1
Continuum of Curriculum Expectations: Geometry and Spatial Sense
Overall Expectations
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Geometric Properties
1m43 • identifycommon two-
dimensional shapes and three-
dimensional figures and sort and classify
them b y their attributes
2m44 • identify two-dimensional shapes
and three- dimensional figures and sort and classify
them b y their geometric prope rties
3m47 • comparetwo-dimensional
shapes and three- dimensional figures and sort them by
their geo metric properties;
4m58 • identifyquadrilaterals and three-dimensional
figures and classify them b y their
geometric prope rties, and comp are various
angles to benchmarks;
5m46 • identify andclassify two-
dimensional shapes by side and angle
properties, and compare and sort three-dimensional
figures;
6m43 • classify andconstruct polygons
and angles;
7m43 • constructrelated lines, and
classify triangles, quadrilaterals, and
prisms;
8m40 • demonstratean understanding of
the geo metric properties of
quadrilaterals and circles and the
applications of geometric properties in the real world;
Geometric Relationships
1m44 • compose anddecompose common
two-dimensional shapes and three-
dimensiona l figures;
2m45 • compose anddecompose two-
dimensional shapes and three-
dimensional figures
3m48 • describerelationships
between two- dimensional shapes, and between two-
dimensional shapes and three-
dimensiona l figures;
4m59 • constructthree-dimensional
figures, using two- dimensiona l shape s;
5m47 • identify andconstruct nets of
prisms and pyram ids;
6m44 • sketch three-dimensional figures,
and construct three- dimensional figures
from drawings;
7m44 • develop anunderstanding of
similarity, and distinguish similarity and congruence;
8m41 • developgeometric
relationships involving lines, triangles, and
polyhedra, and solve problems involving
lines and triangles;
Location and Movement
1m45 • describe therelative locations of
objects using positional language.
2m46 • describe andrepresent the relative
locations of ob jects, and repre sent ob jects
on a map
3m49 • identify anddescribe the locations
and movements of shapes and objects.
4m60 • identify anddescribe the location
of an object, using a grid map, and reflect
two-dimensional shapes.
5m48 • identify anddescribe the location
of an object, using the cardinal
directions, and translate two-
dimensiona l shape s.
6m45 • describelocation in the first quadrant of a
coordinate system, and rotate two-
dimensiona l shape s.
7m45 • describelocation in the four quadrants of a
coordinate system, dilatate two-
dimensional shapes, and apply
transformatio ns to create and analyse
designs.
8m42 • representtransformations using the Cartesian
coordinate plane, and make connections
between transformations and the real world.
2
Specific Expectations
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Geometric Properties
Identify, Sort and Classify
2-D
1m46 – identify anddescribe common
two-dimensional shapes and sort and classify them by
their attributes, using concrete m aterials
and pictorial representations
2m47 – distinguishbetween the
attributes of an object that are
geometric properties and the attributes
that are not geometric properties using a variety of
tools
2m48 – identify anddescribe various
polygons (i.e., triangles,
quadrilaterals, pentago ns, hexagons, heptago ns, octagons)
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
3m51 – identify andcompare 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)
4m62 – identify andcompare different
types of quadrilaterals (i.e., rectangle, square,
trapezoid, parallelogram,
rhombus) and sort and classify them by their geo metric
properties
5m49 – distinguishamong polygons,
regular polygons, and other two-
dimensional shapes
6m47 – sort polygons according to the number of
lines of symm etry and the order of
rotational symmetry, 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
7m47 – sort and classify triangles andquadrilaterals by
geometric properties related to symmetry,
angles, and sides, through investigation using a variety of
tools and strategies
8m43 – sort andclassify
quadrilaterals by geometric prope rties, including those
based on diago nals, through investigation
using a variety of tools
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
3
Geometric Properties
Symmetry 2-D
1m50 – locateshapes in the
environment that have symmetry, and describe the
symmetry.
