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Skills available for Missouri high school math standards

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Missouri Learning Standards: Algebra I Missouri Learning Standards: Algebra I
Missouri Learning Standards: Algebra II Missouri Learning Standards: Algebra II
Missouri Learning Standards: Geometry Missouri Learning Standards: Geometry

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G.GMD Geometric Measurement and Dimension

G.GMD.A Explain volume formulas and use them to solve problems.
- G.GMD.A.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone.
- G.GMD.A.2 Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.
- Checkpoint opportunity
  - Checkpoint: Volume (G-T.14)
G.GMD.B Visualize relationships between two-dimensional and three-dimensional objects.
- G.GMD.B.3 Identify the shapes of two-dimensional cross-sections of three-dimensional objects.
  - Cross sections of three-dimensional figures (G-H.4)
- G.GMD.B.4 Identify three-dimensional objects generated by transformations of two-dimensional objects.
  - Solids of revolution (G-H.5)
- Checkpoint opportunity
  - Checkpoint: Cross sections and solids of revolution (G-H.6)

G.MG Modeling with Geometry

G.MG.A Apply geometric concepts in modeling situations.
- G.MG.A.1 Use geometric shapes, their measures and their properties to describe objects.
  - Pythagorean theorem (G-Q.1)
- G.MG.A.2 Apply concepts of density based on area and volume in modeling situations.
  - Calculate density, mass, and volume (G-W.9)
- G.MG.A.3 Apply geometric methods to solve design mathematical modeling problems.
- Checkpoint opportunity
  - Checkpoint: Geometric modeling and design (G-W.10)
  - Checkpoint: Density (G-W.11)

A1.IF Interpreting Functions

A1.IF.A Understand the concept of a function and use function notation.
- A1.IF.A.1 Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range.
  - A1.IF.A.1.a Represent a function using function notation.
    - Complete a function table from a graph (A1-Q.12)
    - Complete a function table from an equation (A1-Q.13)
  - A1.IF.A.1.b Understand that the graph of a function labeled ∫ is the set of all ordered pairs (x, y) that satisfy the equation y=f(x).
- A1.IF.A.2 Use function notation to evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
A1.IF.B Interpret linear, quadratic and exponential functions in terms of the context.
- A1.IF.B.3 Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.
- A1.IF.B.4 Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.
- A1.IF.B.5 Determine the average rate of change of a function over a specified interval and interpret the meaning.
- A1.IF.B.6 Interpret the parameters of a linear or exponential function in terms of the context.
  - Solve one-step and two-step linear equations: word problems (A1-J.10)
  - Exponential growth and decay: word problems (A1-Y.7)
- Checkpoint opportunity
  - Checkpoint: Function concepts (A1-Q.20)
  - Checkpoint: Average rate of change (A1-Q.21)
A1.IF.C Analyze linear, quadratic and exponential functions using different representations.
- A1.IF.C.7 Graph functions expressed symbolically and identify and interpret key features of the graph.
- A1.IF.C.8 Translate between different but equivalent forms of a function to reveal and explain properties of the function and interpret these in terms of a context.
- A1.IF.C.9 Compare the properties of two functions given different representations.
  - Compare linear functions: graphs and equations (A1-T.15)
  - Compare linear functions: tables, graphs, and equations (A1-T.16)
- Checkpoint opportunity
  - Checkpoint: Features of functions (A1-DD.14)
  - Checkpoint: Graph and analyze functions (A1-EE.13)

G.CP Conditional Probability and Rules of Probability

G.CP.A Understand independence and conditional probability and use them to interpret data.
- G.CP.A.1 Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections or complements of other events.
  - Theoretical and experimental probability (G-X.1)
  - Outcomes of compound events (G-X.2)
- G.CP.A.2 Understand the definition of independent events and use it to solve problems.
- G.CP.A.3 Calculate conditional probabilities of events.
  - Find conditional probabilities (G-X.11)
  - Independence and conditional probability (G-X.12)
- G.CP.A.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
  - Find probabilities using two-way frequency tables (G-X.9)
  - Find conditional probabilities using two-way frequency tables (G-X.13)
- G.CP.A.5 Recognize and explain the concepts of conditional probability and independence in a context.
- G.CP.A.6 Apply and interpret the Addition Rule for calculating probabilities.
  - Find probabilities using the addition rule (G-X.15)
- G.CP.A.7 Apply and Interpret the general Multiplication Rule in a uniform probability model.
  - Find conditional probabilities (G-X.11)
- G.CP.A.8 Use permutations and combinations to solve problems.

