Analyzing situations involving measurements^{1} 
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 
 Mass

6 
1 
2 
3 
4 
5 
 Chooses the appropriate unit of mass for the context








 Estimates and measures mass using unconventional units: grams, kilograms








 Establishes relationships between units of mass








 Time

6 
1 
2 
3 
4 
5 

 Chooses the appropriate unit of time for the context








 Estimates and measures time using conventional units








 Establishes relationships between units of time: second, minute, hour, day, daily cycle, weekly cycle, yearly cycle








 Distinguishes between duration and position in time
Note : This includes the concept of negative time, where the start time t = 0 is arbitrarily chosen.








 Angles

6 
1 
2 
3 
4 
5 

 Compares angles: acute angle, right angle, obtuse angle








 Estimates and determines the degree measure of angles








 Describes the characteristics of different types of angles: complementary, supplementary, adjacent, vertically opposite, alternate interior, alternate exterior and corresponding








 Determines measures of angles using the properties of the following angles: complementary, supplementary, vertically opposite, alternate interior, alternate exterior and corresponding








 Finds unknown measurements using the properties of figures and relations


 measures of angles in a triangle








 degree measures of central angles and arcs








 Defines the concept of radian







CST 


TS 


S 
 Determines the correspondence between degrees and radians







CST 


TS 


S 
 Justifies statements using definitions or properties associated with angles and their measures








 Length

6 
1 
2 
3 
4 
5 

 Chooses the appropriate unit of length for the context








 Estimates and measures the dimensions of an object using conventional units: millimetre, centimetre, decimetre, metre and kilometre








 Establishes relationships between


 units of length: millimetre, centimetre, decimetre, metre and kilometre








 measures of length of the international system (SI)








 Constructs relations that can be used to calculate the perimeter or circumference of figures








 Finds the following unknown measurements, using properties of figures and relations


 perimeter of plane figures








 a segment in a plane figure, circumference, radius, diameter, length of an arc, a segment resulting from an isometry or a similarity transformation








 segments in a solid resulting from an isometry or a similarity transformation








 segments or perimeters resulting from equivalent figures







CST 


TS 


S 
 Justifies statements concerning measures of length








 Area

6 
1 
2 
3 
4 
5 

 Chooses the appropriate unit of area for the context








 Estimates and measures surface areas using conventional units: square centimetre, square decimetre, square metre








 Establishes relationships between SI units of area








 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.








 Uses relations that can be used to calculate the area of a right cone and a sphere








 Finds unknown measurements, using properties of figures and relations


 area of circles and sectors








 area of figures that can be split into circles (sectors), triangles or quadrilaterals








 lateral or total area of right prisms, right cylinders and right pyramids








 lateral or total area of solids that can be split into right prisms, right cylinders or right pyramids








 area of figures resulting from an isometry








 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.








 area of a sphere, lateral or total area of right cones and decomposable solids








 area of equivalent figures







CST 


TS 


S 
 Justifies statements concerning measures of area








 Volume

6 
1 
2 
3 
4 
5 

 Chooses the appropriate unit of volume for the context








 Estimates and measures volume or capacity using conventional units: cubic centimetre, cubic decimetre, cubic metre, millilitre, litre








 Establishes relationships between SI units of volume








 Establishes relationships between


 capacity units : millilitre, litre








 measures of capacity








 measures of volume and of capacity








 Constructs relations that can be used to calculate volumes: right cylinders, right pyramids, right cones and spheres








 Finds unknown measurements using properties of figures and relations


 volume of right prisms, right cylinders, right pyramids, right cones and spheres








 volume of solids that can be split into right prisms, right cylinders, right pyramids, right cones and spheres








 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.








 volume of equivalent solids







CST 


TS 


S 
 Justifies statements concerning measures of volume or capacity








 Metric or trigonometric relations

6 
1 
2 
3 
4 
5 

 Determines, through exploration or deduction, different metric relations associated with plane figures








 Finds unknown measurements in various situations


 in a right triangle rectangle using

 Pythagorean relation








 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.








 trigonometric ratios: sine, cosine, tangent
Note : In TS and S, students also use cosecant, secant and cotangent in Secondary V.








 in any triangle using

 sine law







CST 


TS 


S 
 cosine law







CST 


TS 


S 
 Hero’s formula
Note : In TS and S, this formula may be provided and used, if necessary.







CST 


TS 


S 
 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 
 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








 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 
 Justifies statements concerning


 Pythagorean relation








 metric or trigonometric relations








 Vectors in the Cartesian or Euclidian plane

6 
1 
2 
3 
4 
5 

 Defines a vector: magnitude (length or norm), direction, sense
Note : In Secondary Cycle One, vectors are used in translations.







CST 


TS 


S 
 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 
 Identifies properties of vectors







CST 


TS 


S 
 Performs operations on vectors
Note : In TS, operations on vectors are performed in context.


 determination of the resultant or projection of a vector







CST 


TS 


S 
 addition and subtraction of vectors







CST 


TS 


S 
 multiplication of a vector by a scalar







CST 


TS 


S 
 scalar product of two vectors







CST 


TS 


S 
 linear combination of vectors







CST 


TS 


S 
 application of Chasles relation







CST 


TS 


S 
 Justifies statements using properties associated with vectors







CST 


TS 


S 
 Analyzes and models situations using vectors (e.g. displacements, forces, speeds or velocities)







CST 


TS 


S 