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Continuum of Curriculum Expectations:
Geometry and Spatial Sense
Overall Expectations
Subheadings
Geometric
Properties
Grade 1
1m43 • identify
common twodimensional shapes
and threedimensional figures
and sort and classify
them b y their
attributes
Geometric
Relationships
1m44 • compose and
decompose common
two-dimensional
shapes and threedimensiona l figures;
Grade 2
Grade 3
Grade 4
2m44 • identify twodimensional shapes
3m47 • compare
two-dimensional
and threedimensional figures
and sort and classify
shapes and threedimensional figures
and sort them by
4m58 • identify
quadrilaterals and
three-dimensional
figures and classify
them b y their
them b y their
geometric prope rties
their geo metric
properties;
geometric prope rties,
and comp are various
angles to
benchmarks;
2m45 • compose and
decompose twodimensional shapes
and threedimensional figures
3m48 • describe
relationships
between twodimensional shapes,
and between two-
4m59 • construct
three-dimensional
figures, using twodimensiona l shape s;
Grade 5
5m46 • identify and
classify twodimensional shapes
by side and angle
Grade 6
6m43 • classify and
construct polygons
and angles;
properties, and
compare and sort
three-dimensional
figures;
5m47 • identify and
construct nets of
prisms and pyram ids;
Grade 7
7m43 • construct
related lines, and
classify triangles,
quadrilaterals, and
prisms;
1m45 • describe the
relative locations of
objects using
positional language.
2m46 • describe and
represent the relative
locations of ob jects,
and repre sent ob jects
on a map
3m49 • identify and
describe the locations
and movements of
shapes and objects.
8m40 • demonstrate
an understanding of
the geo metric
properties of
quadrilaterals and
circles and the
applications of
geometric properties
in the real world;
6m44 • sketch threedimensional figures,
and construct threedimensional figures
from drawings;
7m44 • develop an
understanding of
8m41 • develop
geometric
similarity, and
distinguish similarity
and congruence;
relationships
involving lines,
triangles, and
dimensional shapes
and threedimensiona l figures;
Location and
Movement
Grade 8
polyhedra, and solve
problems involving
lines and triangles;
4m60 • identify and
describe the location
of an object, using a
grid map, and reflect
5m48 • identify and
describe the location
of an object, using
the cardinal
two-dimensional
shapes.
directions, and
translate twodimensiona l shape s.
6m45 • describe
location in the first
quadrant of a
7m45 • describe
location in the four
quadrants of a
8m42 • represent
transformations using
the Cartesian
coordinate system,
and rotate twodimensiona l shape s.
coordinate system,
dilatate two-
coordinate plane, and
make connections
dimensional shapes,
and apply
between
transformations and
the real world.
transformatio ns to
create and analyse
designs.
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Specific Expectations
Subheadings
Geometric
Properties
Identify, Sort and
Classify
2-D
Grade 1
1m46 – identify and
describe common
two-dimensional
shapes and sort and
classify them by
their attributes, using
concrete m aterials
and pictorial
representations
Grade 2
Grade 3
2m47 – distinguish
between the
attributes of an
object that are
3m51 – identify and
compare various
polygons (i.e.,
triangles,
geometric properties
and the attributes
quadrilaterals, pentago
ns, hexagons, heptago
ns, octagons)
that are not geometric
properties using a
variety of
tools
2m48 – identify and
describe various
polygons (i.e.,
triangles,
quadrilaterals, pentago
ns, hexagons, heptago
ns, octagons)
and sort them by
their geo metric
properties (i.e., number
of sides; side lengths;
number of
interior angles;
number of right
angles)
Grade 4
Grade 5
Grade 6
Grade 7
6m47 – sort polygons
according to the
number of
7m47 – sort and
classify triangles and
quadrilaterals by
lines of symm etry
and the order of
geometric properties
related to symmetry,
trapezoid,
parallelogram,
rotational symmetry,
through investigation
rhombus) and sort
and classify them by
their geo metric
properties
using a variety of
tools
angles, and sides,
through investigation
using a variety of
tools and strategies
4m62 – identify and
compare different
types of
quadrilaterals (i.e.,
rectangle, square,
5m49 – distinguish
among polygons,
regular polygons,
and other twodimensional shapes
Grade 8
8m43 – sort and
classify
quadrilaterals by
geometric prope rties,
including those
based on diago nals,
through investigation
using a variety of
tools
6m46 – sort and
classify
quadrilaterals by
geometric properties
related to symmetry,
angles, and sides,
through investigation
using a variety of
tools
and sort and classify
them b y their
geometric properties
(i.e., number of sides
or number of
vertices), using
concrete m aterials
and pictorial
representations
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Subheadings
Geometric
Properties
Symmetry 2-D
Grade 1
1m50 – locate
shapes in the
environment that have
symmetry, and
describe the
symmetry.
