• constructing three-dimensional objects:
  • using interlocking cubes to build rectangle-based prisms
  • rolling paper to form cones and cylinders
  • cutting and taping cardboard to form shapes
  • using nets for a variety of objects
  • using building materials for a variety of objects (e.g., modelling clay, sticks)
• sorting real-life objects concretely and using pictures:
  • cubes: Rubik’s cubes, tissue boxes, ice cubes
  • prisms: boxes, aquariums, buildings, ice crystals
  • pyramids: tents, umbrellas, ancient pyramids, roof of a gazebo
  • cylinders: cans, broomsticks, tubes, tree trunks
  • cones: ice cream cones, funnels, party hats, tornadoes
• sorting and identifying cubes, prisms, pyramids, cylinders, and cones:

Triangle-Based Prisms	Rectangle-Based Prisms
Cubes or Square-Based Prisms	Trapezoid-Based Prism
Pyramids
Cones	Cylinders

• Three-dimensional objects have attributes that allow them to be identified, compared, sorted, and classified.
• Geometric properties are attributes that are the same for an entire group of three-dimensional objects. Some attributes are relevant for classifying objects by geometry. Others are not. For example, colour and size are attributes but are not relevant for geometry since there are large cubes, small cubes, blue cubes, and yellow cubes. Having six congruent faces, where each face is a square, is an attribute and a geometric property because all cubes, by definition, have this property.
• When sorting and building objects, some of the attributes that are useful to name and notice are the number and shape of the faces, the number of edges, and the number of vertices and angles.
• When three-dimensional objects are sorted by geometric properties or categories, classes emerge. Each class of three-dimensional object has common geometric properties, and these properties are unaffected by the size or orientation of an object.

Note

• Constructing three-dimensional objects highlights the geometric properties of an object. Properties can be used as a “rule” for constructing a certain class of objects.
• The following table lists properties of some common three-dimensional objects.

Prisms	Prisms have two congruent, polygon faces. These faces form the base of the prism. (Note that the base may or may not be the “bottom” of the prism).   The two bases are connected by rectangles or parallelograms of the same height (e.g., the bases are parallel).   A prism is named by the shape of its base.  For example, triangle-based prisms have two bases that are triangles, which are connected by rectangles or parallelograms.
Cubes	Cubes have six congruent faces, and each face is a square.  Because cubes have all the properties of a prism, they can also be called square-based prisms.
Cylinders	Cylinders have two congruent and parallel bases; straight lines of equal length can be drawn that join one base to the other. Cylinders are named by the shape of their base. For example, a can is a circular cylinder.
Pyramids	Pyramids have a single polygon for a base.  Triangles join each side of the base and meet at a vertex called the apex.   A pyramid is named by the shape of its base. For example, a square-based pyramid has a square for its base and four triangular faces.
Cones	Cones have one base; straight lines can be drawn from any point on the base’s edge to its top point, called its apex. Cones are named by the shape of their base. For example, an ice cream cone is a circular cone.

 

• various structures:
  • student-made structures: fort, snowperson
  • natural structures: spiderwebs, coral, trees, honeycombs, birds’ nests, beaver dams
  • human-engineered structures: bridges, towers, tunnels, pyramids, buildings, tents, play structures, constructed beehives

• Structures are composed of three-dimensional objects with faces that are two-dimensional shapes. Recognizing and describing the shapes and objects in three-dimensional structures provides insight into how structures are built.
• Objects and structures can be decomposed physically and visually (e.g., using the “mind’s eye”). Visualization is an important skill to develop.
• Triangles are useful for strengthening and stabilizing a structure; rectangular prisms are commonly used because of their ability to be stacked. This expectation is closely related to learning in the Grade 3 Structures and Mechanisms strand of the Science and Technology curriculum, 2022.

• identifying congruent objects:
  • mentally matching lengths, angles, and faces
  • directly comparing lengths, angles, and faces
  • indirectly comparing lengths, angles, and faces using a third object
• congruent three-dimensional objects:

• Congruence is a relationship between three-dimensional objects that have the same shape and the same size. Congruent three-dimensional shapes match every face exactly, in the exact same position.
• Checking for congruence is closely related to measurement. Side lengths and angles can be directly compared by matching them, one against the other. They can also be measured.
• Two objects that are not congruent can still have specific elements that are congruent. For example, two objects might have a face that is congruent (i.e., the face is the same size and shape), but if the other faces are different in any way (e.g., the faces have different angles or side lengths), then the two objects are not congruent. Likewise, even if all faces are congruent but they are in a different arrangement, the two objects would not be congruent because they would not be the exact same shape.

Note

• The skill of visualizing congruent objects – mentally manipulating and matching objects to predict congruence – can be developed through hands-on experience.

• multistep instructions:
  • Move 3 steps right, make a quarter-turn clockwise, and move 2 steps left.
  • Make a half-turn, move forward 3 m, make a quarter-turn counterclockwise, and move forward 2 m.
• types of directions:
  • cardinal:
    • north (N), south (S), east (E), west (W)
  • directional language:
    • forward/backward
    • up/down
    • right/left
    • quarter-turn/half-turn
  • clockwise:

• counterclockwise:

• Instructions to move from one location to another location require information about direction and distance from a given location.
  • Numbers and units describe distance (e.g., 5 steps; 3 kilometres).
  • Absolute direction can be conveyed using cardinal language (i.e., N, S, E, W), which was introduced in Grade 2 to locate selected communities, countries, and/or continents on a map (See The Ontario Curriculum: Social Studies, Grades 1 to 6; History and Geography, Grades 7 and 8, 2018, Grade 2, B3.3).
  • Relative direction can be conveyed using qualitative language (right, left, forward, backward, up, down).
  • Relative direction can be quantified and made more precise by describing the amount of turn.
• The amount of a turn involves the measure of angles, a skill that is more formally developed in Grades 4 and 5. In Grade 3, the language of half- and quarter-turn parallels the minute hand of an analog clock. A turn may be clockwise (moving in the same direction as the hands of a clock) or counterclockwise (the opposite direction from the hands of a clock).
  • A full turn is a full circle that results in an object facing in the same direction (e.g., start at 12 o’clock, end at 12 o’clock). A full turn clockwise or counterclockwise produces the same result.
  • A half-turn results in an object facing the opposite direction, (e.g., start at 12 o’clock, end at 6 o’clock). A half-turn clockwise or counterclockwise produces the same result.
  • A quarter-turn results in an object facing either 9 o’clock or 3 o’clock, (i.e., start at 12 o’clock, and go a quarter-turn clockwise, and end at 3 o’clock, or go a quarter-turn counterclockwise, and end at 9 o’clock).