Mathematics

Print section

Geometry

Analyzing situations involving measurements

Spatial sense and analyzing situations involving geometric figures

Analyzing situations involving measurements1

Student constructs knowledge with teacher guidance.

Student applies knowledge by the end of the school year.

 

Student reinvests knowledge.

Elementary

Secondary
Cycle
One
Cycle
Two
  1. Mass
6 1 2 3 4 5
  1. Chooses the appropriate unit of mass for the context
             
  1. Estimates and measures mass using unconventional units: grams, kilograms
           
  1. Establishes relationships between units of mass
           
  1. Time
6 1 2 3 4 5  
  1. Chooses the appropriate unit of time for the context
             
  1. Estimates and measures time using conventional units
             
  1. Establishes relationships between units of time: second, minute, hour, day, daily cycle, weekly cycle, yearly cycle
           
  1. Distinguishes between duration and position in time
    Note : This includes the concept of negative time, where the start time t = 0 is arbitrarily chosen.
         
  1. Angles
6 1 2 3 4 5  
  1. Compares angles: acute angle, right angle, obtuse angle
             
  1. Estimates and determines the degree measure of angles
           
  1. Describes the characteristics of different types of angles: complementary, supplementary, adjacent, vertically opposite, alternate interior, alternate exterior and corresponding
         
  1. Determines measures of angles using the properties of the following angles: complementary, supplementary, vertically opposite, alternate interior, alternate exterior and corresponding
         
  1. Finds unknown measurements using the properties of figures and relations
 
    1. measures of angles in a triangle
           
    1. degree measures of central angles and arcs
         
  1. Defines the concept of radian
            CST
  TS
  S
  1. Determines the correspondence between degrees and radians
            CST
  TS
  S
  1. Justifies statements using definitions or properties associated with angles and their measures
         
  1. Length
6 1 2 3 4 5  
  1. Chooses the appropriate unit of length for the context
             
  1. Estimates and measures the dimensions of an object using conventional units: millimetre, centimetre, decimetre, metre and kilometre
           
  1. Establishes relationships between
 
    1. units of length: millimetre, centimetre, decimetre, metre and kilometre
           
    1. measures of length of the international system (SI)
           
  1. Constructs relations that can be used to calculate the perimeter or circumference of figures
         
  1. Finds the following unknown measurements, using properties of figures and relations
 
    1. perimeter of plane figures
             
    1. a segment in a plane figure, circumference, radius, diameter, length of an arc, a segment resulting from an isometry or a similarity transformation
         
    1. segments in a solid resulting from an isometry or a similarity transformation
           
    1. segments or perimeters resulting from equivalent figures
          CST
  TS
  S
  1. Justifies statements concerning measures of length
         
  1. Area
6 1 2 3 4 5  
  1. Chooses the appropriate unit of area for the context
             
  1. Estimates and measures surface areas using conventional units: square centimetre, square decimetre, square metre
           
  1. Establishes relationships between SI units of area
         
  1. Constructs relations that can be used to calculate the area of plane figures: quadrilateral, triangle, circle (sectors)
    Note : Using relations established for the area of plane figures and the net of solids, students identify relationships to calculate the lateral or total area of right prisms, right cylinders and right pyramids.
         
  1. Uses relations that can be used to calculate the area of a right cone and a sphere
           
  1. Finds unknown measurements, using properties of figures and relations
 
    1. area of circles and sectors
         
    1. area of figures that can be split into circles (sectors), triangles or quadrilaterals
         
    1. lateral or total area of right prisms, right cylinders and right pyramids
         
    1. lateral or total area of solids that can be split into right prisms, right cylinders or right pyramids
         
    1. area of figures resulting from an isometry
         
    1. area of figures resulting from a similarity transformation
      Note : In similar plane figures, the ratio of the areas is equal to the square of the similarity ratio.
         
