Algebra I (South Dakota Content Standards)

Number and Quantity (N)

• A1.N.RN.1 Explain how rational exponents come from extending integer exponent rules, giving a way to write radicals.
• A1.N.RN.2 Rewrite radical and rational-exponent expressions using exponent properties.
• A1.N.RN.3 Explain why rational sums and products stay rational and why mixing rational and irrational numbers gives an irrational.
• A1.N.Q.1 Use unit analysis to guide multi-step problems and choose units, scales and origins consistently (modeling).
• A1.N.Q.2 Define suitable quantities for descriptive modeling (modeling).
• A1.N.Q.3 Report quantities with accuracy that fits the limits of measurement (modeling).

Algebra (A)

• A1.A.SSE.1 Interpret expressions that stand for a quantity in context (shared with Algebra II; modeling).
  • A1.A.SSE.1a Identify an expression's terms, factors and coefficients.
  • A1.A.SSE.1b Read complicated expressions by treating some parts as a single quantity.
• A1.A.SSE.2 Spot and use an expression's structure to find ways to rewrite it (shared with Algebra II).
• A1.A.SSE.3 Pick and produce equivalent forms of an expression to show properties of the quantity (modeling).
  • A1.A.SSE.3a Factor a quadratic to show the zeros of its function.
  • A1.A.SSE.3b Complete the square to show a quadratic function's maximum or minimum.
  • A1.A.SSE.3c Use exponent properties to rewrite exponential function expressions.
• A1.A.APR.1 See polynomials as closed under addition, subtraction and multiplication, and carry out these operations.
• A1.A.CED.1 Write one-variable equations and inequalities from linear, quadratic and exponential situations and solve problems (modeling).
• A1.A.CED.2 Write equations in two or more variables for relationships and graph them with labeled axes and scales (shared; modeling).
• A1.A.CED.3 Express constraints with equations, inequalities or systems and judge which solutions are viable (shared; modeling).
• A1.A.CED.4 Solve a formula for a chosen quantity using equation-solving steps (shared; modeling).
• A1.A.REI.1 Justify each step of solving an equation from the previous one and argue for a solution method.
• A1.A.REI.3 Solve one-variable linear equations and inequalities, including ones with letter coefficients.
• A1.A.REI.4 Solve one-variable quadratic equations (shared with Algebra II).
  • A1.A.REI.4a Complete the square to rewrite a quadratic as (x − p)² = q with the same solutions.
  • A1.A.REI.4b Derive the quadratic formula by completing the square.
  • A1.A.REI.4c Solve quadratics by inspection, square roots, completing the square, the formula or factoring, as the form suggests.
• A1.A.REI.5 Understand the ideas behind the elimination method.
• A1.A.REI.6 Solve pairs of linear equations exactly and approximately, including by graphing.
• A1.A.REI.7 Solve a linear-quadratic system in two variables by algebra and by graphing.
• A1.A.REI.10 Understand that a two-variable equation's graph is the set of all its solutions.
• A1.A.REI.11 Explain why intersections of y = f(x) and y = g(x) solve f(x) = g(x) and approximate them, e.g. with technology (shared).
• A1.A.REI.12 Graph linear inequalities in two variables and solution sets of systems as overlapping half-planes.

Functions (F)

• A1.F.IF.1 Understand a function as assigning each domain element exactly one output, with f(x) as the output and its graph as y = f(x).
• A1.F.IF.2 Use function notation, evaluate functions and interpret notation in context.
• A1.F.IF.3 Recognize sequences as functions on a subset of the integers, sometimes defined recursively.
• A1.F.IF.4 Interpret key features of graphs and tables of linear, quadratic and exponential models and sketch graphs from descriptions (shared).
• A1.F.IF.5 Connect a function's domain to its graph and choose a sensible domain in context (shared; modeling).
• A1.F.IF.7 Graph parent functions and their transformations by hand and with technology, showing key features (shared; modeling).
  • A1.F.IF.7a Graph linear, exponential and quadratic functions showing intercepts, maxima and minima.
• A1.F.IF.8 Rewrite a function in equivalent forms to reveal different properties.
  • A1.F.IF.8a Use graphing, factoring and completing the square on quadratics to show zeros, extremes and symmetry in context.
  • A1.F.IF.8b Interpret expressions for exponential growth and decay.
• A1.F.IF.9 Compare two linear, quadratic or exponential functions given in different representations (shared).
• A1.F.BF.1 Write linear, quadratic or exponential functions for relationships between quantities (modeling).
  • A1.F.BF.1a Find an explicit expression, recursive process or calculation steps from a context.
  • A1.F.BF.1b Find an explicit expression from a graph.
  • A1.F.BF.1c Combine standard function types with arithmetic operations.
• A1.F.BF.2 Write arithmetic and geometric sequences recursively and explicitly and use them as models (modeling).
• A1.F.BF.3 Describe how adding or multiplying by k inside or outside f changes linear, exponential or quadratic graphs, and find k from graphs (shared).
• A1.F.LE.1 Tell apart situations suited to linear versus exponential models (modeling).
  • A1.F.LE.1a Prove linear functions change by equal differences and exponential ones by equal factors over equal intervals.
  • A1.F.LE.1b Spot situations where a quantity changes at a constant rate per unit.
  • A1.F.LE.1c Spot situations where a quantity grows or shrinks by a constant percent per unit.
• A1.F.LE.2 Build linear and exponential functions, including sequences, from graphs, descriptions or input-output pairs (modeling).
• A1.F.LE.3 Use graphs and tables to see exponential growth eventually overtaking linear or quadratic growth (modeling).
• A1.F.LE.5 Interpret the parameters of linear or exponential functions in context (modeling).

Statistics and Probability (S)

• A1.S.ID.1 Show data on a number line with dot plots, histograms and box plots.
• A1.S.ID.2 Compare center and spread of two or more data sets with statistics suited to their shape and context.
• A1.S.ID.3 Explain in context how data sets differ in shape, center and spread, allowing for outliers.
• A1.S.ID.5 Summarize two categorical variables in two-way tables, read joint, marginal and conditional relative frequencies and spot trends.
• A1.S.ID.6 Make a scatter plot of two numeric variables and describe how they relate.
  • A1.S.ID.6a Pick the best-fitting model (linear, quadratic or exponential) for data and solve problems with it.
  • A1.S.ID.6b Judge a fit informally and with technology by plotting and studying residuals.
  • A1.S.ID.6c Fit a line to a scatter plot that shows a linear trend.
• A1.S.ID.7 Interpret the slope and intercept of a linear model in context.
• A1.S.ID.8 Use technology to compute a line fit's correlation coefficient and explain it.
• A1.S.ID.9 Tell correlation apart from causation.