C1.4 Create and describe patterns to illustrate relationships among integers.
Skill: Creating and Describing Number Patterns that Include Integers
When students understand the mathematical operations between numbers, they can then determine the next terms in both linear and non-linear number patterns.
Skill: Representing Relationships Between Numbers in a Pattern
Patterns can be used to demonstrate relationships within and among number properties, such as expressing numbers in exponential notation. Using patterns is a useful strategy in developing understanding of mathematical concepts, such as knowing what sign to use when two integers are added or subtracted.
Source: The Ontario Curriculum. Mathematics, Grades 1-8 Ontario Ministry of Education, 2020.
Skill: Making Generalizations from Conjectures
Generalization is at the heart of mathematical activity. In Algebra, it allows students to develop their algebraic thinking.
To arrive at a generalization, students observe and analyze situations and then propose conjectures. When proposing a conjecture, they must be able to express their reasoning in their own words. Students must then check whether their conjecture is valid in other situations. They support their conjectures with concrete and semi-concrete representations and mathematical arguments. This process, sometimes informal, allows students to learn to formulate their generalizations more clearly.
Knowledge: Conjecture
A conjecture is the expression of an idea that is perceived to be true in any similar situation. The student must be able to propose a conjecture, verify it in order to formulate a generalization.
Source: L'@telier - Online Educational Resources (atelier.on.ca).
Knowledge: Integers
Integers are numbers that have no decimal part or whose decimal part is zero. Integers can be positive or negative. Also, they are considered rational numbers, since any integer can be expressed as a fraction.
Examples
\(2.0 = \frac{2}{1}\)
\(-7 = - \frac{7}{1}\)