Expressions and Equations

Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents.

Write, read, and evaluate algebraic expressions. • Write expressions that record operations with numbers and with letters standing for numbers. • Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. • Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems.

Apply the properties of operations to generate equivalent expressions without exponents.

Identify when two expressions are equivalent and justify with mathematical reasoning.

Use substitution to determine whether a given number in a specified set makes an equation true.

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem.

Solve real-world and mathematical problems by writing and solving equations of the form: • 𝑥 + 𝑝 = 𝑞 in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers; and, • 𝑝 ∙ 𝑥 = 𝑞 for cases in which 𝑝, 𝑞 and 𝑥 are all nonnegative rational numbers.

Reason about inequalities by: • Using substitution to determine whether a given number in a specified set makes an inequality true. • Writing an inequality of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 to represent a constraint or condition in a real-world or mathematical problem. • Recognizing that inequalities of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 have infinitely many solutions. • Representing solutions of inequalities on number line diagrams.

Represent and analyze quantitative relationships by: • Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. • Analyze the relationship between quantities in different representations (context, equations, tables, and graphs).