The Common Core in Missouri

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Skills available for Missouri 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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NQ Number and Quantity

SSE Seeing Structure in Expressions

CED Creating Equations

REI Reasoning with Equations and Inequalities

  • REI.A Understand solving equations as a process, and solve equations and inequalities in one variable.

    • REI.A.1 Explain how each step taken when solving an equation or inequality in one variable creates an equivalent equation or inequality that has the same solution(s) as the original.

    • REI.A.2 Solve problems involving quadratic equations.

      • REI.A.2.a Use the method of completing the square to create an equivalent quadratic equation.

      • REI.A.2.b Derive the quadratic formula.

      • REI.A.2.c Analyze different methods of solving quadratic equations.

  • REI.B Solve systems of equations.

    • REI.B.1 Solve a system of linear equations algebraically and/or graphically.

    • REI.B.2 Solve a system consisting of a linear equation and a quadratic equation algebraically and/or graphically.

    • REI.B.3 Justify that the technique of linear combination produces an equivalent system of equations.

  • REI.C Represent and solve linear and exponential equations and inequalities graphically.

    • REI.C.1 Explain that the graph of an equation in two variables is the set of all its solutions plotted in the Cartesian coordinate plane.

    • REI.C.2 Graph the solution to a linear inequality in two variables.

    • REI.C.3 Solve problems involving a system of linear inequalities.

APR Arithmetic with Polynomials and Rational Expressions

  • APR.A Perform operations on polynomials.

    • APR.A.1 Add, subtract and multiply polynomials, and understand that polynomials follow the same general rules of arithmetic and are closed under these operations.

    • APR.A.2 Divide polynomials by monomials.

IF Interpreting Functions

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

    • 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.

      • IF.A.1.a Represent a function using function notation.

      • IF.A.1.b Understand that the graph of a function labeled ?? is the set of all ordered pairs (??, y) that satisfy the equation ??=f(??).

    • 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.

  • IF.B Interpret linear, quadratic and exponential functions in terms of the context.

    • IF.B.1 Using tables, graphs and verbal descriptions, interpret key characteristics of a function that models the relationship between two quantities.

    • IF.B.2 Relate the domain and range of a function to its graph and, where applicable, to the quantitative relationship it describes.

    • IF.B.3 Determine the average rate of change of a function over a specified interval and interpret the meaning.

    • IF.B.4 Interpret the parameters of a linear or exponential function in terms of the context.

  • IF.C Analyze linear, quadratic and exponential functions using different representations.

    • IF.C.1 Graph functions expressed symbolically and identify and interpret key features of the graph.

    • IF.C.2 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.

    • IF.C.3 Compare the properties of two functions given different representations.

BF Building Functions

  • BF.A Build new functions from existing functions (limited to linear, quadratic and exponential).

    • BF.A.1 Analyze the effect of translations and scale changes on functions.

FM Modeling

LQE Linear, Quadratic and Exponential Models

  • LQE.A Construct and compare linear, quadratic and exponential models and solve problems.

    • LQE.A.1 Distinguish between situations that can be modeled with linear or exponential functions.

      • LQE.A.1.a Determine that linear functions change by equal differences over equal intervals.

      • LQE.A.1.b Recognize exponential situations in which a quantity grows or decays by a constant percent rate per unit interval.

    • LQE.A.2 Describe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.

    • LQE.A.3 Construct linear, quadratic and exponential equations given graphs, verbal descriptions or tables.

  • LQE.B Use arithmetic and geometric sequences.

    • LQE.B.1 Write arithmetic and geometric sequences in recursive and explicit forms, and use them to model situations and translate between the two forms.

    • LQE.B.2 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the set of integers.

    • LQE.B.3 Find the terms of sequences given an explicit or recursive formula.

DS Data and Statistical Analysis

  • DS.A Summarize, represent and interpret data.

    • DS.A.1 Analyze and interpret graphical displays of data.

    • 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.

    • DS.A.3 Interpret differences in shape, center and spreads in the context of the data sets, accounting for possible effects of outliers.

    • DS.A.4 Summarize data in two-way frequency tables.

      • DS.A.4.a Interpret relative frequencies in the context of the data.

      • DS.A.4.b Recognize possible associations and trends in the data.

    • 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.

      • DS.A.5.a Construct a linear function to model bivariate data represented on a scatter plot that minimizes residuals.

      • DS.A.5 Construct an exponential function to model bivariate data represented on a scatter plot that minimizes residuals.

    • 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.

    • DS.A.7 Determine and interpret the correlation coefficient for a linear association.

    • DS.A.8 Distinguish between correlation and causation.

NQ Number and Quantity

  • NQ.A Extend and use the relationship between rational exponents and radicals.

    • NQ.A.1 Extend the system of powers and roots to include rational exponents.

    • NQ.A.2 Create and recognize equivalent expressions involving radical and exponential forms of expressions.

    • NQ.A.3 Add, subtract, multiply and divide radical expressions.

    • NQ.A.4 Solve equations involving rational exponents and/or radicals and identify situations where extraneous solutions may result.

  • NQ.B Use complex numbers.

    • NQ.B.1 Represent complex numbers.

    • NQ.B.2 Add, subtract, multiply and divide complex numbers.

    • NQ.B.3 Know and apply the Fundamental Theorem of Algebra.

SSE Seeing Structure in Expressions

  • SSE.A Define and use logarithms.

    • SSE.A.1 Develop the definition of logarithms based on properties of exponents.

    • SSE.A.2 Use the inverse relationship between exponents and logarithms to solve exponential and logarithmic equations.

    • SSE.A.3 Use properties of logarithms to solve equations or find equivalent expressions.

