Patterns in Linear Equations

Strand: Patterns and Relations (Patterns)
Outcomes: 1 and 2

Step 1: Identify Outcomes to Address

What do I want my students to learn?
What can my students currently understand and do?
What do I want my students to understand and be able to do, based on the Big Ideas and specific outcomes in the program of studies?

Strand: Patterns and Relations (Patterns)

Grade 8

Grade 9

Grade 10

Specific Outcome
1.	Graph and analyze two-variable linear relations. [C, ME, PS, R, T, V] [ICT: P2–3.3]

Specific Outcomes
1.	Generalize a pattern arising from a problem-solving context, using a linear equation, and verify by substitution. [C, CN, PS, R, V]
2.	Graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems. [C, CN, PS, R, T, V] [ICT: C7–3.1 P2–3.3]

Specific Outcomes
1.	Interpret and explain the relationships among data, graphs and situations. [C, CN, R, T, V] [ICT: C6–4.3, C7–4.2]
4.	Describe and represent linear relations. using words ordered pairs table of values graphs equations. [C, CN, R, V]
5.	Determine the characteristics of the graphs of linear relations, including the: intercepts slope domain range. [CN, PS, R, V]

Patterns represent identified regularities. Types of patterns include complex repeating patterns, increasing and decreasing patterns, and recursive patterns (Small 2009, p.3).
A variable is a symbol that can stand for any one of a set of numbers or other objects and can be represented by boxes or letters (Van de Walle and Lovin 2006, p. 274).
Patterns are key factors in understanding mathematical concepts. The ability to create, recognize and extend patterns is essential for making generalizations, seeing relationships and understanding the order and logic of mathematics (Burns 2000, p. 112).
Patterns can be recognized, extended and generalized into symbols, words, diagrams, number lines, charts and graphs (Van de Walle and Lovin 2006, p. 265).