Algebra I (Iowa Core)

Number and Quantity (N)

• A1.N-RN.B.3 Explain why sums and products of rational numbers are rational and why rational plus irrational, or nonzero rational times irrational, is irrational.
• A1.N-Q.A.1 Use units to understand and solve multi-step problems, using units consistently in formulas and choosing scales and origins for graphs.
• A1.N-Q.A.2 Define suitable quantities for descriptive modeling.
• A1.N-Q.A.3 Choose a level of accuracy that suits the limits of measurement when reporting quantities.

Algebra (A)

• A1.A-SSE.A.1a Interpret an expression in context by naming its parts, such as terms, factors and coefficients.
• A1.A-SSE.A.2 Use the structure of an expression to find ways to rewrite it, e.g. spotting a difference of squares.
• A1.A-SSE.B.3 Choose an equivalent form of an expression or equation to reveal properties, e.g. factoring a quadratic to show its zeros.
• A1.A-CED.A.1 Write one-variable equations and inequalities, including from linear, quadratic, simple rational and exponential functions, and solve problems.
• A1.A-CED.A.2 Write equations in two or more variables for relationships and graph them on labeled, scaled axes.
• A1.A-CED.A.3 Represent constraints with equations, inequalities or systems and judge whether solutions are viable in a model.
• A1.A-CED.A.4 Solve a formula for the quantity you need, e.g. Ohm's law for resistance.
• A1.A-REI.A.1 Justify every step of solving an equation from the one before and defend the solution method.
• A1.A-REI.A.2 Solve one-variable rational and radical equations and show how extraneous solutions can arise.
• A1.A-REI.B.3 Solve one-variable linear equations and inequalities, including with letter coefficients.
• A1.A-REI.B.4 Solve one-variable quadratic equations (a: completing the square; b: inspection, roots, the formula, factoring).
• A1.A-REI.C.5 Explain how elimination leads to the solution of a system of equations.
• A1.A-REI.C.6 Solve systems of linear equations exactly and approximately, e.g. with graphs.
• A1.A-REI.C.7 Solve a simple system of a linear and a quadratic equation algebraically and graphically.
• A1.A-REI.D.10 Understand the graph of a two-variable equation as the set of all its solutions, often a curve or line.
• A1.A-REI.D.11 Explain why solutions of a system are where the graphs intersect and find them approximately, e.g. with technology.
• A1.A-REI.D.12 Graph and interpret solutions of a two-variable linear inequality as a half-plane and of a system of linear inequalities.

Functions (F)

• A1.F-IF.A.1 Understand a function as assigning each element of the domain exactly one element of the range, and the meaning of f(x).
• A1.F-IF.A.2 Use function notation, evaluate functions and interpret notation in context.
• A1.F-IF.A.3 Recognize sequences as functions, sometimes defined recursively, with integer domains.
• A1.F-IF.B.4 Interpret key features of graphs and tables of a model in context and sketch graphs from a description.
• A1.F-IF.B.5 Relate a function's domain to its graph and to the relationship it describes.
• A1.F-IF.B.6 Find and interpret a nonlinear function's average rate of change over an interval and estimate it from a graph.
• A1.F-IF.C.7 Graph functions and show key features, by hand in simple cases and with technology otherwise (parts for linear, quadratic and other types).
• A1.F-IF.C.8 Write a function in equivalent forms to reveal properties, e.g. factoring or completing the square for a quadratic.
• A1.F-BF.A.1a Write a function for a relationship between two quantities as an explicit expression, recursive process or calculation steps.
• A1.F-BF.A.2 Write arithmetic and geometric sequences recursively and explicitly, use them as models and convert between forms.
• A1.F-BF.B.3 Identify how f(x) + k, k·f(x), f(kx) and f(x + k) change linear and quadratic graphs.
• A1.F-LE.A.1 Tell apart situations modeled by linear and by exponential functions (parts: equal differences vs equal factors, constant rates).
• A1.F-LE.A.2 Build linear and exponential functions, including sequences, from a graph, description or two input–output pairs.
• A1.F-LE.A.3 Use graphs and tables to show exponential growth eventually exceeds linear, quadratic or polynomial growth.
• A1.F-LE.B.5 Interpret the parameters of a linear or exponential function in context.

Statistics and Probability (S)

• A1.S-ID.A.1 Display data in dot plots, histograms and box plots when modeling.
• A1.S-ID.A.2 Use statistics suited to the shape of the data to compare center and spread of two or more data sets.
• A1.S-ID.A.3 Explain in context how data sets differ in shape, center and spread, allowing for outliers.
• A1.S-ID.B.5 Summarize two categorical variables in two-way frequency tables and interpret joint, marginal and conditional relative frequencies.
• A1.S-ID.B.6 Show two quantitative variables on a scatter plot, describe the relationship and fit functions to the data.
• A1.S-ID.C.7 Interpret the slope and intercept of a linear model in context.
• A1.S-ID.C.8 Compute with technology and interpret the correlation coefficient of a linear fit.
• A1.S-ID.C.9 Tell correlation apart from causation.