    • SSE.A.4 Understand why logarithmic scales are used, and use them to solve problems.

CED Creating Equations

REI Reasoning with Equations and Inequalities

  • REI.A Solve equations and inequalities.

    • REI.A.1 Create and solve equations and inequalities, including those that involve absolute value.

    • REI.A.2 Solve rational equations where numerators and denominators are polynomials and where extraneous solutions may result.

  • REI.B Solve general systems of equations and inequalities.

    • REI.B.1 Create and solve systems of equations that may include non-linear equations and inequalities.

APR Arithmetic with Polynomials and Rational Expressions

  • APR.A Perform operations on polynomials and rational expressions.

    • APR.A.1 Extend the knowledge of factoring to include factors with complex coefficients.

    • APR.A.2 Understand the Remainder Theorem and use it to solve problems.

    • APR.A.3 Find the least common multiple of two or more polynomials.

    • APR.A.4 Add, subtract, multiply and divide rational expressions.

    • APR.A.5 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to sketch the function defined by the polynomial.

IF Interpreting Functions

  • IF.A Use and interpret functions.

    • IF.A.1 Identify and interpret key characteristics of functions represented graphically, with tables and with algebraic symbolism to solve problems.

    • IF.A.2 Translate between equivalent forms of functions.

BF Building Functions

  • BF.A Create new functions from existing functions.

    • BF.A.1 Create new functions by applying the four arithmetic operations and composition of functions (modifying the domain and range as necessary).

    • BF.A.2 Derive inverses of functions, and compose the inverse with the original function to show that the functions are inverses.

    • 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.

FM Modeling

  • FM.A Use functions to model real-world problems.

    • FM.A.1 Create functions and use them to solve applications of quadratic and exponential function model problems.

LQE Linear, Quadratic and Exponential Models

DS Data and Statistical Analysis

  • DS.A Make inferences and justify conclusions.

    • DS.A.1 Analyze how random sampling could be used to make inferences about population parameters.

    • DS.A.2 Determine whether a specified model is consistent with a given data set.

    • DS.A.3 Describe and explain the purposes, relationship to randomization and differences among sample surveys, experiments and observational studies.

    • 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.

    • DS.A.5 Describe and explain how the relative sizes of a sample and the population affect the margin of error of predictions.

    • DS.A.6 Analyze decisions and strategies using probability concepts.

    • DS.A.7 Evaluate reports based on data.

  • DS.B Fit a data set to a normal distribution.

    • DS.B.1 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.

    • DS.B.2 Fit a data set to a distribution using its mean and standard deviation to determine whether the data is approximately normally distributed.

CO Congruence

  • CO.A Experiment with transformations in the plane.

    • 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.

    • 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.

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

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

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

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

    • CO.B.1 Develop the definition of congruence in terms of rigid motions.

    • CO.B.2 Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.

  • CO.C Prove geometric theorems.

    • CO.C.1 Prove theorems about lines and angles.

    • CO.C.2 Prove theorems about triangles.

    • CO.C.3 Prove theorems about polygons.

  • CO.D Make geometric constructions.

    • CO.D.1 Construct geometric figures using various tools and methods.

SRT Similarity, Right Triangles, and Trigonometry

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

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

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

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

  • SRT.B Prove theorems involving similarity.

    • SRT.B.1 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

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

    • SRT.C.1 Understand that side ratios in right triangles define the trigonometric ratios for acute angles.

    • SRT.C.2 Explain and use the relationship between the sine and cosine of complementary angles.

    • SRT.C.3 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.

    • SRT.C.4 Derive the formula A = 1/2 ab sin(C) for the area of a triangle.

C Circles

  • C.A Understand and apply theorems about circles.

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

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

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

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

    • C.B.1 Derive the formula for the length of an arc of a circle.

    • C.B.2 Derive the formula for the area of a sector of a circle.

GPE Exploring Geometric Properties with Equations

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

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

    • GPE.A.2 Derive the equation of a parabola given a focus and directrix.

  • GPE.B Use coordinates to prove geometric theorems algebraically.

    • GPE.B.1 Use coordinates to prove geometric theorems algebraically.

    • GPE.B.2 Prove the slope criteria for parallel and perpendicular lines and use them to solve problems.

    • GPE.B.3 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

    • GPE.B.4 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

GMD Geometric Measurement and Dimension

  • GMD.A Explain volume formulas and use them to solve problems.

    • 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.

    • GMD.A.2 Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.

  • GMD.B Visualize relationships between two-dimensional and three-dimensional objects.

    • GMD.B.1 Identify the shapes of two-dimensional cross-sections of three-dimensional objects.

    • GMD.B.2 Identify three-dimensional objects generated by transformations of two-dimensional objects.

MG Modeling with Geometry

  • MG.A Apply geometric concepts in modeling situations.

    • MG.A.1 Use geometric shapes, their measures and their properties to describe objects.

    • MG.A.2 Apply concepts of density based on area and volume in modeling situations.

    • MG.A.3 Apply geometric methods to solve design mathematical modeling problems.

CP Conditional Probability and Rules of Probability

  • CP.A Understand independence and conditional probability and use them to interpret data.

    • 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.

    • CP.A.2 Understand the definition of independent events and use it to solve problems.

    • CP.A.3 Calculate conditional probabilities of events.

    • 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.

    • CP.A.5 Recognize and explain the concepts of conditional probability and independence in a context.

    • CP.A.6 Apply and interpret the Addition Rule for calculating probabilities.

    • CP.A.7 Apply and Interpret the general Multiplication Rule in a uniform probability model.

    • CP.A.8 Use permutations and combinations to solve problems.