A1.BF Building Functions

A1.BF.A Build new functions from existing functions (limited to linear, quadratic and exponential).
- A1.BF.A.1 Analyze the effect of translations and scale changes on functions.
  - Transformations of linear functions (A1-T.29)
  - Transformations of quadratic functions (A1-CC.4)
- Checkpoint opportunity
  - Checkpoint: Function transformations (A1-EE.14)

A1.LQE Linear, Quadratic and Exponential Models

A1.LQE.A Construct and compare linear, quadratic and exponential models and solve problems.
- A1.LQE.A.1 Distinguish between situations that can be modeled with linear or exponential functions.
  - A1.LQE.A.1.a Determine that linear functions change by equal differences over equal intervals.
  - A1.LQE.A.1.b Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.
- A1.LQE.A.2 Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.
- A1.LQE.A.3 Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.
- Checkpoint opportunity
  - Checkpoint: Compare linear and exponential functions (A1-DD.15)
A1.LQE.B Use arithmetic and geometric sequences.
- A1.LQE.B.4 Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.
- A1.LQE.B.5 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers.
- A1.LQE.B.6 Find the terms of sequences given an explicit or recursive formula.
  - Evaluate variable expressions for number sequences (A1-P.4)
  - Evaluate recursive formulas for sequences (A1-P.5)
- Checkpoint opportunity
  - Checkpoint: Sequences (A1-P.13)

A1.DS Data and Statistical Analysis

A1.DS.A Summarize, represent and interpret data.
- A1.DS.A.1 Analyze and interpret graphical displays of data.
  - Interpret bar graphs, line graphs, and histograms (A1-N.5)
  - Box plots (A1-N.9)
- A1.DS.A.2 Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets.
- A1.DS.A.3 Interpret differences in shape, center and spreads in the context of the data sets, accounting for possible effects of outliers.
- A1.DS.A.4 Summarize data in two-way frequency tables.
  - A1.DS.A.4.a Interpret relative frequencies in the context of the data.
    - Find probabilities using two-way frequency tables (A1-LL.3)
    - Find conditional probabilities using two-way frequency tables (A1-LL.4)
  - A1.DS.A.4.b Recognize possible associations and trends in the data.
- A1.DS.A.5 Construct a scatter plot of bivariate quantitative data describing how the variables are related; determine and use a function that models the relationship.
  - A1.DS.A.5.a Construct a linear function to model bivariate data represented on a scatter plot that minimizes residuals.
    - Write equations for lines of best fit (A1-MM.12)
    - Find the equation of a regression line (A1-MM.13)
  - A1.DS.A.5.b Construct an exponential function to model bivariate data represented on a scatter plot that minimizes residuals.
- A1.DS.A.6 Interpret the slope (rate of change) and the y-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)
- A1.DS.A.7 Determine and interpret the correlation coefficient for a linear association.
  - Match correlation coefficients to scatter plots (A1-MM.10)
  - Calculate correlation coefficients (A1-MM.11)
- A1.DS.A.8 Distinguish between correlation and causation.
- Checkpoint opportunity

A2.NQ Number and Quantity

A2.NQ.A Extend and use the relationship between rational exponents and radicals.
- A2.NQ.A.1 Extend the system of powers and roots to include rational exponents.
  - Evaluate rational exponents (A2-N.1)
- A2.NQ.A.2 Create and recognize equivalent expressions involving radical and exponential forms of expressions.
- A2.NQ.A.3 Add, subtract, multiply and divide radical expressions.
- A2.NQ.A.4 Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.
  - Solve radical equations (A2-M.14)
A2.NQ.B Use complex numbers.
- A2.NQ.B.5 Represent complex numbers.
  - Introduction to complex numbers (A2-I.1)
- A2.NQ.B.6 Add, subtract, multiply and divide complex numbers.
- A2.NQ.B.7 Know and apply the Fundamental Theorem of Algebra.
  - Fundamental Theorem of Algebra (A2-L.17)