Grade 2
2m51 – locate the line
of symmetry in a twodimensional
shape
Grade 3
symmetry is part of
3m62in Location and
Mo vement
Grade 4
Grade 5
4m61 – draw the lines
of symmetry of twodimensional
5m53 – identify
triangles (i.e., acute,
right, obtuse,
shapes, through
investigation using a
variety of tools and
strategies
scalene, isosceles,
equilateral), and
classify them
acco rding to angle
and side p roperties
Grade 6
6m46 – sort and
classify
quadrilaterals by
geometric properties
related to sym metry,
angles, and sides,
through investigation
using a variety of
tools
Grade 7
Grade 8
7m47 – sort and
classify triangles and
quadrilaterals by
geometric properties
related to sym metry,
angles, and sides,
through investigation
using a variety of
tools and strategies
6m47 – sort polygons
according to the
number of
lines of sym metry
and the order of
rotatio nal sym metry,
through investigation
using a variety of
tools
3
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Geometric
Properties
5m54 – construct
triangles, using a
6m49 – construct
polygons using a
7m46 – construct
related lines (i.e.,
2-D Construction
variety of tools,
given acute or right
angles and side
measurem ents
variety of tools, given
angle and side
measurem ents
parallel;
perpendicular;
8m44 – construct a
circle, given its
centre and radius, or
its centre and a point
intersecting at 30º,
45º, and 60º), using
on the circle, or three
points on the circle
angle properties and a
variety of tools and
strategies
7m48 – construct
angle bisectors and
perpendicular
bisectors, using a
variety of tools and
strategies, and
represent equal
angles and equal
lengths using
mathematical
notation
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Subheadings
Geometric
Properties
Lines and
Angles
Grade 1
Grade 2
Grade 3
3m50 – use a
reference tool to
identify right angles
and to describe
angles as greater than,
equal to, or less than a
right angle
3m52 – compare
various angles, using
concrete m aterials
and pictorial
representations, and
describe angles as
bigger than, smaller
than, or about the
same as other angles
Grade 4
4m63 – identify
benchmark angles
(i.e., straight angle,
right angle, half a
right angle), using a
reference tool, and
compare other angles
to these benchmarks
4m64 – relate the
names of the
benchmark angles to
their me asures in
degrees
Grade 5
5m51 – identify and
classify acu te, right,
obtuse, and straight
angles
5m52 – measure and
construct angles up
to 90º, using a
protractor
Grade 6
Grade 7
6m48 – measure and
construct angles up
to 180/ using a
protractor, and
7m46 – construct
related lines (i.e.,
classify them as
acute, right, obtuse,
or straight angles
intersecting at 30º,
45º, and 60º), using
Grade 8
parallel;
perpendicular;
angle properties and a
variety of tools and
strategies
7m48 – construct
angle bisectors and
perpendicular
bisectors, using a
variety of tools and
strategies, and
represent equal
angles and equal
lengths using
mathematical
notation
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Subheadings
Geometric
Properties
Identify and
Describe 3-D
Grade 1
Grade 2
1m48 – identify and
describe common
three-dimensional
figures and sort and
2m49 – identify and
describe various
three-dimensional
figures (i.e., cubes,
classify them by their
attributes, using
concrete m aterials
prisms, pyramids)
and sort and classify
them b y their
and pictorial
representations
geometric properties
(i.e., number and
1m49 – describe
similarities and
differences between
an everyday object
shape of faces),
using co ncrete
materials
Grade 3
Grade 4
3m53 – compare and
sort prisms and
4m65 – identify and
describe prisms and
pyramids by
geometric properties
(i.e., number and
pyramids, and
classify them by
their geo metric
shape of faces,
numbe r of edges,
properties (i.e., shape
of faces, number of
number of vertices),
using co ncrete
materials
edges, number of
vertices), using
concrete m aterials
3m54 – construct
rectangular prism s,
4m70 – construct
three-dimensional
and describe
geometric properties
(i.e., number and
figures, using only
congruent shapes
Grade 5
5m50 – distinguish
among prisms, right
prisms, pyramids,
and other threedimensional figures
Grade 6
Grade 7
Grade 8
7m49 – investigate,
using co ncrete
materials, the angles
between the faces of
a prism , and id entify
right prisms
and a three
dimensional figure
3-D Construction 1m47 – trace and
identify the twodimensional faces of
three-dimensional
figures, using
concrete m odels
2m50 – create models
and skeletons of prisms
and
pyramids, using
concrete m aterials
and describe their
geometric properties
(i.e., number and
shape of faces,
number of edges)
Miscellaneous
shape of faces,
numbe r of edges,
numbe r of vertices)
of the prisms
8m45 – investigate
and describe
applications of
geometric properties
in the real world.
