Patterning and Algebra.
One of the central themes in mathematics is the study of patterns and relationships. This study requires students to recognize, describe, and generalize patterns and to build mathematical models to simulate the behaviour of real-world phenomena that exhibit observable patterns.
Young students identify patterns in shapes, designs, and movement, as well as in sets of numbers. They study both repeating patterns and growing and shrinking patterns and develop ways to extend them. Concrete materials and pictorial displays help students create patterns and recognize relationships. Through the observation of different representations of a pattern, students begin to identify some of the properties of the pattern.
In the junior grades, students use graphs, tables, and verbal descriptions to represent relationships that generate patterns.Through activities and investigations, students examine how patterns change, in order to develop an understanding of variables as changing quantities. In the intermediate grades, students represent patterns algebraically and use these representations to make predictions.
A second focus of this strand is on the concept of equality. Students look at different ways of using numbers to represent equal quantities.Variables are introduced as “unknowns”, and techniques for solving equations are developed. Problem solving provides students with opportunities to develop their ability to make generalizations and to deepen their understanding of the relationship between patterning and algebra.