A2.SSE Seeing Structure in Expressions

A2.SSE.A Define and use logarithms.
- A2.SSE.A.1 Develop the definition of logarithms based on properties of exponents.
- A2.SSE.A.2 Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations.
- A2.SSE.A.3 Use properties of logarithms to solve equations or find equivalent expressions.
- A2.SSE.A.4 Understand why logarithmic scales are used, and use them to solve problems.

A2.REI Reasoning with Equations and Inequalities

A2.REI.A Solve equations and inequalities.
- A2.REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.
- A2.REI.A.2 Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.
  - Solve rational equations (A2-O.7)
A2.REI.B Solve general systems of equations and inequalities.
- A2.REI.B.3 Create and solve systems of equations that may include non-linear equations and inequalities.

A2.APR Arithmetic with Polynomials and Rational Expressions

A2.APR.A Perform operations on polynomials and rational expressions.
- A2.APR.A.1 Extend the knowledge of factoring to include factors with complex coefficients.
  - Factor polynomials (A2-J.7)
- A2.APR.A.2 Understand the Remainder Theorem and use it to solve problems.
- A2.APR.A.3 Find the least common multiple of two or more polynomials.
- A2.APR.A.4 Add, subtract, multiply and divide rational expressions.
- A2.APR.A.5 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.

A2.IF Interpreting Functions

A2.IF.A Use and interpret functions.
- A2.IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.
- A2.IF.A.2 Translate between equivalent forms of functions.

A2.BF Building Functions

A2.BF.A Create new functions from existing functions.
- A2.BF.A.1 Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).
- A2.BF.A.2 Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.
- A2.BF.A.3 Describe the effects of transformations algebraically and graphically, creating vertical and horizontal translations, vertical and horizontal reflections and dilations (expansions/compressions) for linear, quadratic, cubic, square and cube root, absolute value, exponential and logarithmic functions.

A2.FM Modeling

A2.FM.A Use functions to model real-world problems.
- A2.FM.A.1 Create functions and use them to solve applications of quadratic and exponential function model problems.

A2.DS Data and Statistical Analysis

A2.DS.A Make inferences and justify conclusions.
- A2.DS.A.1 Analyze how random sampling could be used to make inferences about population parameters.
- A2.DS.A.2 Determine whether a specified model is consistent with a given data set.
- A2.DS.A.3 Describe and explain the purposes, relationship to randomization and differences among sample surveys, experiments and observational studies.
  - Experiment design (A2-FF.12)
- A2.DS.A.4 Use data from a sample to estimate characteristics of the population and recognize the meaning of the margin of error in these estimates.
  - Find confidence intervals for population means (A2-FF.9)
  - Find confidence intervals for population proportions (A2-FF.10)
- A2.DS.A.5 Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.
  - Identify biased samples (A2-FF.1)
- A2.DS.A.6 Analyze decisions and strategies using probability concepts.
- A2.DS.A.7 Evaluate reports based on data.
  - Analyze the results of an experiment using simulations (A2-FF.13)
A2.DS.B Fit a data set to a normal distribution.
- A2.DS.B.8 Know and use the characteristics of normally distributed data sets; predict what percentage of the data will be above or below a given value that is a multiple of standard deviations above or below the mean.
- A2.DS.B.9 Fit a data set to a distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.

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G.CO Congruence

G.CO.A Experiment with transformations in the plane.

G.CO.A.1 Define angle, circle, perpendicular line, parallel line, line segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc.

G.CO.A.2 Represent transformations in the plane, and describe them as functions that take points in the plane as inputs and give other points as outputs.

G.CO.A.3 Describe the rotational symmetry and lines of symmetry of two-dimensional figures.

G.CO.A.4 Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

G.CO.A.5 Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.

