| 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. | Solving Equations — Chaining reasoning across equations, Checking value constraints, Choosing what to substitute, Distinguishing inequality types, Finding inequality solutions, Finding unknown values, Finding value ranges, Graphing inequalities, 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 Systems — Checking points in inequalities, Classifying inequality solutions, Counting solutions to a system, Eliminating by adding equations, Finding solutions by graphing, Graphing inequality constraints, Graphing inequality solutions, Identifying inequality solutions, Scaling equations to eliminate, Solving systems by graphing, Testing points in equations
Linear Equations — Classifying equations by solutions, Combining fractional terms, Combining groups of expressions, Combining like terms to solve, Combining negatives to solve, Dividing by negatives in inequalities, Finding missing values with negatives, Finding unknown values, Graphing compound inequalities, Identifying inequality solutions, 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. | Introduction to Functions — Following conditional rules, Following function rules, Matching input-output pairs, Plotting conditional functions, Plotting numeric functions
Real-World Algebra — Using a formula |
| 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. | Exponential Functions — Build a decay function with a fractional base, Evaluate an exponential expression, Graph and compare compound interest functions, Identify exponential decay from a dot pattern, Identify exponential growth from a dot pattern, Write a compound growth or decay expression, Write a function for a growth or decay scenario, Write a shifted exponential for a scenario approaching a limit
Logarithms — Find the exponent in an exponential equation
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 |
| 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 order of operations with exponents, 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, Estimating with scientific notation, Evaluating cube roots and higher roots, Evaluating cubes, Evaluating expressions inside radicals, Evaluating fraction bar expressions, Evaluating general fractional exponents, Evaluating multi-operation expressions, Evaluating negative-base powers, Evaluating nested grouping expressions, Evaluating perfect squares, Evaluating powers and roots with arithmetic, Evaluating powers of negative one, Evaluating square roots, Evaluating unit fraction exponents, Evaluating whole-number powers, Evaluating zero-exponent expressions, Expressing numbers in scientific notation, Identifying exponential bases, Locating consecutive powers on number lines, Locating cubes on number lines, Locating multiples of powers, Locating negative powers on number lines, 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 biquadratic polynomials, Factoring out monomials, Factoring power differences, Multiplying monomials, Multiplying polynomials, Subtracting polynomials, Working with multivariable polynomials
Equations and Curves — Adding rational expressions, Analyzing implicit equations, Completing hyperbola equations, 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, Describing exponential growth, Describing growth that speeds up, Finding counts when growth speeds up, Identifying equivalent expressions, Identifying types of growth, Seeing squares inside patterns, Writing equivalent expressions, Writing exponential expressions, Writing expressions as length times width
Exponential Functions — Classify a relationship as linear or exponential, Express decay with a negative exponent
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
Coordinate Geometry — Identifying equivalent area expressions |
| 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, Classifying even and odd powers, Comparing power functions, Connecting roots and factors, Deducing roots from symmetry, Determining sign between roots, Evaluating polynomials, Evaluating power functions, Finding roots from graphs, Finding the y-intercept, Identifying sign regions, Identifying transformed features, Matching equations to graphs, Matching graphs to factored form, Reading polynomial graphs, Recognizing polynomial symmetry, Solving by factoring, Using power function symmetry
Exponential Functions — Build a shifted exponential from its graph, 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, Deduce an exponential function from two points, Evaluate an exponential at negative x-values, Evaluate an exponential at non-integer x-values, Find the base of an exponential function, Set the coefficient of an exponential function
Equations and Curves — Building equations from intersections, Evaluating equations at points, Evaluating roots and inverse compositions, Evaluating square roots of squares, Evaluating squaring and square roots, Finding intersection points, Finding points on a curve, Finding vertical asymptotes, Identifying power function graphs, Identifying transformed graphs, Matching equations to graphs, Matching rational functions to graphs, Reading values from graphs, Solving systems and unions of curves, Verifying points on curves
Quadratics — Checking solutions by substitution, Classifying solution types, Completing squares with fractions, Connecting intercepts to factors, Determining number of solutions, 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 discriminant, Using the quadratic formula, Writing equations from graphs, Writing vertex form equations
Introduction to Functions — Reading continuous function graphs, Reading discontinuous function graphs |
