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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. 1 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 2 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 4 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 5 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. 6 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 8 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 9 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. 13