North Dakota flagNorth Dakota: HS Math Standards

178 standards · 22 domains

HS.A-APR

  • HS.A-APR.1 Add, subtract, and multiply polynomials. Understand that polynomials form a system comparable to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
  • HS.A-APR.2 Apply the Remainder Theorem.
  • HS.A-APR.3 Identify zeros of polynomials when suitable factorizations are available. Use the zeros to construct a rough graph of the function defined by the polynomial.
  • HS.A-APR.6 Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
  • HS.A-APR.7 Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system comparable to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.

HS.A-CED

  • HS.A-CED.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.
  • HS.A-CED.2 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.
  • HS.A-CED.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.
  • HS.A-CED.4 Rearrange formulas to isolate a quantity of interest, using the same reasoning as in solving equations.

HS.A-REI

  • HS.A-REI.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.
  • HS.A-REI.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
  • HS.A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • HS.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. (+) Derive the quadratic formula from this form.
  • HS.A-REI.4.b Solve quadratic equations by inspection (e.g., for x = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a +/- bi for real numbers a and b.
  • HS.A-REI.5 This standard has been moved/removed by the committee
  • HS.A-REI.6 Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables.
  • HS.A-REI.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
  • HS.A-REI.8 (+)Represent a system of linear equations as a single matrix equation.
  • HS.A-REI.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).
  • HS.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.
  • HS.A-REI.11 Using graphs, technology, tables, or successive approximations, show that the solution(s) to the equation f(x) = g(x) are the x-value(s) that result in the y-values of f(x) and g(x) being the same.
  • HS.A-REI.12 Graph the solutions to a linear inequality in two variables as a half-plane. Graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

HS.A-SSE

  • HS.A-SSE.1.a Interpret parts of an expression, such as terms, factors, and coefficients.
  • HS.A-SSE.1.b Interpret complicated expressions by examining one or more of their parts as a single entity.
  • HS.A-SSE.2 Use the structure of an expression to identify ways to rewrite it.
  • HS.A-SSE.3.a Factor a quadratic expression to reveal the zeros of the function it defines.
  • HS.A-SSE.3.b Complete the square in a quadratic expression to produce an equivalent expression.
  • HS.A-SSE.3.c Use the properties of exponents to transform exponential expressions.
  • HS.A-SSE.4 This standard has been moved/removed by the committee

HS.F-BF

  • HS.F-BF.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
  • HS.F-BF.1.b Combine standard function types using arithmetic operations.
  • HS.F-BF.1.c Compose functions.
  • HS.F-BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula and convert between the two forms. Use sequences to model situations.
  • HS.F-BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, f(x + k), k f(x), and f(x + k), for specific values of k (both positive and negative); find the value of k given the graphs. Recognize even and odd functions from their graphs.
  • HS.F-BF.4.a Write an equation for the inverse given a function has an inverse.
  • HS.F-BF.4.b Verify by composition that one function is the inverse of another.
  • HS.F-BF.4.c Read values of an inverse function from a graph or a table, given that the function has an inverse.
  • HS.F-BF.4.d Produce an invertible function from a non-invertible function by restricting the domain.
  • HS.F-BF.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

HS.F-IF

  • HS.F-IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain 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 of f is the graph of the equation y = f(x).
  • HS.F-IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • HS.F-IF.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
  • HS.F-IF.4 Use tables, graphs, verbal descriptions, and equations to interpret and sketch the key features of a function modeling the relationship between two quantities.
  • HS.F-IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  • HS.F-IF.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.
  • HS.F-IF.7.a Graph linear and quadratic functions and show intercepts, maxima, and minima where appropriate.
  • HS.F-IF.7.b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
  • HS.F-IF.7.c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
  • HS.F-IF.7.d (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
  • HS.F-IF.7.e Graph exponential and logarithmic functions, showing intercepts and end behavior.
  • HS.F-IF.7.f Graph f(x) = sin x and f(x) = cos x as representations of periodic phenomena.
  • HS.F-IF.7.g (+) Graph trigonometric functions, showing period, midline, phase shift and amplitude.
  • HS.F-IF.8.a 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.
  • HS.F-IF.8.b Use the properties of exponents to interpret expressions for exponential functions.
  • HS.F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

HS.F-LE

  • HS.F-LE.1 Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays.
  • HS.F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a table, a description, or two input-output pairs given their relationship.
  • HS.F-LE.3 Compare the end behavior of linear, quadratic, and exponential functions using graphs and/or tables to show that a quantity increasing exponentially eventually exceeds a quantity increasing as a linear or quadratic function.
  • HS.F-LE.4 Use logarithms to express the solution to ab^ct = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.
  • HS.F-LE.5 Interpret the parameters in a linear, quadratic, or exponential function in context.

