C1.4 Create and describe patterns to illustrate relationships among rational numbers.
Skill: Creating and Describing Number Patterns that Include Rational Numbers
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: Ontario Curriculum, Mathematics Curriculum, Grades 1-8, 2020, Ontario Ministry of Education.
Skill: Making Generalizations from Conjectures
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 pictorial representations, and mathematical arguments. This process, sometimes informal, allows students to learn to formulate their generalizations more clearly.
Source: translated from Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, Modélisation et algèbre, p. 9-10.
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: translated from Guide d’enseignement efficace des mathématiques de la 4e à la 6e année, Modélisation et algèbre, p. 10.