    1. area of a sphere, lateral or total area of right cones and decomposable solids
           
    1. area of equivalent figures
          CST
  TS
  S
  1. Justifies statements concerning measures of area
         
  1. Volume
6 1 2 3 4 5  
  1. Chooses the appropriate unit of volume for the context
             
  1. Estimates and measures volume or capacity using conventional units: cubic centimetre, cubic decimetre, cubic metre, millilitre, litre
           
  1. Establishes relationships between SI units of volume
           
  1. Establishes relationships between
 
    1. capacity units : millilitre, litre
             
    1. measures of capacity
           
    1. measures of volume and of capacity
           
  1. Constructs relations that can be used to calculate volumes: right cylinders, right pyramids, right cones and spheres
           
  1. Finds unknown measurements using properties of figures and relations
 
    1. volume of right prisms, right cylinders, right pyramids, right cones and spheres
           
    1. volume of solids that can be split into right prisms, right cylinders, right pyramids, right cones and spheres
           
    1. volume solids resulting from an isometry or a similarity transformation
      Note : In similar solids, the ratio of the volumes is equal to the cube of the similarity ratio.
           
    1. volume of equivalent solids
          CST
  TS
  S
  1. Justifies statements concerning measures of volume or capacity
           
  1. Metric or trigonometric relations
6 1 2 3 4 5  
  1. Determines, through exploration or deduction, different metric relations associated with plane figures
   
  1. Finds unknown measurements in various situations
 
    1. in a right triangle rectangle using
      1. Pythagorean relation
           
      1. the following metric relations
        • The length of a leg of a right triangle is the geometric mean between the length of its projection on the hypotenuse and the length of the hypotenuse.
        • The length of the altitude to the hypotenuse of a right triangle is the geometric mean between the lengths of the segments of the hypotenuse.
        • The product of the lengths of the legs of a right triangle is equal to the product of the length of the hypotenuse and the length of the altitude to the hypotenuse.
           
      1. trigonometric ratios: sine, cosine, tangent
        Note : In TS and S, students also use cosecant, secant and cotangent in Secondary V.
           
    1. in any triangle using
      1. sine law
          CST
  TS
  S
      1. cosine law
          CST
  TS
  S
      1. Hero’s formula
        Note : In TS and S, this formula may be provided and used, if necessary.
          CST
    TS
    S
    1. in a circle: measure of arcs, chords, inscribed angles, interior angles and exterior angles
      Note : See Avenues of Exploration, Secondary Cycle Two Mathematics program, p. 127.
            CST
  TS
    S
  1. Calculates the area of a triangle given the measure of an angle and the lengths of two sides or given the measures of two angles and the length of one side
           
  1. Proves trigonometric identities by using algebraic properties, definitions (sine, cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetry
    Note : Formulas for finding the sum or difference of angles are compulsory in S only.
            CST
  TS
  S
  1. Justifies statements concerning
 
    1. Pythagorean relation
           
    1. metric or trigonometric relations
           
  1. Vectors in the Cartesian or Euclidian plane
6 1 2 3 4 5  
  1. Defines a vector: magnitude (length or norm), direction, sense
    Note : In Secondary Cycle One, vectors are used in translations.
            CST
  TS
  S
  1. Represents a vector graphically (arrow in a plane or pair in a Cartesian plane)
    Note : In TS, students may use a matrix with geometric transformations.
            CST
  TS
  S
  1. Identifies properties of vectors
            CST
  TS
  S
  1. Performs operations on vectors
    Note : In TS, operations on vectors are performed in context.
 
    1. determination of the resultant or projection of a vector
            CST
  TS
  S
    1. addition and subtraction of vectors
            CST
  TS
  S
    1. multiplication of a vector by a scalar
            CST
  TS
  S
    1. scalar product of two vectors
            CST
  TS
  S
    1. linear combination of vectors
            CST
    TS
  S
    1. application of Chasles relation
            CST
    TS
  S
  1. Justifies statements using properties associated with vectors
            CST
    TS
  S
  1. Analyzes and models situations using vectors (e.g. displacements, forces, speeds or velocities)
            CST
  TS
  S
1.  Depending on the context, measurement prefixes (e.g. nano, micro, milli, deca, kilo, mega, giga) are introduced.

Haut de page