2m51 – locate the line of symmetry in a two-dimensional
shape
symmetry is part of 3m62in Location and
Mo vement
4m61 – draw thelines of symmetry of two-dimensional
shapes, through investigation using a variety of tools and
strategies
5m53 – identifytriangles (i.e., acute, right, obtuse,
scalene, isosceles, equilateral), and
classify them
acco rding to angle and side p roperties
6m46 – sort andclassify
quadrilaterals by geometric properties related to sym metry,
angles, and sides, through investigation using a variety of
tools
6m47 – sortpolygons according to the number of
lines of sym metry and the order of
rotatio nal sym metry, through investigation
using a variety of tools
7m47 – sort andclassify triangles and quadrilaterals by
geometric properties related to sym metry,
angles, and sides, through investigation using a variety of
tools and strategies
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
4
Geometric Properties
2-D Construction
5m54 – constructtriangles, using a
variety of tools, given acute or right angles and side
measurem ents
6m49 – constructpolygons using a
variety of tools, given angle and side measurem ents
7m46 – construct related lines (i.e.,
parallel; perpendicular;
intersecting at 30º, 45º, and 60º), using
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
8m44 – construct acircle, given its
centre and radius, or its centre and a point
on the circle, or three points on the circle
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
5
Geometric Properties
Lines and Angles
3m50 – use areference tool to
identify right angles and to describe
angles as greater than, equal to, or less than a right angle
3m52 – comparevarious angles, using concrete m aterials
and pictorial representations, and describe angles as
bigger than, smaller than, or about the
same as other angles
4m63 – identifybenchmark angles (i.e., straight angle,
right angle, half a right angle), using a reference tool, and
compare other angles to these benchmarks
4m64 – relate thenames of the
benchmark angles to their me asures in
degrees
5m51 – identify andclassify acu te, right,
obtuse, and straight angles
5m52 – measure andconstruct angles up
to 90º, using a protractor
6m48 – measure andconstruct angles up
to 180/ using a protractor, and
classify them as acute, right, obtuse, or straight angles
7m46 – constructrelated lines (i.e.,
parallel; perpendicular;
intersecting at 30º, 45º, and 60º), using
angle properties and a variety of tools and
strategies
7m48 – constructangle bisectors and perpendicular
bisectors, using a variety of tools and
strategies, and represent equal
angles and equal lengths using
mathematical notation
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
6
Geometric Properties
Identify and Describe 3-D
1m48 – identify anddescribe common
three-dimensional figures and sort and
classify them by their attributes, using concrete m aterials
and pictorial representations
1m49 – describesimilarities and
differences between an everyday object
and a three dimensional figure
2m49 – identify anddescribe various
three-dimensional figures (i.e., cubes,
prisms, pyramids) and sort and classify them b y their
geometric properties (i.e., number and
shape of faces), using co ncrete
materials
3m53 – compare andsort prisms and
pyramids by geometric properties (i.e., number and
shape of faces, numbe r of edges,
number of vertices), using co ncrete
materials
4m65 – identify anddescribe prisms and
pyramids, and classify them by their geo metric
properties (i.e., shape of faces, number of
edges, number of vertices), using
concrete m aterials
5m50 – distinguishamong prisms, right
prisms, pyramids, and other three-
dimensional figures
7m49 – investigate,using co ncrete
materials, the angles between the faces of
a prism , and id entify right prisms
3-D Construction
1m47 – trace andidentify the two-
dimensional 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)
3m54 – constructrectangular prism s,
and describe geometric properties (i.e., number and
shape of faces, numbe r of edges,
numbe r of vertices) of the prisms
4m70 – construct three-dimensional
figures, using only congruent shapes
Miscellaneous
8m45 – investigateand describe
applications of geometric properties in the real world.
