The Common Core in South Dakota

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Skills available for South Dakota high school math standards

Standards are in black and IXL math skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practice that skill.

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South Dakota Content Standards: 4th Year Course South Dakota Content Standards: 4th Year Course
South Dakota Content Standards: Algebra I South Dakota Content Standards: Algebra I
South Dakota Content Standards: Algebra II South Dakota Content Standards: Algebra II
South Dakota Content Standards: Geometry South Dakota Content Standards: Geometry
South Dakota Content Standards: Mathematics I South Dakota Content Standards: Mathematics I
South Dakota Content Standards: Mathematics II South Dakota Content Standards: Mathematics II
South Dakota Content Standards: Mathematics III South Dakota Content Standards: Mathematics III
Common Core State Standards: Algebra 1 Common Core State Standards: Algebra 1
Common Core State Standards: Algebra 2 Common Core State Standards: Algebra 2
Common Core State Standards: All High School Pathways Common Core State Standards: All High School Pathways
Common Core State Standards: Fourth Courses Common Core State Standards: Fourth Courses
Common Core State Standards: Geometry Common Core State Standards: Geometry
Common Core State Standards: Mathematical Practices Common Core State Standards: Mathematical Practices
Common Core State Standards: Mathematics I Common Core State Standards: Mathematics I
Common Core State Standards: Mathematics II Common Core State Standards: Mathematics II
Common Core State Standards: Mathematics III Common Core State Standards: Mathematics III
Common Core State Standards: Precalculus Common Core State Standards: Precalculus

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S Statistics and Probability

S.ID Interpreting Categorical and Quantitative Data
- Summarize, represent and interpret data on a single count or measurement variable.
  - S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
  - S.ID.2 Use statistics appropriate to the shape and context of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  - S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
    - Box plots (A1-N.9)
    - Identify an outlier and describe the effect of removing it (A1-MM.5)
  - Checkpoint opportunity
    - Checkpoint: Line plots, histograms, and box plots (A1-N.10)
    - Checkpoint: Compare data sets (A1-MM.17)
- Summarize, represent and interpret data on two categorical and quantitative variables.
  - S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
    - Find probabilities using two-way frequency tables (A1-LL.3)
    - Find conditional probabilities using two-way frequency tables (A1-LL.4)
  - S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
    - S.ID.6.a Determine the function (linear, quadratic, or exponential model) that best fits a set of data and use that function fitted to data to solve problems within context.
    - S.ID.6.b Informally and using technology assess the fit of a function by plotting and analyzing residuals.
      - Interpret a scatter plot (A1-MM.8)
    - S.ID.6.c Fit a linear function for a scatter plot that suggests a linear association.
      - Write equations for lines of best fit (A1-MM.12)
  - Checkpoint opportunity
    - Checkpoint: Two-way frequency tables (A1-LL.11)
- Interpret linear models.
  - S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
    - Interpret regression lines (A1-MM.14)
    - Analyze a regression line of a data set (A1-MM.15)
  - S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
    - Match correlation coefficients to scatter plots (A1-MM.10)
    - Calculate correlation coefficients (A1-MM.11)
  - S.ID.9 Distinguish between correlation and causation.
    - Correlation and causation (A1-MM.16)
  - Checkpoint opportunity
    - Checkpoint: Linear modeling (A1-MM.18)

The Common Core in South Dakota

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N Number and Quantity

N.RN The Real Number System

Extend the properties of exponents to rational exponents.

N.RN.1 Explain how the definition of rational exponents follows from extending the properties of integer exponents, allowing for a notation for radicals in terms of rational exponents.

N.RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Use properties of rational and irrational numbers.

N.RN.3 Explain why the sum or product of two rational numbers is rational; the sum of a rational and an irrational number is irrational; and the product of a nonzero rational and an irrational number is irrational.

Checkpoint opportunity

N.Q Quantities

Reason quantitatively and use units to solve problems.

N.Q.1 Use unit analysis to understand and guide the process of solving multi-step problems; choose and interpret units consistently in formulas; and choose and interpret the scale and origin in graphs and data displays.

N.Q.2 Define appropriate quantities for the purpose of descriptive modeling.

N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Checkpoint opportunity

A Algebra

A.SSE Seeing Structure in Expression

Interpret the structure of expressions.

A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

A.SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.

A.SSE.1.b Interpret complicated expressions by viewing one or more of their parts as a single entity in context.

A.SSE.2 Recognize and use the structure of an expression to identify ways to rewrite it.

Write expressions in equivalent forms to solve problems.

A.SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A.SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.

A.SSE.3.b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

A.SSE.3.c Use the properties of exponents to write equivalent expressions for exponential functions.

Checkpoint opportunity

A.APR Arithmetic with Polynomials and Rational Expressions

Perform arithmetic operations on polynomials.

A.APR.1 Understand that polynomials form a system closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Checkpoint opportunity

A.CED Creating Equations

Create equations that describe numbers or relationships.

A.CED.1 Create equations and inequalities in one variable arising from situations in which linear, quadratic, and exponential functions are appropriate and use them to solve problems.

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

A.CED.4 Rewrite formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Checkpoint opportunity

A.REI Reasoning With Equations and Inequalities

Understand solving equations as a process of reasoning.

A.REI.1 Explain each step in solving an equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

Solve equations and inequalities in one variable.

A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A.REI.4 Solve quadratic equations in one variable.

A.REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)² = q that has the same solutions.

A.REI.4.b Derive the quadratic formula from completing the square.

A.REI.4.c Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation.

Checkpoint opportunity

Solve systems of equations.

A.REI.5 Understand the principles of the elimination method.

A.REI.6 Solve systems of linear equations exactly and approximately by graphing, focusing on pairs of linear equations in two variables.

A.REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Represent and solve equations and inequalities graphically.

A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A.REI.12 Graph a linear inequality (strict or inclusive) in two variables; graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Checkpoint opportunity

F Functions

F.IF Interpreting Functions

Understand the concept of a function and use functions notation.

F.IF.1 Understand that a function maps each element of the domain to exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph off is the graph of the equation y = f(x).

F.IF.2 Use function notation, evaluate functions, and interpret statements that use function notation in terms of a context.

F.IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

Interpret functions that arise in applications in terms of the context.

F.IF.5 Relate the domain of a function to its graph and find an appropriate domain in the context of the problem.

F.IF.6 Calculate and interpret the average rate of change of a function, both symbolically and from a table over a specified interval. Estimate the rate of change from a graph.

Checkpoint opportunity

Analyze functions using different representations.

F.IF.7 Graph parent functions and their transformations expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F.IF.7.a Graph linear, exponential, and quadratic functions and show intercepts, maxima, and minima.

F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F.IF.8.a Use the process of graphing, factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F.IF.8.b Interpret expressions for exponential growth and decay.

F.IF.9 Compare properties of two functions (linear, quadratic and exponential) each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Checkpoint opportunity

F.BF Building Functions

Build a function that models a relationship between two quantities.

F.BF.1 Write a function (linear, quadratic, and exponential) that describes a relationship between two quantities.