The Distributive Property and Factoring Monomials

Read, write, and analyze algebraic expressions using precise vocabulary including terms, variables, coefficients, and operations.

Evaluate one-step and multi-step algebraic expressions for specific whole number, decimal, and fractional values using the order of operations.

Apply commutative, associative, identity, and inverse properties to identify and combine like terms and generate equivalent algebraic expressions.

Expand algebraic expressions using the distributive property and factor out common numerical and monomial factors.

Understand equations as balanced mathematical statements, test candidate solutions from replacement sets, and represent solutions on number lines.

Solve one-step equations of the forms x + p = q and x - p = q involving nonnegative rational numbers using inverse operations and balance strategies.

Solve one-step equations of the forms px = q and x/p = q involving nonnegative rational numbers using inverse operations and multiplicative inverses.

Write, interpret, solve, and graph one-variable inequalities representing real-world constraints on number lines.

Identify independent and dependent variables in relationships, distinguish cause from effect, and represent relationships with algebraic equations.

Translate dynamically between verbal rules, input-output tables, algebraic equations (y = kx and y = x + b), and Cartesian graphs.

Generate and analyze arithmetic sequences and geometric visual patterns, express general rules with algebraic notation, and model rules using flowcharts.