Algebra

Interpret expressions that represent a quantity in terms of its context.

Identify and interpret parts of a linear, exponential, or quadratic expression, including terms, factors, coefficients, and exponents.

Interpret a linear, exponential, or quadratic expression made of multiple parts as a combination of entities to give meaning to an expression.

Write an equivalent form of a quadratic expression 𝑎𝑥 2 + 𝑏𝑥 + 𝑐, where a is an integer, by factoring to reveal the solutions of the equation or the zeros of the function the expression defines.

Build an understanding that operations with polynomials are comparable to operations with integers by adding and subtracting quadratic expressions and by adding, subtracting, and multiplying linear expressions.

Understand the relationships among the factors of a quadratic expression, the solutions of a quadratic equation, and the zeros of a quadratic function.

Create equations and inequalities in one variable that represent linear, exponential, and quadratic relationships and use them to solve problems.

Create and graph equations in two variables to represent linear, exponential, and quadratic relationships between quantities.

Create systems of linear equations and inequalities to model situations in context.

Solve for a quantity of interest in formulas used in science and mathematics using the same reasoning as in solving equations.

Justify a chosen solution method and each step of the solving process for linear and quadratic equations using mathematical reasoning.

Solve linear equations and inequalities in one variable.

Solve for the real solutions of quadratic equations in one variable by taking square roots and factoring.

Explain why replacing one equation in a system of linear equations by the sum of that equation and a multiple of the other produces a system with the same solutions.

Use tables, graphs, or algebraic methods (substitution and elimination) to find approximate or exact solutions to systems of linear equations and interpret solutions in terms of a context.

Understand that the graph of a two variable equation represents the set of all solutions to the equation.

Build an understanding of why the x-coordinates of the points where the graphs of two linear, exponential, and/or quadratic equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥) and approximate solutions using graphing technology or successive approximations with a table of values.

Represent the solutions of a linear inequality or a system of linear inequalities graphically as a region of the plane.