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
Operations involving numbers
Number sense is a concept that is developed in early childhood and is refined as students progress through school. In elementary school, it is developed first by looking at natural numbers and then enriched by studying rational numbers.^{1}
At the outset, counting rhymes, counting, constructions, representations, ordering and establishing relationships among numbers are essential in order for students to understand number systems. Using appropriate manipulatives, students first learn about counting groups (grouping) and gradually replace this concept with place value. However, care must be taken not to progress too quickly from one concept to another, as this could affect the way students understand operations or learn new numbers.
It is in elementary school that students acquire the basic tools for understanding and using fractions. Students must first understand concepts (meaning) before they can understand calculation processes (operations). This can be achieved by allowing students to systematically use concrete materials and pictorial representations when dealing with situations involving fractions.
The table below presents the learning content associated with understanding and writing numbers. The concepts and processes targeted will provide students with increasingly complex tools that will help them develop and use all three mathematics competencies.
Understanding and writing 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  

1000  100 000  1 000 000  




















































Grouping, digit, number, unit, tens place, hundreds place Natural number, even number, odd number Is equal to, is bigger than (is greater than); is smaller than (is less than) Increasing order, decreasing order Number line Symbols 0 to 9, <, >, =, numbers written using digits 

Base ten, position, place value, thousand, thousands place, ten thousands Is not equal to; is greater than; is less than Square number, composite number, prime number Symbols ≠, numbers written using digits 

Hundred thousands, million Exponent, power, squared, cubed Parenthesis Symbols ( ), numbers written using digits, exponential notation 


1  2  3  4  5  6  


























Fraction, half, one third, one quarter 

Numerator, denominator Whole, equivalent part, equivalent fraction Symbol Fractional notation 


1  2  3  4  5  6  
hundredths 
thousandths 































Decimal, tenth, hundredth Symbol Decimal notation 

Thousandth Symbol Decimal notation 


1  2  3  4  5  6  










Integer Negative number, positive number Symbols Integer notation, +/– calculator key 
Meaning of operations involving numbers
Operations involving numbers
1.  The set of rational numbers includes the set of integers, which contains the set of natural numbers. 