HS.F-TF

  • HS.F-TF.1 Understand that the radian measure of an angle is the ratio of the length of the arc to the length of the radius of a circle.
  • HS.F-TF.2 Extend right triangle trigonometry to the four quadrants. (+) Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
  • HS.F-TF.3 Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6. (+) Use the unit circle to express the values of sine, cosine, and tangent for π - x, π + x, and 2π -x, in terms of their values for x, where x is any real number.
  • HS.F-TF.4 (+)Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
  • HS.F-TF.5 (+)Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
  • HS.F-TF.6 (+)Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
  • HS.F-TF.7 (+)Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
  • HS.F-TF.8 Prove the Pythagorean identity sin^2(ϴ) + cos^2(ϴ) = 1 and use it to find n(ϴ), cos(ϴ), or tan(ϴ) given sin(ϴ), cos(ϴ), or tan(ϴ)and the quadrant of the angle.
  • HS.F-TF.9 (+)Know and apply the addition and subtraction formulas for sine, cosine, and tangent.

HS.G-C

  • HS.G-C.1 Understand and apply theorems about relationships with line segments and circles including radii, diameter, secants, tangents, and chords.
  • HS.G-C.2 Understand and apply theorems about relationships with angles formed by radii, diameter, secants, tangents, and chords. Understand and apply properties of angles for a quadrilateral inscribed in a circle.
  • HS.G-C.3 Construct the incenter and circumcenter of a triangle. Relate the incenter and circumcenter to the inscribed and circumscribed circles.
  • HS.G-C.4 (+)Construct a tangent line from a point outside a given circle to the circle.
  • HS.G-C.5 Explain and use the formulas for arc length and area of sectors of circles.

HS.G-CO

  • HS.G-CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane.
  • HS.G-CO.2 Represent transformations in the plane. Describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
  • HS.G-CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
  • HS.G-CO.4 Develop or verify experimentally the characteristics of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
  • HS.G-CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
  • HS.G-CO.6 Use geometric descriptions of rigid motions to predict the effect of a given rigid motion on a given figure. Use the definition of congruence in terms of rigid motions to decide if two figures are congruent.
  • HS.G-CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
  • HS.G-CO.8 Prove two triangles are congruent using the congruence theorems such as ASA, SAS, and SSS.
  • HS.G-CO.9 Prove and apply theorems about lines and angles.
  • HS.G-CO.10 Prove and apply theorems about triangle properties.
  • HS.G-CO.11 Prove and apply theorems about parallelograms.
  • HS.G-CO.12 Make basic geometric constructions with a variety of tools and methods.
  • HS.G-CO.13 (+)Apply basic constructions to create polygons such as equilateral triangles, squares, and regular hexagons inscribed in circles.

HS.G-GMD

  • HS.G-GMD.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.
  • HS.G-GMD.2 Calculate the surface area for prisms, cylinders, pyramids, cones, and spheres to solve problems.
  • HS.G-GMD.3 Know and apply volume formulas for prisms, cylinders, pyramids, cones, and spheres to solve problems.
  • HS.G-GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

HS.G-GPE

  • HS.G-GPE.1 Derive the equation of a circle of given center and radius. Derive the equation of a parabola given a focus and directrix. (+) Derive the equations of ellipses and hyperbolas given foci, using the fact that the sum or difference of distances from the foci is constant.
  • HS.G-GPE.2 Convert between the standard and general form equations of conic sections.
  • HS.G-GPE.3 Identify key features of conic sections given their equations. Apply properties of conic sections in real world situations.
  • HS.G-GPE.4 Use coordinates to verify simple geometric theorems algebraically. Use coordinates to verify algebraically that a given set of points produces a particular type of triangle or quadrilateral.
  • HS.G-GPE.5 Develop and verify the slope criteria for parallel and perpendicular lines. Apply the slope criteria for parallel and perpendicular lines to solve geometric problems using algebra.
  • HS.G-GPE.6 Use coordinates to find the midpoint or endpoint of a line segment. (+) Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
  • HS.G-GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles, parallelograms, trapezoids and kites.

HS.G-MG

  • HS.G-MG.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
  • HS.G-MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
  • HS.G-MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

HS.G-SRT

  • HS.G-SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor.
  • HS.G-SRT.2 Given two figures, use transformations to decide if they are similar. Apply the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
  • HS.G-SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
  • HS.G-SRT.4 Prove similarity theorems about triangles.
  • HS.G-SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
  • HS.G-SRT.6 Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine, and tangent of an acute angle in a right triangle.
  • HS.G-SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
  • HS.G-SRT.8 Use special right triangles (30-60а-90 and 45а-45-90а), trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
  • HS.G-SRT.9 (+)Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
  • HS.G-SRT.10 (+)Solve unknown sides and angles of non-right triangles using the Laws of Sines and Cosines.
  • HS.G-SRT.11 (+)Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in context.

