| AR.1 | Solve linear equations, inequalities, and systems of linear equations. The student will recognize and use algebraic properties, concepts, procedures, and algorithms to solve equations, inequalities, and systems of linear equations, as well as make connections among graphical, tabular, and algebraic representations. | Linear Systems — Checking points in inequalities, Classifying inequality solutions, Counting solutions to a system, Eliminating by adding equations, Finding solutions by graphing, Graphing inequality solutions, Identifying inequality solutions, Interpret the solution of a system in context, Reading points on a graph, Scaling equations to eliminate, Set up a system from a scenario, Solving systems by graphing, Testing points in equations; Solving Equations — Choosing what to substitute, Finding inequality solutions, Finding unknown values, Finding value ranges, Multiplying to eliminate, Setting up elimination, Solving after combining, Solving by subtracting equations, Solving for boundary values, Solving grouped equations, Solving one-step equations, Solving systems by combining, Solving systems by substitution, Solving with substitution, Substituting known values; Linear Equations — Classifying equations by solutions, Combining fractional terms, Combining groups of expressions, Combining like terms to solve, Combining negatives to solve, Comparing deals with percentages, Dividing by negatives in inequalities, Finding missing values with negatives, Finding unknown values, Recognizing equations with many solutions, Recognizing equations with no solution, Solving compound inequalities, Solving equations by distributing, Solving equations by factoring, Solving equations with fractions, Solving equations with parentheses, Solving for negative answers, Solving multi-step inequalities, Solving multi-step negative inequalities, Solving one-step inequalities, Solving two-step equations, Solving with reciprocals, Solving with subtracted variables, Solving with variables on both sides, Working with negative coefficients |
| AR.2 | Evaluate linear functions. The student will evaluate a linear function for a particular value. | Linear Relationships — Evaluating linear equations, Reading linear patterns; Introduction to Functions — Following function rules, Identifying function rules, Matching input-output pairs |
| AR.3 | Solve quadratic and exponential relationship problems in context (e.g., exponential decay/growth, compound interest, and depreciation). The student will formulate a solution to a real-world situation based on the solution to a mathematical problem. | Quadratics — Finding the best possible value, Finding when objects arrive, Interpreting results in context, Predicting whether a target is reached, Understanding motion equations, Writing equations for motion, Writing equations for real situations; Exponential Functions — Graph and compare compound interest functions, Write a compound growth or decay expression |
| AR.4 | Identify and manipulate quadratic, polynomial, exponential, rational, and radical equations and expressions. The student will recognize and use algebraic properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions and equations. | Exponents and Radicals — Adding and subtracting like square roots, Applying the power rule for exponents, Applying the product rule for exponents, Applying the quotient rule for exponents, Combining exponent rules to simplify, Connecting fractional exponents to radicals, Distinguishing negation from negative bases, Dividing with prime factorizations, Evaluating cube roots and higher roots, Evaluating cubes, Evaluating general fractional exponents, Evaluating negative-base powers, Evaluating perfect squares, Evaluating powers of negative one, Evaluating square roots, Evaluating unit fraction exponents, Evaluating whole-number powers, Evaluating zero-exponent expressions, Identifying exponential bases, Multiplying and dividing in scientific notation, Multiplying square root expressions, Multiplying with prime factorizations, Rewriting with negative exponents, Simplifying and combining unlike radicals, Simplifying multi-base quotients, Simplifying negative exponents in denominators, Simplifying products with exponent zero, Simplifying with negative exponents, Writing expressions from patterns; Polynomials — Adding polynomials, Factoring out monomials, Factoring power differences, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials; Equations and Curves — Adding rational expressions, Rewriting equivalent equations, Simplifying by factoring, Simplifying fractional exponents, Simplifying rational expressions, Simplifying with exponent rules, Simplifying with exponent rules; Visual Algebra — Breaking patterns into parts, Identifying equivalent expressions, Seeing squares inside patterns, Writing equivalent expressions, Writing exponential expressions, Writing expressions as length times width; Exponential Functions — Build a decay function with a fractional base, Deduce an exponential function from two points, Evaluate an exponential expression, Express decay with a negative exponent, Find the base of an exponential function, Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern, Set the coefficient of an exponential function; Quadratics — Combining like terms, Combining signed terms, Combining terms with coefficients, Completing factors with negatives, Completing partial factorizations, Completing the square, Converting to vertex form, Determining signs in products, Expanding binomial products, Factoring signed quadratics fully, Factoring simple quadratics, Factoring with leading coefficients, Factoring with negative constants, Finding constant terms, Finding linear terms, Multiplying with area models, Multiplying with negative numbers, Recognizing perfect square patterns |
| AR.5 | Solve equations and evaluate functions (e.g., quadratic, polynomial, exponential, rational, and radical). The student will recognize and use algebraic properties, concepts, procedures, and algorithms to solve equations and evaluate functions, as well as make connections among graphical, tabular, and algebraic representations. | Polynomials — Applying parity properties, Connecting roots and factors, Deducing roots from symmetry, Evaluating polynomials, Evaluating power functions, Factoring biquadratic polynomials, Finding roots from graphs, Finding the y-intercept, Identifying transformed features, Matching equations to graphs, Matching graphs to factored form, Reading polynomial graphs, Solving by factoring; Exponential Functions — Build an exponential function from non-integer points, Build an exponential function from plotted points, Build an exponential function over negative domain, Compare exponential growth to linear growth, Compare exponential growth to quadratic growth, Compare two exponential functions, Evaluate an exponential at negative x-values, Evaluate an exponential at non-integer x-values; Quadratics — Checking solutions by substitution, Completing squares with fractions, Connecting intercepts to factors, Evaluating quadratic equations, Finding maximum and minimum values, Finding the axis of symmetry, Finding the vertex, Finding vertices using symmetry, Graphing by factoring, Graphing parabolas from vertex form, Isolating squared variables, Plotting points on parabolas, Reading solutions from graphs, Solving by completing the square, Solving equations by factoring, Solving shifted square equations, Solving with square roots, Using the quadratic formula, Writing equations from graphs, Writing vertex form equations; Equations and Curves — Evaluating equations at points, Evaluating squaring and square roots, Finding intersection points, Finding points on a curve, Identifying power function graphs, Identifying transformed graphs, Matching equations to graphs, Matching rational functions to graphs, Verifying points on curves; Logarithms — Find the exponent in an exponential equation; Introduction to Functions — Reading continuous function graphs |