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Subheadings
Geometric
Relationships
Compose and
Decompose
2-D
Grade 1
Grade 2
1m51 – com pose
patterns, pictures,
2m52 – compose and
describe p ictures,
and designs, using
common twodimensional shapes
designs, and patterns
by combining twodimensional shapes
1m52 – identify and
describe shapes
2m53 – compo se and
decompose two-
within other shap es
dimensional shapes
1m54 – cover outline
puzzles with twodimensional shapes
2m54 – cover an
outline p uzzle with
two-dimensional
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
3m55 – solve
problems requiring
the greatest or least
number of twodimensional shapes
needed to compose a
larger shape in a
variety of ways
shapes in more than
one way
7
Subheadings
Geometric
Relationships
Congruent and
Similar 2-D and
3-D
Grade 1
Grade 2
Grade 3
Grade 4
3m59 – identify
congruent two-
4m70 – construct
three-dimensional
dimensional shapes
by manipulating and
figures, using only
congruent shapes
matching co ncrete
materials
Grade 5
Grade 6
Grade 7
Grade 8
7m51 – determine,
through investigation
using a variety of
8m46 – determine,
through investigation
using a variety of
tools, relationships
among area,
tools, relationships
among area,
perimeter,
corresponding side
lengths, and
perimeter,
corresponding side
lengths, and
corresponding angles
of congruent shapes
corresponding angles
of similar shapes
7m52 – demonstrate an
understanding that
enlarging or
reducing twodimensional shapes
creates similar
shapes
7m53 – distinguish
between and
compare similar shapes
and congruent shapes,
using a
variety of tools and
strategies
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Subheadings
Geometric
Relationships
3-D
Grade 1
1m53 – build threedimensional
structures using
concrete m aterials,
Construction and describe the two
dimensional shapes
the structures co ntain
Grade 2
2m55 – build a
structure using threedimensional figures,
and describe the twodimensional shapes
and threedimensional figures
in the structure
Grade 3
3m57 – identify and
describe the two-
Grade 4
dimensional shapes
that can b e found in
4m66– construct a
three-dimensional
figure from a picture
or model of the
a three dimensional
figure
figure, using
connecting cubes
4m67 – construct
skeletons of threedimensional figures,
using a variety of
tools, and sketch the
skeletons
4m68 – draw and
describe nets of
rectangular and
triangular prisms
Grade 5
5m56– construct nets of
prisms and
pyramids, using a
variety of tools
Grade 6
Grade 7
Grade 8
6m50 – build threedimensiona l mod els
using connecting
cubes, given
isometric sketches or
different views (i.e.,
top, side, front) of
the structure
6m51 – sketch, using a
variety of tools,
isome tric
perspectives and
different views (i.e.,
top, side, front) of
three-dimensional
figures built with
interlocking cubes
4m69 – construct
prisms and pyramids
from given nets
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Subheadings
Geometric
Relationships
Identify and
Describe
Relationships
Grade 1
Grade 2
Grade 3
1m52 – identify and
describe shapes
2m52 – compose and
describe p ictures,
3m57 – identify and
describe the two-
within other shap es
designs, and patterns
by combining twodimensional shapes
dimensional shapes
that can b e found in
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
5m55– identify prisms
and pyramids from
their nets
a three dimensional
figure
3m58 – describe and
name prisms and
pyramids by the
shape of their base
Angle and Line
Relationships
8m47 – determine,
through investigation
using a variety of
tools and strategies,
the angle
relationships for
intersecting lines and
for parallel lines and
transversals, and the
sum of the angles of
a triangle
8m48 – solve anglerelationship
problems involving
triangles, intersecting
lines, and parallel lines
and transversals
10
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
8m49 – determine
the Pythagorean
relationship, through
investigation using a
variety of tools
Geometric
Relationships
Pythagorean
Relationships
8m50 – solve
problems involving
right triangles
geometrically, using
the Pythagorean
relationship
Miscellaneous
