Mathematics

Print section

Arithmetic

Operations involving real numbers

Understanding real numbers
Understanding operations involving real numbers
Understanding and analyzing proportional situations

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
  1. Natural numbers less than 1 000 000
    1. Approximates the result of an operation
           
    1. Using personal processes, mentally computes operations
           
    1. Determines in writing
        • the sum of two natural numbers of up to 4 digits
        • the difference between two natural numbers of up to 4 digits whose result is greater than 0
        • the product of a three-digit number by a two-digit number
        • the quotient of a four-digit number and a two-digit number and expresses the remainder of a division as a decimal that does not go beyond the second decimal place
        • the result of a sequence of operations in accordance with the order of operations
               
    1. Fractions (using objects or diagrams)
      1. Generates a set of equivalent fractions
               
      1. Reduces a fraction to its simplest form
               
      1. Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction
               
      1. Multiplies a natural number by a fraction and a fraction by a natural number
               
    1. Decimal numbers up to thousandths
      1. Approximates the result of an operation
               
      1. Mentally computes
          • operations (addition, subtraction, multiplication, division by a natural number)
          • multiplications by 10, 100, 1000
               
      1. Computes in writing
          • additions and subtractions of numbers whose result does not go beyond the second decimal place
          • multiplications of numbers whose product does not go beyond the second decimal place
          • divisions of a decimal by a natural number less than 11
               
    1. Properties of divisibility
      1. Determines the divisibility of a number by 2, 3, 4, 5, 6, 8, 9 and 10
               
      1. Uses, in different contexts, the properties of divisibility: 2, 3, 4, 5 and 10
               
    1. Approximates the result of an operation or sequence of operations
             
    1. Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations
             
    1. Computes, in writing, the four operations1 with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations
      1. numbers written in decimal notation, using rules of signs
               
      1. positive numbers written in fractional notation, with or without the use of objects or diagrams
             
      1. numbers written in fractional notation
               
    1. Computes, in writing, sequences of operations (numbers written in decimal notation) in accordance with the order of operations, using equivalent ways of writing numbers and the properties of operations (with no more than two levels of parentheses)
               
    1. Computes, using a calculator, operations and sequences of operations in accordance with the order of operations
               
    1. Switches, as needed, from one way of writing numbers to another: from fractional to percentage notation, from decimal to fractional notation, from decimal to percentage notation, and vice versa
               
    1. Switches, as needed, from one way of writing numbers to another
      Note : In Secondary Cycle One, the students should use positive numbers when switching from one type of notation to another. In Secondary Cycle Two, new types of notation are introduced: exponential, scientific notation, etc.
             
    1. Calculates the power of a natural number
               
    1. Decomposes a natural number into prime factors
               
    1. Manipulates numerical expressions involving
      1. integral exponents (rational base) and fractional exponents
        Note : When manipulating numerical expressions, students learn to deduce the properties of powers.
               
      1. powers of bases (change of base), exponents, radicals (nth root), using their properties
        Note : In CST, radicals and their properties are not covered. For base changes in TS in Secondary IV, students use bases 2 and 10. In S, students learn to deduce the properties of radicals.
              CST
    TS
      S
      1. logarithms
     
        1. definition and change of base
              CST
      TS
      S
        1. properties
                CST
      TS
      S
      1. absolute values
                CST
        TS
      S
    1.  Students use technological tools for operations in which the divisors or multipliers have more than two digits; however, for written computation, the understanding and mastery of the processes is more important than the ability to do complex calculations.

    Haut de page