Through their various mathematical activities in elementary school, students were introduced to prerequisites for algebra, such as finding unknown terms using properties of operations and relationships between these operations, developing an understanding of equality and equivalence relationships, following the order of operations and looking for patterns in different situations.
In Secondary Cycle One, students move from arithmetic thinking to algebraic thinking. They use and further develop their understanding of numbers, operations and proportionality. For example, in studying patterns, elementary school students learned to determine rules for constructing number sequences between terms, whereas in secondary school, students learn to establish the relationship between a term and its rank. Algebraic expressions are added to known registers (types) of representation to observe situations from different perspectives. Students refine their ability to switch from one register of representation to another in order to analyze situations in the register(s) of their choice. Thus, they learn to manipulate algebraic expressions with or without technological aids, and interpret tables of values and graphs. The use of technology makes it easier to explore and examine these relationships in greater depth and makes it possible to describe and explain them more fully. Lastly, students learn to search for mathematical models representing various situations.
In Secondary Cycle Two, students hone their ability to evoke a situation by drawing on several registers of representation and switching from one register to another, without any restrictions. For example, functions may be represented using graphs, tables or rules, and each of these representations conveys a specific point of view and is complementary or equivalent to other types of representation. Students learn to analyze and deal with situations that involve a set of algebraic concepts and processes. They establish dependency relationships between variables; model, compare and optimize situations, if necessary; and make informed decisions about these situations, depending on the case.
The following tables present the learning content associated with algebra. By basing themselves on the concepts and processes targeted, students develop the three competencies of the program, which in turn enable students to better integrate the mathematical concepts and processes presented.