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.