Algebra
Program of Studies
Algebra: Equations express relationships between quantities.
How can expressions enhance communication of number?
Students interpret numerical and algebraic expressions.
Knowledge
Numerical expressions with multiple operations may include parentheses to group numbers and operations. The conventional order of operations includes performing operations in parentheses before other operations.
Expressions that include variables are called algebraic expressions. A variable can be interpreted as a specific unknown value and is represented symbolically with a letter. Products with variables are expressed without the multiplication sign. Quotients with variables are expressed using fraction notation. An algebraic term is the product of a number, called a coefficient, and a variable. A constant term is a number. A variable can be replaced by a given number in order to evaluate an expression. The process of applying inverse operations can be used to solve an equation. The value of the variable obtained by solving an equation is the solution. |
Understanding
Numerical expressions represent a quantity of known value. Parentheses change the order of operations in a numerical expression.
Algebraic expressions use variables to represent quantities of unknown value. Algebraic expressions may be composed of one algebraic term or the sum of algebraic and constant terms. Equality is preserved by applying inverse operations to algebraic expressions on each side of an equation. The expressions on each side of an equation will be equal when evaluated using the correct solution. |
Skills and Procedures
Evaluate numerical expressions involving addition or subtraction in parentheses according to the order of operations.
Relate repeated addition of a variable to the product of a number and a variable. Express the product of a number and a variable using a coefficient. Express the quotient of a variable and a number as a fraction. Recognize a product with a variable, a quotient with a variable, or a number as a single term. Write an algebraic expression involving one or two terms to describe an unknown value. Evaluate an algebraic expression by substituting a given number for the variable. Write equations involving one or two operations to represent a situation. Investigate order of operations when performing inverse operations on both sides of an equation. Apply inverse operations to solve an equation, limited to equations with one or two operations. Verify the solution to an equation by evaluating expressions on each side of the equation. Solve problems using equations, limited to equations with one or two operations. |