Solving Equations

Strand: Patterns and Relations (Variables and Equations)
Outcome: 2

Step 1: Identify Outcomes to Address

Guiding Questions

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?

See Sequence of Outcomes from the Program of Studies

Strand: Patterns and Relations (Variables and Equations)

Grade 7

Grade 8

Grade 9

Specific Outcomes

Model and solve, concretely, pictorially and symbolically, problems that can be represented by one-step linear equations of the form x + a = b, where a and b are integers.

Model and solve, concretely, pictorially and symbolically, problems that can be represented by linear equations of the form:

ax + b = c

ax = b

= b, a ≠ 0

where a, b, and c are whole numbers.

Specific Outcomes

Model and solve problems concretely, pictorially and symbolically, using linear equations of the form:

ax = b
= b, a = 0
ax + b = c
+ b = c, a = 0
a(x + b) = c

where a, b, and c are integers.

Specific Outcomes
1.	Generalize a pattern arising from a problem-solving context, using a linear equation, and verify by substitution.
2.	Graph a linear relation, analyze the graph, and interpolate or extrapolate to solve problems.
3.	Model and solve problems, using linear equations of the form: ax = b = b, a = 0 ax + b = c + b =c, a = 0 ax = b + cx a(x + b) = cx + d a(bx + c) = d (ex + f) = b, x = 0 where a, b, c, d, e and f are rational numbers.

Big Ideas

Algebraic reasoning involves representing, generalizing and formalizing patterns and regularity in all aspects of mathematics. It is this type of reasoning that is at the heart of mathematics as a science of pattern and order (Van de Walle 2001, p. 384).
Patterns are key factors in understanding mathematical concepts (Burns 2000, p. 112).
Patterns can be created, recognized and extended. When this happens, making generalizations, seeing relationships and understanding the order and logic of mathematics will occur (Burns 2000, p. 112).
Functions evolve from the investigation of patterns and this allows us to investigate results beyond the information at hand (Burns 2000, p. 112).
Studying patterns, functions and algebra involves investigating numerical and geometrical patterns. These can be represented verbally and symbolically in several ways, including in tables, with symbols and graphically (Burns 2000, p. 112).
Variables are symbols that take the place of numbers or range of numbers
(Van de Walle 2001, p. 384).
Equations and inequalities are used to express relationships between two quantities
(Van de Walle 2001, p. 384).