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
7
Geometric Relationships
Compose and Decompose
2-D
1m51 – com posepatterns, pictures,
and designs, using common two-
dimensional shapes
1m52 – identify anddescribe shapes
within other shap es
1m54 – cover outlinepuzzles with two-
dimensional shapes
2m52 – compose anddescribe p ictures,
designs, and patterns by combining two-
dimensional shapes
2m53 – compo se anddecompose two-
dimensional shapes
2m54 – cover anoutline p uzzle with two-dimensional
shapes in more than one way
3m55 – solveproblems requiring the greatest or least
number of two- dimensional shapes needed to compose a
larger shape in a variety of ways
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
8
Geometric Relationships
Congruent and Similar 2-D and
3-D
3m59 – identifycongruent two-
dimensional shapes by manipulating and
matching co ncrete materials
4m70 – constructthree-dimensional
figures, using only congruent shapes
7m51 – determine,through investigation using a variety of
tools, relationships among area,
perimeter, corresponding side lengths, and
corresponding angles of congruent shapes
7m52 – demonstratean understanding that
enlarging or reducing two-
dimensional shapes creates similar
shapes
7m53 – distinguishbetween and
compare similar shapes and congruent shapes, using a
variety of tools and strategies
8m46 – determine,through investigation using a variety of
tools, relationships among area,
perimeter, corresponding side lengths, and
corresponding angles of similar shapes
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
9
Geometric Relationships
3-D Construction
1m53 – build three-dimensional
structures using concrete m aterials, and describe the two
dimensional shapes the structures co ntain
2m55 – build astructure using three- dimensional figures,
and describe the two- dimensional shapes
and three- dimensional figures in the structure
3m57 – identify anddescribe the two-
dimensional shapes that can b e found in
a three dimensional figure
4m66– construct athree-dimensional
figure from a picture or model of the
figure, using connecting cubes
4m67 – constructskeletons of three-
dimensional figures, using a variety of
tools, and sketch the skeletons
4m68 – draw anddescribe nets of
rectangular and triangular prisms
4m69 – constructprisms and pyramids from given nets
5m56– construct netsof prisms and
pyramids, using a variety of tools
6m50 – build three-dimensiona 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
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
10
Geometric Relationships
Identify and Describe
Relationships
1m52 – identify anddescribe shapes
within other shap es
2m52 – compose anddescribe p ictures,
designs, and patterns by combining two-
dimensional shapes
3m57 – identify anddescribe the two-
dimensional shapes that can b e found in
a three dimensional figure
3m58 – describe andname prisms and
pyramids by the shape of their base
5m55– identifyprisms and pyramids from their nets
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 angle-relationship
problems involving triangles, intersecting
lines, and parallel lines and transversals
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
11
Geometric Relationships
Pythagorean Relationships
8m49 – determinethe Pythagorean
relationship, through investigation using a
variety of tools
8m50 – solveproblems involving right triangles
geometrically, using the Pythagorean
relationship
Miscellaneous
3m56– explain therelationships
between different types of
quadrilaterals
7m50 – identify,through
investigation, the minimum side and
angle information (i.e., side-side-side;
side-angle-side; angle-side angle)
needed to describe a unique triangle
8m51 – determine,through investigation using co ncrete
materials, the relationship between the numbers of faces,
edges, and vertices of a polyhed ron (i.e.,
numbe r of faces + numbe r of vertices = number of edges + 2)
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
12
Location and Movement
Co-Ordinate Systems
1m55 – describe therelative locations of
objects or people using positional
language
2m56 – describe therelative locations and
the movements of objects on a map
3m60 – describemovement from one location to another
using a grid map
4m71 – identify anddescribe the general
location of an object using a grid system
5m57 – locate anobject using the
cardinal directions (i.e., north, south,
east, west) and a coordinate system
6m52 – explain how a coordinate system
represents location, and plot points in the
first quad rant of a Cartesian co ordinate plane
7m54 – plot pointsusing all four
quadrants of the Cartesian co ordinate plane
8m52 – graph theimage 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 x- axis, 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 therelative locations of
objects on conc rete maps created in the
classroom
2m57 – draw simplemaps of familiar
settings, and describe the relative locations
of objects on the maps
3m60 – describemovement from one location to another
using a grid map
5m58 – comparegrid 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)
Subheadings
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
13
Location and Movement
Transformations
3m61 – identifyflips, slides, and
turns, through investigation using concrete m aterials
and physical motion, and nam e flips,
slides, and turns as reflections,
translations, and rotations
4m72 – identify,perform, and
describe reflections using a variety of
tools
5m59 – identify,perform, and
describe translations, using a variety of
tools
6m53 – identify,perform, and
describe, through investigation using a variety of tools,
rotations of 180º and clockwise and
counterclockwise rotations of 90/, with the centre of rotation
inside or outside the shape
7m55 – identify,perform, and
describe dilatations (i.e., enlargements
and reductions), through investigation using a variety of
tools
8m53 – identify,through
investigation, real- world movements
that are translations, reflections, and
rotations
Create and Describe
Designs
1m57 – createsymmetrical designs and pictures, using
concrete m aterials, and describe the
relative locations of the parts.
2m58 – create anddescribe symmetrical designs using a
variety of tools
3m62 – complete and describe designs and pictures of
images that have a vertical, horizo ntal,
or diagonal line of symmetry
4m73 – create andanalyze symmetrical
designs by reflecting a shape, or shapes,
using a variety of tools, and identify
the congruent shapes in the designs
5m60 – create andanalyse designs by
translating and/or reflecting a shape, or shapes, using a
variety of tools
6m54 – create andanalyse designs
made by reflecting, translating, and/or
rotating a shape, or shapes, by 90º or
180º
7m56 – create andanalyse 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.