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# Solving Equations

Strand: Patterns and Relations (Variables and Equations)
Outcomes: 5, 6

## 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)  Specific Outcomes 4. Solve one-step addition and subtraction equations involving a symbol to represent an unknown number.

 Specific Outcomes 5. Express a given problem as an equation in which a symbol is used to represent an unknown number. 6. Solve one-step equations involving a symbol to represent an unknown number.

 Specific Outcomes 2. Express a given problem as an equation in which a letter variable is used to represent an unknown number (limited to whole numbers). 3. Solve problems involving single-variable, one-step equations with whole number coefficients and whole number solutions.

### Big Ideas

Mathematics is often referred to as the science of patterns. Patterns permeate every mathematical concept and are found in the everyday contexts. The various representations of patterns, including symbols and variables, provide valuable tools in making generalizations of mathematical relationships. Some characteristics of patterns include the following:

• There are different types of patterns that can be modelled in a variety of ways.
• Patterns using concrete and pictorial representations of a problem can be translated into patterns using numbers and symbols in equations.
• Patterns are used to generalize relationships; e.g., numbers may be added or multiplied in any order without changing the sum or product.
• Equality is used to express relationships. The symbols used on either side of the equal sign represent a quantity. The equal sign is "a symbol of equivalence and balance" (NCTM 2000, p. 39).
• Patterns using symbols and variables provide a means of describing change mathematically; e.g., 5 more than, 3 less than.
• Variables and equations are used to mathematically model everyday problems that describe quantitative relationships.

Variables and symbols stand for any one of a set of numbers or objects and have multiple meanings. They are used as:

• representations of specific unknown values; e.g., 3 + = 15
• representations of quantities that vary or change; e.g.,  + = 15
• placeholders in a generalized expression or formula; e.g., = 10 , where   represents the number of centimetres and represents the number of metres.

• If different variables or symbols are used in the same equation, then there are many different possible solutions, one of which may be the same number replacing each variable or symbol; e.g., =  20, some solutions include 0 + 20, 10 + 10, ½ + 19 ½, and 25 – 5. 