HS.N-CN

  • HS.N-CN.1 Know there is an imaginary number i, such that i² = −1, and every complex number has the form a + bi where a and b are real. Understand the hierarchal relationships among subsets of the complex number system.
  • HS.N-CN.2 Use the definition i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
  • HS.N-CN.3 Use conjugates to find quotients of complex numbers.
  • HS.N-CN.4 (+)Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers). Find moduli (absolute value) of a complex number. Explain why the rectangular and polar forms of a given complex number represent the same number.
  • HS.N-CN.5 (+)Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
  • HS.N-CN.6 (+)This standard has been moved/removed by the committee
  • HS.N-CN.7 Solve quadratic equations with real coefficients that have complex solutions.
  • HS.N-CN.8 (+)Extend polynomial identities to the complex numbers.
  • HS.N-CN.9 (+)Apply the Fundamental Theorem of Algebra to determine the number of zeros for polynomial functions. Find all solutions to a polynomial equation.

HS.N-Q

  • HS.N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems (e.g., unit analysis). Choose and interpret units consistently in formulas. Choose and interpret the scale and the origin in graphs and data displays.
  • HS.N-Q.2 Define appropriate quantities for the purpose of descriptive modeling.
  • HS.N-Q.3 Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

HS.N-RN

  • HS.N-RN.1 Explain how the definition of the meaning 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.
  • HS.N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
  • HS.N-RN.3 Demonstrate that the sum or product of two 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.
  • HS.N-RN.4 Perform basic operations on radicals and simplify radicals to write equivalent expressions.

HS.N-VM

  • HS.N-VM.1 (+)Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments and use appropriate symbols for vectors and their magnitudes (e.g., v, |v|, ||v||, v).
  • HS.N-VM.2 (+)Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
  • HS.N-VM.3 (+)Solve problems involving velocity and other quantities that can be represented by vectors.
  • HS.N-VM.4.a Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
  • HS.N-VM.4.b Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
  • HS.N-VM.4.c Understand that vector subtraction v – w is defined as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order and use the components to perform vector subtraction.
  • HS.N-VM.5.a Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction. Use the components to perform scalar multiplication (e.g., as c(v_x , v_y) = (cv_x, cv_y)).
  • HS.N-VM.5.b multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
  • HS.N-VM.6 Use matrices to represent and manipulate data.
  • HS.N-VM.7 Multiply matrices by scalars to produce new matrices.
  • HS.N-VM.8 Add, subtract, and multiply matrices of appropriate dimensions.
  • HS.N-VM.9 Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
  • HS.N-VM.10 (+)Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
  • HS.N-VM.11 (+)Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Understand a matrix as a transformation of vectors.
  • HS.N-VM.12 (+)Understand a 2 2 matrix as a transformation of the plane. Interpret the absolute value of the determinant in terms of area.

HS.S-CP

  • HS.S-CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).
  • HS.S-CP.2 Understand that event A is independent from event B if the probability of event A does not change in response to the occurrence of event B. Apply the formula P(A and B) = P(A) * P(B) given that event A and B are independent.
  • HS.S-CP.3 Understand that the conditional probability of an event A given B is the probability that event A will occur given the knowledge that event B has already occurred. Apply the formula P(A given B) = P(A and B)/P(B) given a conditional probability situation.
  • HS.S-CP.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.
  • HS.S-CP.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
  • HS.S-CP.6 Find the conditional probability of A given B and interpret the answer in terms of the model.
  • HS.S-CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
  • HS.S-CP.8 Apply the general Multiplication Rule in a uniform probability model, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
  • HS.S-CP.9 Use permutations and combinations to determine the number of outcomes in terms of the model. (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

HS.S-IC

  • HS.S-IC.1 Understand the process of making inferences about population parameters based on a random sample from that population.
  • HS.S-IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.
  • HS.S-IC.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
  • HS.S-IC.4 (+)Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.
  • HS.S-IC.5 This standard has been moved/removed by the committee
  • HS.S-IC.6.a Evaluate articles, reports or websites based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed.
  • HS.S-IC.6.b Identify and explain misleading use of data; recognize when claims based on data confuse correlation and causation.
  • HS.S-IC.6.c Recognize and describe how graphs and data can be distorted to support different points of view.

HS.S-ID

  • HS.S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • HS.S-ID.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.
  • HS.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).
  • HS.S-ID.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, or tables to estimate areas under the normal curve.
  • HS.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.
  • HS.S-ID.6.a Fit a function to the data (with or without technology). Use functions fitted to data to solve problems in the context of the data.
  • HS.S-ID.6.b (+) Informally assess the fit of a function by plotting and analyzing residuals.
  • HS.S-ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. Interpolate and extrapolate the linear model to predict values.
  • HS.S-ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.
  • HS.S-ID.9 Distinguish between correlation and causation.

HS.S-MD

  • HS.S-MD.1 (+)Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space. Graph the corresponding probability distribution using the same graphical displays as for data distributions.
  • HS.S-MD.2 (+)Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
  • HS.S-MD.3 (+)Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.
  • HS.S-MD.4 (+)Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
  • HS.S-MD.5.a Find the expected payoff for a game of chance.
  • HS.S-MD.5.b Evaluate and compare strategies on the basis of expected values.
  • HS.S-MD.6 (+)Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
  • HS.S-MD.7 (+)Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).