The Common Core in Wyoming

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Skills available for Wyoming high school math standards

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Wyoming Content and Performance Standards: Algebra 1 Wyoming Content and Performance Standards: Algebra 1
Wyoming Content and Performance Standards: Algebra 2 Wyoming Content and Performance Standards: Algebra 2
Wyoming Content and Performance Standards: Geometry Wyoming Content and Performance Standards: Geometry
Wyoming Content and Performance Standards: Mathematics 1 Wyoming Content and Performance Standards: Mathematics 1
Wyoming Content and Performance Standards: Mathematics 2 Wyoming Content and Performance Standards: Mathematics 2
Wyoming Content and Performance Standards: Mathematics 3 Wyoming Content and Performance Standards: Mathematics 3
Wyoming Content and Performance Standards: Precalculus Wyoming Content and Performance Standards: Precalculus
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
- S.ID.A Summarize, represent, and interpret data on a single count or measurement variable.
  - S.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots) by hand or using technology.
  - S.ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  - S.ID.A.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)
- S.ID.B Summarize, represent, and interpret data on two categorical and quantitative variables.
  - S.ID.B.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 in the data, and use inferential statistical techniques to show association.
    - Find probabilities using two-way frequency tables (A1-LL.3)
    - Find conditional probabilities using two-way frequency tables (A1-LL.4)
  - S.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
    - S.ID.B.6A Use a function to describe data trends to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
    - S.ID.B.6C Using technology, fit a least squares linear regression function for a scatter plot that suggests a linear association.
      - Write equations for lines of best fit (A1-MM.12)
    - S.ID.B.6B Informally assess the fit of a function by plotting and analyzing residuals.
      - Interpret a scatter plot (A1-MM.8)
  - Checkpoint opportunity
    - Checkpoint: Two-way frequency tables (A1-LL.11)
- S.ID.C Interpret linear models.
  - S.ID.C.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.C.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.C.9 Distinguish between correlation and causation.
    - Correlation and causation (A1-MM.16)
  - Checkpoint opportunity
    - Checkpoint: Linear modeling (A1-MM.18)

The Common Core in Wyoming

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N Number and Quantity

N.RN The Real Number System

N.RN.A Extend the properties of exponents to rational exponents.

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

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

N.RN.B Use properties of rational and irrational numbers.

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

Checkpoint opportunity

N.Q Quantities

N.Q.C Reason quantitatively and use units to solve problems.

N.Q.C.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

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

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

Checkpoint opportunity

A Algebra

A.SSE Seeing Structure in Expressions

A.SSE.A Interpret the structure of expressions.

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

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

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

A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

A.SSE.B Write expressions in equivalent forms to solve problems.

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

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

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

A.SSE.B.3C Use the properties of exponents to transform expressions for exponential functions. Apply the concepts of decimal and scientific notation to solve real-world and mathematical problems.

A.SSE.B.3C.i Multiply and divide numbers expressed in both decimal and scientific notation.

A.SSE.B.3C.ii Add and subtract numbers in scientific notation with the same integer exponent.

A.SSE.B.4 Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

Checkpoint opportunity

A.APR Arithmetic with Polynomials and Rational Expressions

A.APR.C Perform arithmetic operations on polynomials.

A.APR.C.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Checkpoint opportunity

A.CED Creating Equations

A.CED.G Create equations that describe numbers or relationships.

A.CED.G.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

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

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

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

Checkpoint opportunity

A.REI Reasoning with Equations and Inequalities

A.REI.H Understand solving equations as a process of reasoning and explain the reasoning.

A.REI.H.1 Explain each step in solving a simple 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.

A.REI.I Solve equations and inequalities in one variable.

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

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

A.REI.I.4A 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.I.4C Derive the quadratic formula from the general form of a quadratic equation.

Checkpoint opportunity

A.REI.J Solve systems of equations.

A.REI.J.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other, produces a system with the same solutions.

A.REI.J.6 Estimate solutions graphically and determine algebraic solutions to linear systems, focusing on pairs of linear equations in two variables.

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

A.REI.J.8 Represent a system of linear equations as a single matrix equation in a vector variable.

A.REI.J.9 Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

A.REI.K Represent and solve equations and inequalities graphically.

A.REI.K.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.

A.REI.K.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and 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

F.IF.A Understand the concept of a function and use function notation.

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

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

F.IF.B Interpret functions that arise in application in terms of the context.

F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

Checkpoint opportunity

F.IF.C Analyze functions using different representations.

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

F.IF.C.7A Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.IF.C.7B Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.C.7E Graph exponential and logarithmic functions, showing intercepts and end behavior.

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

F.IF.C.8A Use the process of 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.C.8B Use the properties of exponents to interpret expressions for exponential functions.