Understanding operations involving real numbers 
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 

6 
1 
2 
3 
4 
5 
 Natural numbers less than 1 000 000

 Determines the operation(s) to perform in a given situation







 Uses objects, diagrams or equations to represent a situation and, conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of the four operations)







 Establishes equality relations between numerical expressions
(e.g. 3 + 2 = 6 – 1)







 Determines numerical equivalencies using relationships between operations, the commutative and associative properties of addition and multiplication, the distributive property of multiplication over addition or subtraction







 Translates a situation using a sequence of operations in accordance with the order of operations







 Fractions

 Uses objects, diagrams or an operation to represent a situation and, conversely, describes a situation represented by objects, diagrams or an operation (use of different meanings of addition, subtraction and multiplication by a natural number)







 Uses an operation to represent a situation (use of different meanings of operations)







 Decimals

 Uses objects, diagrams or equations to represent a situation and, conversely, describes a situation represented by objects, diagrams or equations (use of different meanings of the four operations)







 Determines numerical equivalencies using relationships between operations (inverse operations), the commutative and associative properties of addition and multiplication, the distributive property of multiplication over addition or subtraction







 Translates a situation using a sequence of operations in accordance with the order of operations







 Chooses an appropriate way of writing numbers for a given context
Note : Over the years, new notation systems such as scientific notation are added to the students’ repertoire.







 Looks for equivalent expressions: decomposing (additive, multiplicative, etc.), equivalent fractions, simplifying and reducing, factoring, etc.







 Translates (mathematizes) a situation using a sequence of operations (no more than two levels of parentheses)







 Anticipates the results of operations







 Interprets the results of operations in light of the context






