Mathematics

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Arithmetic

Understanding real numbers

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

Understanding 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. Reads and writes any natural number
           
    1. Represents natural numbers in different ways
           
    1. Composes and decomposes a natural number in a variety of ways and identifies equivalent expressions
           
    1. Approximates a natural number
           
    1. Compares natural numbers or arranges natural numbers in increasing or decreasing order
           
    1. Classifies natural numbers in various ways, based on their properties
      (e.g. even numbers, composite numbers)
           
  1. Fractions
    1. Represents a fraction in a variety of ways (using objects or drawings)
           
    1. Identifies the different meanings of fractions: part of a whole, division, ratio, operator, measurement
       
    1. Verifies whether two fractions are equivalent
           
    1. Compares a fraction to 0, ½ or 1
             
    1. Orders fractions with the same denominator or where one denominator is a multiple of the other or with the same numerator
             
  1. Decimals up to thousandths
    1. Represents decimals in a variety of ways (using objects or drawings) and identifies equivalent representations
           
    1. Reads and writes numbers written in decimal notation
           
    1. Approximates a number written in decimal notation
           
    1. Composes and decomposes a number written in decimal notation and recognizes equivalent expressions
           
    1. Compares numbers written in decimal notation or arranges them in increasing or decreasing order
           
  1. Integers
    1. Represents integers in a variety of ways (using objects or drawings)
           
    1. Reads and writes integers
           
    1. Compares integers or arranges integers in increasing or decreasing order
           
  1. Expresses numbers in a variety of ways (fractional, decimal percentage notation)
           
  1. Represents, reads and writes numbers written in fractional or decimal notation
           
  1. Approximates, in various contexts, the numbers under study
    (e.g. estimates, rounds off, truncates)
           
  1. Distinguishes rational numbers from irrational numbers in the set of real numbers
    Note : Although students do not systematically study sets of numbers in Secondary Cycle One, they should still be encouraged to use the proper terms learned in elementary school (natural numbers, integers, decimals).
           
  1. Represents, in different types of notation, various subsets of real numbers (discrete or continuous): interval, list/roster, on a number line
    Note : In TS and S, set builder notation may be introduced as needed.
           
  1. Defines the concept absolute value in context (e.g. difference between two numbers, distance between two points)
    Note : In Cycle One and Secondary III, the concept of absolute value is introduced informally, using examples.
     
  1. Represents and writes
    1. the power of a natural number
           
    1. squares and square roots
         
    1. numbers in exponential notation (integral exponent)
         
    1. numbers in scientific notation
           
    1. cubes and cube roots
           
    1. numbers in exponential notation (fractional exponents)
           
    1. numbers using radicals or rational exponents
            CST
  TS
  S
    1. numbers in logarithmic notation using the equivalence loga x = n  an = x, if necessary
          CST
TS
  S
  1. Estimates the value of the power of an exponential expression with respect to its components: base (between 0 and 1, greater than 1), exponent (positive or negative, integral or fractional)
    Note : The same applies for a logarithmic expression in TS and S.
        CST
  TS
  S
  1. Estimates the order of magnitude of a real number in different contexts
     
  1. Estimates the order of magnitude of a real number using scientific notation
           
  1. Compares and arranges in order
    1. numbers written in fractional or decimal notation
           
    1. numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)
      Note : Scientific notation is introduced in Secondary III.
         
1.  Mathematical knowledge is constructed using prerequisites or by making connections between concepts and processes. The elements described in the tables will be reinvested and further developed as students progress through secondary school. When actions are included as part of other actions carried out in subsequent years, the shading in the table is not extended to cover all five years of secondary school.

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