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Mathematics

Geometry

Before they enter preschool, children explore the shapes of objects in their surroundings and begin to understand basic topological concepts such as inside-outside, above-below; they also acquire the rudiments of spatial sense. In preschool, they begin to organize space and establish relationships between objects by comparing, classifying and grouping them.

Throughout elementary school, by participating in activities and manipulating objects, students acquire the vocabulary of geometry and learn to get their bearings in space, identify plane figures and solids, describe categories of figures and observe their properties. Geometry in elementary school focuses on two-dimensional (plane) and three-dimensional figures and on key concepts, such as the ability to locate objects in space and observe their geometric and topological properties. Knowledge of vocabulary is not enough; the words must be closely tied to precise concepts such as shape, similarity, dissimilarity, congruency and symmetry. Thus, the use of varied activities and a wide range of objects is essential for students to develop spatial sense and geometric thought. This will allow students to progress from the concrete to the abstract, first by manipulating and observing objects, then by making various representations, and finally by creating mental images of figures and their properties. 

The ability to discern and recognize the properties of a geometric object or a category of objects must be developed before students can learn about the relationships among elements in a figure or among distinct figures. It is also required in order to develop the ability to identify new properties and use known or new properties in problem solving.

The table below presents the learning content associated with geometry. The concepts and processes targeted will provide students with increasingly complex tools that will help them develop and use all three mathematics competencies.

Student constructs knowledge with teacher guidance.

Student applies knowledge by the end of the school year.

 

Student reinvests knowledge.

Elementary
Cycle
One
Cycle
Two
Cycle
Three
  1. Space
1 2 3 4 5 6
  1. Gets his/her bearings and locates objects in space (spatial relationships)
       
  1. Locates objects in a plane
   
  1. Locates objects on an axis (based on the types of numbers studied)
  1. Locates points in a Cartesian plane
    1. in the first quadrant
   
    1. in all four quadrants
       
    Vocabulary
    Reference system, plane, Cartesian plane, ordered pair
   
    Symbols
    Writing ordered pairs (a, b)
  1. Solids
1 2 3 4 5 6
  1. Compares objects or parts of objects in the environment with solids
    (e.g. spheres, cones, cubes, cylinders, prisms, pyramids)
       
  1. Compares and constructs solids
    (e.g. spheres, cones, cubes, cylinders, prisms, pyramids)
       
  1. Identifies the main solids
    (e.g. spheres, cones, cubes, cylinders, prisms, pyramids)
       
    Vocabulary
    Solid, base of a solid, face, flat surface, curved surface
    Sphere, cone, cube, cylinder, prism, pyramid
       
  1. Identifies and represents the different faces of a prism or pyramid
       
  1. Describes prisms and pyramids in terms of faces, vertices and edges
       
  1. Classifies prisms and pyramids
       
  1. Constructs a net of a prism or pyramid
       
  1. Matches the net of
    1. a prism to the corresponding prism and vice versa
     
    1. a pyramid to the corresponding pyramid and vice versa
     
    1. a convex polyhedron to the corresponding convex polyhedron
       
    Vocabulary
    Vertex, edge, net of a solid
       
  1. Tests Euler’s theorem on convex polyhedrons
       
    Vocabulary
    Polyhedron, convex polyhedron
       
  1. Plane figures
1 2 3 4 5 6
  1. Compares and constructs figures made with closed curved lines or closed straight lines
       
  1. Identifies plane figures (square, rectangle, triangle, rhombus and circle)
       
  1. Describes plane figures (square, rectangle, triangle and rhombus)
       
    Vocabulary
    Straight line, closed straight line, curved line
    Plane figure, side
    Square, circle, rectangle, triangle, rhombus
       
  1. Describes convex and nonconvex polygons
       
  1. Identifies and constructs parallel lines and perpendicular lines
       
  1. Describes quadrilaterals (e.g. parallel segments, perpendicular segments, right angles, acute angles, obtuse angles)
       
  1. Classifies quadrilaterals
       
    Vocabulary
    Quadrilateral, parallelogram, trapezoid, polygon
    Convex polygon, nonconvex polygon, segment
    Is parallel to . . ; is perpendicular to . . .
    Symbols
    //, ⊥
       
  1. Describes triangles: scalene triangles, right triangles, isosceles triangles, equilateral triangles
       
  1. Classifies triangles 
       
  1. Describes circles
       
    Vocabulary
    Equilateral triangles, isosceles triangle, right triangle, scalene triangle
    Circle, central angle, diameter, radius, circumference
       
  1. Frieze patterns and tessellations
1 2 3 4 5 6
  1. Identifies congruent figures
       
  1. Observes and produces patterns using geometric figures
   
  1. Observes and produces frieze patterns and tessellations
    1. using reflections
       
    1. using translations
       
    Vocabulary
    Frieze pattern, tesselation
    Reflection, line of reflection, symmetric figure
       
    Vocabulary
    Translation, translation arrow
       

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