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 
 Natural numbers less than 1 000 000

 Reads and writes any natural number








 Represents natural numbers in different ways








 Composes and decomposes a natural number in a variety of ways and identifies equivalent expressions








 Approximates a natural number








 Compares natural numbers or arranges natural numbers in increasing or decreasing order








 Classifies natural numbers in various ways, based on their properties
(e.g. even numbers, composite numbers)








 Fractions

 Represents a fraction in a variety of ways (using objects or drawings)








 Identifies the different meanings of fractions: part of a whole, division, ratio, operator, measurement








 Verifies whether two fractions are equivalent








 Compares a fraction to 0, ½ or 1








 Orders fractions with the same denominator or where one denominator is a multiple of the other or with the same numerator








 Decimals up to thousandths

 Represents decimals in a variety of ways (using objects or drawings) and identifies equivalent representations








 Reads and writes numbers written in decimal notation








 Approximates a number written in decimal notation








 Composes and decomposes a number written in decimal notation and recognizes equivalent expressions








 Compares numbers written in decimal notation or arranges them in increasing or decreasing order








 Integers

 Represents integers in a variety of ways (using objects or drawings)








 Reads and writes integers








 Compares integers or arranges integers in increasing or decreasing order








 Expresses numbers in a variety of ways (fractional, decimal percentage notation)








 Represents, reads and writes numbers written in fractional or decimal notation








 Approximates, in various contexts, the numbers under study
(e.g. estimates, rounds off, truncates)








 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).








 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.








 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.








 Represents and writes

 the power of a natural number








 squares and square roots








 numbers in exponential notation (integral exponent)








 numbers in scientific notation








 cubes and cube roots








 numbers in exponential notation (fractional exponents)








 numbers using radicals or rational exponents







CST 


TS 


S 
 numbers in logarithmic notation using the equivalence log_{a} x = n
a^{n} = x, if necessary







CST 


TS 


S 
 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 
 Estimates the order of magnitude of a real number in different contexts








 Estimates the order of magnitude of a real number using scientific notation








 Compares and arranges in order

 numbers written in fractional or decimal notation








 numbers expressed in different ways (fractional, decimal, exponential [integral exponent], percentage, square root, scientific notation)
Note : Scientific notation is introduced in Secondary III.