Checkpoint opportunity

G.CO.B Understand congruence in terms of rigid motions.

G.CO.B.6 Develop the definition of congruence in terms of rigid motions.

G.CO.B.7 Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.

Checkpoint opportunity

G.CO.C Prove geometric theorems.

G.CO.C.8 Prove theorems about lines and angles.

G.CO.C.9 Prove theorems about triangles.

G.CO.C.10 Prove theorems about polygons.

Checkpoint opportunity

G.CO.D Make geometric constructions.

G.CO.D.11 Construct geometric figures using various tools and methods.

Checkpoint opportunity

A1.NQ Number and Quantity

A1.NQ.A Extend and use properties of rational exponents.

A1.NQ.A.1 Explain how the meaning of rational exponents extends from the properties of integer exponents.

A1.NQ.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents. Limit to rational exponents with a numerator of 1.

Checkpoint opportunity

A1.NQ.B Use units to solve problems.

A1.NQ.B.3 Use units of measure as a way to understand and solve problems involving quantities.

A1.NQ.B.3.a Identify, label and use appropriate units of measure within a problem.

A1.NQ.B.3.b Convert units and rates.

A1.NQ.B.3.c Use units within problems.

A1.NQ.B.3.d Choose and interpret the scale and the origin in graphs and data displays.

A1.NQ.B.4 Define and use appropriate quantities for representing a given context or problem.

A1.NQ.B.5 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

Checkpoint opportunity

G.SRT Similarity, Right Triangles, and Trigonometry

G.SRT.A Understand similarity in terms of similarity transformations.

G.SRT.A.1 Construct and analyze scale changes of geometric figures.

G.SRT.A.2 Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures.

G.SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

Checkpoint opportunity

G.SRT.B Prove theorems involving similarity.

G.SRT.B.4 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Checkpoint opportunity

G.SRT.C Define trigonometric ratios, and solve problems involving right triangles.

G.SRT.C.5 Understand that side ratios in right triangles define the trigonometric ratios for acute angles.

G.SRT.C.6 Explain and use the relationship between the sine and cosine of complementary angles.

G.SRT.C.7 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.

G.SRT.C.8 Derive the formula A = 1/2 ab sin(C) for the area of a triangle.

Checkpoint opportunity

A1.SSE Seeing Structure in Expressions

A1.SSE.A Interpret and use structure.

A1.SSE.A.1 Interpret the contextual meaning of individual terms or factors from a given problem that utilizes formulas or expressions.

A1.SSE.A.2 Analyze the structure of polynomials to create equivalent expressions or equations.

A1.SSE.A.3 Choose and produce equivalent forms of a quadratic expression or equations to reveal and explain properties.

A1.SSE.A.3.a Find the zeros of a quadratic function by rewriting it in factored form.

A1.SSE.A.3.b Find the maximum or minimum value of a quadratic function by completing the square.

Checkpoint opportunity

A1.CED Creating Equations

A1.CED.A Create equations that describe linear, quadratic and exponential relationships.

A1.CED.A.1 Create equations and inequalities in one variable and use them to model and/or solve problems.

A1.CED.A.2 Create and graph linear, quadratic and exponential equations in two variables.

A1.CED.A.3 Represent constraints by equations or inequalities and by systems of equations or inequalities, and interpret the data points as a solution or non-solution in a modeling context.

A1.CED.A.4 Solve literal equations and formulas for a specified variable that highlights a quantity of interest.

Checkpoint opportunity

G.C Circles

G.C.A Understand and apply theorems about circles.

G.C.A.1 Prove that all circles are similar using similarity transformations.

G.C.A.2 Identify and describe relationships among inscribed angles, radii and chords of circles.

G.C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

Checkpoint opportunity

G.C.B Find arc lengths and areas of sectors of circles.

G.C.B.4 Derive the formula for the length of an arc of a circle.

G.C.B.5 Derive the formula for the area of a sector of a circle.

Checkpoint opportunity

G.GPE Exploring Geometric Properties with Equations

G.GPE.A Translate between the geometric description and the equation for a conic section.

G.GPE.A.1 Derive the equation of a circle.