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ALGEBRA 1 MATHEMATICS STANDARDS List of Core Content #1: Performance Solving Problems Expectations Select and justify functions and equations to model and A solve problems. B C D E F A Solve problems that can be represented by linear functions, equations, and inequalities. A Solve problems that can be represented by a system of two linear equations or inequalities. A Solve problems that can be represented by quadratic functions and equations. (see also A2.1.C) Core Content #2: Numbers, Expressions, & Operations Know the relationship between real numbers and the number line, and compare and order real numbers with and without the number line. N Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables. A Interpret and use integer exponents, square/cube roots, apply the laws and properties of exponents to simplify and evaluate exponential expressions. A Determine whether approximations or exact values of real numbers are appropriate, depending on the context, and justify the selection. A Solve problems that can be represented by exponential functions and equations. N Use algebraic properties to factor and combine like terms in polynomials. A NA Add, subtract, multiply, and divide polynomials. Core Content #3: Characteristics & Behaviors of Functions Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. A Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. A Evaluate f(x) at a (i.e., f(a)) and solve for x in the equation f(x) = b. Core Content #4: Linear Functions, Equations, & Inequalities Write and solve linear equations and inequalities in one variable. A A Write and solve systems of two linear equations and inequalities in two variables. A Write and graph an equation for a line given the slope and the yintercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations. A Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines. A Describe how changes in the parameters of linear functions & functions containing an absolute value of a linear expression affect their graphs & the relationships they represent. A Core Content #5: Quadratic Functions and Equations Represent a quadratic function with a symbolic expression, a graph, in a table, and with a description, make connections among representations. A Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, interpret x-intercepts as solutions to quadratic equation. A Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers. Core Content #6: Data and Distributions Core Processes: Reasoning, Problem Solving, Communication Use and evaluate the accu- Sketch exponential function’s graph Analyze a problem situation racy of summary statistics in the form y = abn where n is an and represent it to describe and compare integer, describe effects that changes mathematically. data sets. in the parameters a and b have on the graph, & answer questions that arise in situations modeled by expoDSP nential functions. A CP Make valid inferences and Find and approximate solutions to Select and apply strategies draw conclusions based on exponential equations. to solve problems. data. A Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific A DSP terms in the sequence. AN Solve quadratic equations Find the equation of a Solve an equation involving several that have real roots by linear function that best fits variables by expressing one variable completing the square bivariate data that are in terms of the others. and by using the linearly related, interpret quadratic formula. the slope and y-intercept of the line, and use the equation to make predictions. A DSP A Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative. NA G H N Numbers, O Operations, A Algebra, GM Geometry Measurement, DSP Data/Statistics/Probability, CP Core Process DSP Describe how linear transformations affect the center and spread of univariate data. Core Content #7: Additional Key Content DSP CP Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem. CP Generalize a solution strategy for a single problem to a class of related problems, and apply a strategy for a class of related problems to solve specific problems. CP Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. CP Summarize mathematical ideas with precision and efficiency for a given audience and purpose. Synthesize information to draw conclusions, and evaluate the arguments and conclusions of others. Use inductive reasoning about algebra and properties of numbers to make conjectures, use deductive reasoning to prove or ALGEBRA 1 MATHEMATICS STANDARDS List of Core Content #1: Performance Solving Problems Expectations Core Content #2: Numbers, Expressions, & Operations Core Content #3: Core Content #4: Characteristics & Be- Linear Functions, Equations, haviors of Functions & Inequalities Core Content #5: Quadratic Functions and Equations N Numbers, O Operations, A Algebra, GM Geometry Measurement, DSP Data/Statistics/Probability, CP Core Process Core Content #6: Data and Distributions Core Content #7: Additional Key Content Core Processes: Reasoning, Problem Solving, Communication disprove conjectures.