Learners will graph and solve absolute value equations and inequalities, and represent piecewise-defined functions.

Solve absolute value equations and graph and analyze absolute value functions.

Add and subtract polynomials of degree one and degree two using multiple methods and representations, and apply these operations to real-world and abstract contexts.

Explain and use auxiliary views, revolutions, intersections, and engineered drawings in technical contexts

Solve complex linear inequalities including those requiring distribution, variables on both sides, and compound inequalities, and apply these skills to real-world contexts.

Convert specialized units such as temperature and compound units, read technical measurement tools, interpret tolerances, and solve multi-step measurement problems in manufacturing.

Compare multiple linear graphs, use graphing technology, select appropriate scales, and interpret key features in real-world contexts.

Analyze relationships between variables from graphs, interpret average rate of change in real-world contexts, and create real-world problems from linear equations.

Classify linear equations by their number of solutions (one, none, or infinitely many), verify solutions algebraically and graphically, and justify the algebraic properties used in solving.

Model real-world situations with quadratic functions and write quadratic equations from given roots or graph points.

Estimate solutions graphically and write systems of two linear equations from verbal descriptions, tables, and graphs to solve real-world problems.

Apply systems of linear equations to model and solve real-world problems including cost, mixture, and distance scenarios, and solve systems of linear inequalities graphically and with technology.

Translate real-world problems into quadratic equations, solve them, and use technology to fit quadratic models to data and make predictions.

Learners will model real-world scenarios—projectile motion, area optimization, and data fitting—with quadratic functions, and use them to solve practical problems.

Translate real-world scenarios into linear equations and apply structured problem-solving models to solve and justify solutions using precise mathematical language.

Apply exponential functions to model and solve real-world problems, and compare them with linear and quadratic models.

Apply real number concepts to estimate values, solve real-world problems, and justify mathematical reasoning.