3m56– explain the
relationships
between different
types of
quadrilaterals
7m50 – identify,
through
investigation, the
minimum side and
8m51 – determine,
through investigation
using co ncrete
angle information
(i.e., side-side-side;
materials, the
relationship between
the numbers of faces,
side-angle-side;
angle-side angle)
edges, and vertices of
a polyhed ron (i.e.,
needed to describe a
unique triangle
numbe r of faces +
numbe r of vertices =
number of edges + 2)
11
Subheadings
Location and
Movement
Co-Ordinate
Systems
Grade 1
1m55 – describe the
relative locations of
objects or people
using positional
language
Grade 2
2m56 – describe the
relative locations and
the movements of
objects on a map
Grade 3
3m60 – describe
movement from one
location to another
using a grid map
Grade 4
4m71 – identify and
describe the general
location of an object
using a grid system
Grade 5
Grade 6
5m57 – locate an
object using the
cardinal directions
(i.e., north, south,
6m52 – explain how a
coordinate system
represents location,
and plot points in the
east, west) and a
coordinate system
first quad rant of a
Cartesian co ordinate
plane
Grade 7
7m54 – plot points
using all four
quadrants of the
Cartesian co ordinate
plane
Grade 8
8m52 – graph the
image of a point, or
set of points, on the
Cartesian co ordinate
plane after applying
a transfo rmatio n to
the original point(s)
(i.e., translation;
reflection in the xaxis, the y-axis, or
the angle bisector of
the axes that passes
through the first and
third quadrants;
rotation of 90/, 180/,
or 270/ about the
origin)
Maps
1m56 – describe the
relative locations of
objects on conc rete
maps created in the
classroom
2m57 – draw simple
maps of familiar
settings, and describe
the relative locations
of objects on the
maps
3m60 – describe
movement from one
location to another
using a grid map
5m58 – compare
grid systems
commonly used on
maps (i.e., the use of
numbers and letters
to identify an area;
the use of a
coordinate system
based on the cardinal
directions to describe
a specific location)
12
Subheadings
Grade 1
Grade 2
Grade 3
Location and
Movement
3m61 – identify
flips, slides, and
Transformations
turns, through
investigation using
concrete m aterials
Grade 4
4m72 – identify,
perform, and
describe reflections
using a variety of
tools
Grade 5
5m59 – identify,
perform, and
describe translations,
using a variety of
tools
Designs
1m57 – create
symmetrical designs
and pictures, using
concrete m aterials,
and describe the
2m58 – create and
describe symmetrical
designs using a
variety of tools
relative locations of
the parts.
6m53 – identify,
perform, and
describe, through
investigation using a
variety of tools,
and physical motion,
and nam e flips,
rotations of 180º and
clockwise and
slides, and turns as
reflections,
counterclockwise
rotations of 90/, with
the centre of rotation
translations, and
rotations
Create and
Describe
Grade 6
3m62 – complete and
describe designs and
pictures of
images that have a
vertical, horizo ntal,
or diagonal line of
symmetry
Grade 7
Grade 8
7m55 – identify,
perform, and
describe dilatations
(i.e., enlargements
8m53 – identify,
through
investigation, realworld movements
and reductions),
through investigation
using a variety of
tools
that are translations,
reflections, and
rotations
inside or outside the
shape
4m73 – create and
analyze symmetrical
designs by reflecting
a shape, or shapes,
using a variety of
tools, and identify
the congruent shapes
in the designs
5m60 – create and
analyse designs by
translating and/or
reflecting a shape, or
shapes, using a
variety of tools
6m54 – create and
analyse designs
made by reflecting,
translating, and/or
rotating a shape, or
shapes, by 90º or
180º
7m56 – create and
analyse designs
involving
translations,
reflections,
dilatations, and/or
simple rotations of
two-dimensional
shapes, using a
variety of tools and
strategies
7m57 - determine,
through investigation
using a variety of
tools, polygons or
combinations of
polygons that tile a
plane, and describe
the transformation(s)
involved
Note: Italicized expectations are repeated in two categories.
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