with, and
generalisations about, existing
knowledge and understanding in
relation to Stage 3 content.
Activities
Activities:
1. Review properties of some 3D shapes using mathematical language to describe them eg. I have a square base, 5 vertices
and 4 triangular faces. What am I?( smartkiddies interactive black 3D space What am I?) Ask students to draw both the 3D
shape and its net.
Students write their own descriptions of some pictured solids. (BLM 4 Targeting Maths)
2. Review terms faces, edges, vertices (corners) curved and flat surfaces- fill in table for 3D objects with this information.
Top Group: Test Euler’s Theorem: Edges= faces + vertices – 2 to see if it works for all solid shapes. (only works for
Assessment
3D shapes with flat surfaces.) p82.
3rd Group: label some common 3D shapes, count their faces, edges, corners and sketch their nets.
3. Display examples of top view, side view and front view of a 3D shape and ask students to identify it. Students
then draw given views for selected 3D shapes. Construct 3D models with centicubes given a drawing of its top view.
Students then sketch models of from other views. (Sample Units of Work p146)
4. On isometric dot paper demonstrate constructing a 3D shape. Students select some examples to draw and label.
Resources
Targeting Maths BLM 4
NSW Signpost Maths 6
p73
NSW Signpost Maths
Teachers Resource
Book p LIII, 194
Advanced Primary Maths
6 p82
Jigsaw Maths
Checkbook 4 p43
Maths Plus 6 p46
Centicubes
Isometric dot paper
5. With 24 interlocking cubes students build a rectangular prism. Describe the prism in terms of its length, width and
height? Ask students to draw a simple perspective drawing on grid paper noting length, width and height. Ask
students if they can build other models using the same number of cubes. Repeat drawing each model and recording
the length, width and height. Ask students if they noticed anything. (Each cube will have the same volume.)
Centicubes
Sample Units of Work
p146
Evaluation
Maths Plus 6 p62
Top Group: Using the volume formula calculate the volume of 3D shapes and rank them in ascending order.
6. Cube Puzzle: A wooden cube 3cmx3cmx3cm is painted red. The painted cube is then broken up into 1cm cubes.
Get students to estimate:
* how many cubes are there altogether?
* how many cubes do not have any paint on them? Will there be some? Why/why not?
* how many will have paint on one face?
* how many will have paint on two faces?
* how many will have paint on four or more faces?
Computer: Interactive
Smartkiddies – Black – What am I? – identifying objects based on properties.
Computers: Students access Targeting Maths 5/6, Smart kiddies and Copacabana: Get Smart activities based on 3D Space.
Students work at their own level to enhance differentiation.www.copacabana-p.schools.nsw.edu.au/Get_Smart.htm
Computers
Internet
Mathematics – 2D Space
Strand: Space & Geometry
Stage: 3
Term: 4
Stage 3
Term 4
Key Ideas:
Substrand: 2D Space
Week: 5
Language:
Week 5
scalene, isosceles, equilateral, regular shape, irregular shape, rotational symmetry,
protractor, acute angle, obtuse angle, straight angle, reflex angle, revolution, circle, circumference, diameter,
radius, quadrant, tessellating

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Outcomes
SGS3.2a:
Manipulates,
classifies and draws
2D shapes and
describes side and
angle properties.
Maintenance
* Tables with
missing units.
* Balancing
equations.
* Reading a
protractor
correctly.
* Correctly
using a
compass using
language of
radius/diameter.
Assessment
Observation
of students
correctly
using a
protractor
and the
compass.
SGS3.2b :
Measures,
constructs and
classifies
angles.
Identify right-angled, isosceles, equilateral and scalene triangles.
The sum of angles of a triangle is 180º and the sum of the angles of a quadrilateral is 360º.
Correctly identify parts of a circle.
Measure angles using a protractor.
Construct angles using a protractor.
Working Mathematically
Questioning:
Applying Strategies:
Communicating:
Reasoning:
Reflecting:
WMS3.1 - Asks questions that could be
explored using mathematics in relation to
Stage 3 content.
WMS3.2 - Selects and applies
appropriate problem-solving
strategies, including
technological applications, in
undertaking investigations.
WMS3.3 - Describes and
represents a
Mathematical situation in a
variety of ways using
mathematical terminology and
some conventions.
WMS3.4 - Gives a
valid reason for
supporting one
possible solution over
another.
WMS3.5 - Links mathematical ideas
and makes connections with, and
generalisations about, existing
knowledge and understanding in
relation to Stage 3 content.
Activities
1. Students identify, record and classify angles in the environment using the correct terms. Divide page into 6
rectangles with headings Right, Acute, Obtuse, Straight, Reflex and Revolution. Extend activity by asking students to
estimate each angle and then, if possible, check. Correctly label angles and draw shapes that have specific properties.
eg. 3 sides and 3 acute angles. Look at a picture and identify angles and answer a series of true or false questions.
2. Review the 4 types of triangles and their properties. Label triangles-ask students why they chose that name for the
triangle. On those same triangles ask students to label which are acute, right and obtuse.
Watch smartkiddies interactive (Black 417) to review using a protractor to measure angles. On worksheet (MP 6
p54) use a protractor to measure each angle and fill in the missing angles.
3. Construct triangles using the protractor- demonstrate on the whiteboard how to construct an angle at one end of a
line and another angle at the other end. Explain where the two lines intersect forms the vertex of a triangle. Ask: What
will be the size of that angle? How did you get that answer? Allow students to construct their own triangles and
measure and label the types of angles formed.
4. Constructing Circles: review how we set the compass to get an exact radius/diameter. Let students practise on
scrap paper until they can accurately construct a compass (put pressure on compass point and not pencil point, move
paper if it is hard to turn compass, etc). Allow students to make designs on paper. Construct circles with specific
properties eg. radius 3cm.
Resources
Sample Units of Work
p153
NSW Targeting Maths 6
p32
Maths Plus 5 p42
Maths Plus 6 p54
Reference: Maths Plus
6 p80.
NSW Signpost Maths 6
p86
Maths Plus 6 p134
Targeting Maths 6
p154-156
Advanced Primary
Maths 6 p144
Evaluation
5. Angles at intersecting lines : explain intersecting lines to the student and point out an example in the classroom.
eg.doorframes. Students try and identify others. Create intersecting lines and label types of angles created.
Extension
Resources
Top Group
Look at parallel lines and an intersecting line. Which angles will be equal. Given a measurement of an angle, calculate the
size of other angles.
Excel Year 7
6. Tessellations: look at woodlandsjuniorschool or amblesideprimary for interactive activities/computer time activities
for examples. Students design their own tessellating patterns in their workbook.
Computer sites.
Computer: Students have access to computers to develop and explore 2D Space activities. Specifically Targeting
Maths, Smart kiddies, Cococabana-GetSmart, Woodlands Junior School , Amblesideprimary
Evaluation
Computers: Students access Targeting Maths 5/6, Smart kiddies and Copacabana: Get Smart activities based on addition &
subtraction, Chance & Data. Students work at their own level to enhance differentiation.www.copacabanap.schools.nsw.edu.au/Get_Smart.htm
Computers
Internet