Print section

Mathematics

Arithmetic

The concepts and processes to be acquired and mastered in arithmetic constitute the building blocks of mathematics, since they are applied in all other branches of this subject.

Meaning of operations involving numbers

Understanding and writing numbers
Operations involving numbers

In order to fully understand operations and their different meanings in various contexts, students must understand the relationships among data and among operations, and choose and perform the correct operations, taking into account the properties and order of operations. Students must also have a general idea of the result expected.

Students will thus be encouraged to use concrete, semi-concrete or symbolic means to mathematize a variety of situations illustrating different meanings. In these situations, students will learn to break problems down into simpler ones and identify the relationships among data that will help them to arrive at a solution. Since operation sense is developed at the same time as number sense, the two should be taught concurrently. 

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

Meaning of operations involving numbers

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 2 3 4 5 6
  1. Natural numbers less than . . .
1000 100 000 1 000 000
  1. Determines the operation(s) to perform in a given situation
  1. 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 addition and subtraction)
    1. transformation (adding, taking away), uniting, comparing
    1. composition of transformations: positive, negative
   
    1. composition of mixed transformations
       
  1. 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 multiplication and division) 
    1. rectangular arrays, repeated addition, Cartesian product, sharing, and number of times x goes into y (using objects and diagrams)
       
    1. rectangular arrays, repeated addition, Cartesian product, area, volume, repeated subtraction, sharing, number of times x goes into y, and comparisons (using objects, diagrams or equations)
   
  1. Establishes equality relations between numerical expressions (e.g.  3 + 2 = 6 – 1)
  1. Determines numerical equivalencies using relationships between
    1. operations (addition and subtraction) and the commutative property of addition
       
    1. operations (the four operations), the commutative property of addition and multiplication and the associative property
       
    1. operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtraction
       
  1. Translates a situation using a series of operations in accordance with the order of operations
       
    Vocabulary
    Plus, minus, less, more
    Addition, subtraction, sum, difference
    Symbols
    +, –
       
    Vocabulary
    At least, at most, term, missing term
    Multiplication, factor, product
    Division, divisor, dividend, quotient, remainder, sharing
    Equality, inequality, equation, inverse operation, multiple
    Symbols
    ×, ÷
       
  1. Decimals up to . . .
1 2 3 4 5 6
  hundredths thousandths
  1. 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 addition and subtraction)
    1. transformation (adding, taking away), uniting, comparing
   
    1. composition of transformations: positive, negative
   
    1. composition of mixed transformations
       
  1. 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 multiplication and division: rectangular arrays, Cartesian product, area, volume, sharing, number of times x goes into y, and comparisons)
   
  1. Determines numerical equivalencies using 
    1. the relationship between operations (addition and subtraction), the commutative property of addition and the associative property
       
    1. relationships between operations (the four operations), the commutative property of addition and multiplication, the associative property and the distributive property of multiplication over addition or subtraction
       
  1. Translates a situation into a series of operations in accordance with the order of operations
       
  1. Fractions
1 2 3 4 5 6
  1. 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 addition, subtraction and multiplication by a natural number)
       

Understanding and writing numbers
Operations involving numbers

Haut de page