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

 Approximates the result of an operation








 Using personal processes, mentally computes operations








 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 threedigit number by a twodigit number
 the quotient of a fourdigit number and a twodigit 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








 Fractions (using objects or diagrams)

 Generates a set of equivalent fractions








 Reduces a fraction to its simplest form








 Adds and subtracts fractions when the denominator of one fraction is a multiple of the other fraction








 Multiplies a natural number by a fraction and a fraction by a natural number








 Decimal numbers up to thousandths

 Approximates the result of an operation








 Mentally computes
 operations (addition, subtraction, multiplication, division by a natural number)
 multiplications by 10, 100, 1000








 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








 Properties of divisibility

 Determines the divisibility of a number by 2, 3, 4, 5, 6, 8, 9 and 10








 Uses, in different contexts, the properties of divisibility: 2, 3, 4, 5 and 10








 Approximates the result of an operation or sequence of operations








 Mentally computes the four operations, especially with numbers written in decimal notation, using equivalent ways of writing numbers and the properties of operations








 Computes, in writing, the four operations^{1} with numbers that are easy to work with (including large numbers), using equivalent ways of writing numbers and the properties of operations

 numbers written in decimal notation, using rules of signs








 positive numbers written in fractional notation, with or without the use of objects or diagrams








 numbers written in fractional notation








 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)








 Computes, using a calculator, operations and sequences of operations in accordance with the order of operations








 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








 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. 







 Calculates the power of a natural number








 Decomposes a natural number into prime factors








 Manipulates numerical expressions involving

 integral exponents (rational base) and fractional exponents
Note : When manipulating numerical expressions, students learn to deduce the properties of powers.








 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 
 logarithms


 definition and change of base







CST 


TS 


S 
 properties







CST 


TS 


S 
 absolute values







CST 


TS 


S 