Alaska Content Standards: Mathematics 2
Skills available for Alaska Integrated 2 math standards
Standard
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9-12.N
Number and Quantity
9-12.N-RN The Real Number System
Extend the properties of exponents to rational exponents.
Extend the properties of exponents to rational exponents.
9-12.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.
9-12.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.
9-12.N-RN.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Rational exponents
Radical expressions
9-12.N-RN.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Rational exponents
Radical expressions
Use properties of rational and irrational numbers.
Use properties of rational and irrational numbers.
9-12.N-RN.3: Explain why 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.
9-12.N-RN.3: Explain why 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.
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9-12.N-CN The Complex Number System
Perform arithmetic operations with complex numbers.
Perform arithmetic operations with complex numbers.
9-12.N-CN.1: Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.
9-12.N-CN.1: Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.
9-12.N-CN.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
9-12.N-CN.2: Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Use complex numbers in polynomial identities and equations.
Use complex numbers in polynomial identities and equations.
9-12.N-CN.7: Solve quadratic equations with real coefficients that have complex solutions.
9-12.N-CN.7: Solve quadratic equations with real coefficients that have complex solutions.
9-12.N-CN.8: Extend polynomial identities to the complex numbers.
9-12.N-CN.8: Extend polynomial identities to the complex numbers.
9-12.N-CN.9: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
9-12.N-CN.9: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
9-12.A
Algebra
9-12.A-SSE Seeing Structure in Expressions
Interpret the structure of expressions.
Interpret the structure of expressions.
9-12.A-SSE.1: Interpret expressions that represent a quantity in terms of its context.
9-12.A-SSE.1: Interpret expressions that represent a quantity in terms of its context.
9-12.A-SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.
9-12.A-SSE.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.
9-12.A-SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
9-12.A-SSE.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.
9-12.A-SSE.2: Use the structure of an expression to identify ways to rewrite it.
Quadratic expressions
Integer exponents
Rational exponents
Radical expressions
9-12.A-SSE.2: Use the structure of an expression to identify ways to rewrite it.
Quadratic expressions
Integer exponents
Rational exponents
Radical expressions
Write expressions in equivalent forms to solve problems.
Write expressions in equivalent forms to solve problems.
9-12.A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
9-12.A-SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
9-12.A-SSE.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.
Factor quadratics
Zeros of a function
9-12.A-SSE.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.
Factor quadratics
Zeros of a function
9-12.A-SSE.3.b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
9-12.A-SSE.3.b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
9-12.A-SSE.3.c: Use the properties of exponents to transform expressions for exponential functions.
9-12.A-SSE.3.c: Use the properties of exponents to transform expressions for exponential functions.
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9-12.A-APR Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials.
Perform arithmetic operations on polynomials.
9-12.A-APR.1: Add, subtract, and multiply polynomials. Understand that polynomials form a system similar to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
Model polynomials
Addition and subtraction
Multiplication
9-12.A-APR.1: Add, subtract, and multiply polynomials. Understand that polynomials form a system similar to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.
Model polynomials
Addition and subtraction
Multiplication
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9-12.A-CED Creating Equations and Inequalities
Create equations and inequalities that describe numbers or relationships.
Create equations and inequalities that describe numbers or relationships.
9-12.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.
9-12.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.
9-12.A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quadratic equations
Linear, quadratic, and exponential equations
9-12.A-CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Quadratic equations
Linear, quadratic, and exponential equations
9-12.A-CED.4: Rearrange formulas (literal equations) to highlight a quantity of interest, using the same reasoning as in solving equations.
9-12.A-CED.4: Rearrange formulas (literal equations) to highlight a quantity of interest, using the same reasoning as in solving equations.
9-12.A-REI Reasoning with Equations and Inequalities
Solve equations and inequalities in one variable.
Solve equations and inequalities in one variable.
9-12.A-REI.4: Solve quadratic equations in one variable.
9-12.A-REI.4: Solve quadratic equations in one variable.
9-12.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.
9-12.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.
9-12.A-REI.4.b: 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. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Square roots
Factoring
Completing the square
Quadratic formula
Any method
9-12.A-REI.4.b: 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. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Square roots
Factoring
Completing the square
Quadratic formula
Any method
Solve systems of equations.
Solve systems of equations.
9-12.A-REI.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
9-12.A-REI.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
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9-12.F
Functions
9-12.F-IF Interpreting Functions
Interpret functions that arise in applications in terms of the context.
Interpret functions that arise in applications in terms of the context.
9-12.F-IF.4: For a function that models a relationship between two quantities,
9-12.F-IF.4: For a function that models a relationship between two quantities,
9-12.F-IF.4.a: interpret key features of graphs and tables in terms of the quantities, and
Quadratic functions
Linear, quadratic, and exponential functions
Linear functions
9-12.F-IF.4.a: interpret key features of graphs and tables in terms of the quantities, and
Quadratic functions
Linear, quadratic, and exponential functions
Linear functions
9-12.F-IF.4.b: sketch graphs showing key features given a verbal description of the relationship.
Quadratic functions
Absolute value functions
Linear functions
Word problems
9-12.F-IF.4.b: sketch graphs showing key features given a verbal description of the relationship.
Quadratic functions
Absolute value functions
Linear functions
Word problems
9-12.F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Absolute value functions
Quadratic functions
9-12.F-IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Absolute value functions
Quadratic functions
9-12.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.
9-12.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.
Analyze functions using different representations.
Analyze functions using different representations.
9-12.F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
9-12.F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
9-12.F-IF.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
Linear functions
Quadratic functions
9-12.F-IF.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.
Linear functions
Quadratic functions
9-12.F-IF.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
9-12.F-IF.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
9-12.F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
9-12.F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
9-12.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.
9-12.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.
9-12.F-IF.8.b: Use the properties of exponents to interpret expressions for exponential functions.
9-12.F-IF.8.b: Use the properties of exponents to interpret expressions for exponential functions.
9-12.F-IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions).
9-12.F-IF.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically, in tables, or by verbal descriptions).
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9-12.F-BF Building Functions
Build a function that models a relationship between two quantities.
Build a function that models a relationship between two quantities.
9-12.F-BF.1: Write a function that describes a relationship between two quantities.
9-12.F-BF.1: Write a function that describes a relationship between two quantities.
9-12.F-BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
Sequences
Linear, quadratic, and exponential functions
9-12.F-BF.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.
Sequences
Linear, quadratic, and exponential functions
9-12.F-BF.1.b: Combine standard function types using arithmetic operations.
9-12.F-BF.1.b: Combine standard function types using arithmetic operations.
Build new functions from existing functions.
Build new functions from existing functions.
9-12.F-BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Quadratic functions
Absolute value functions
Function transformations
9-12.F-BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs.
Quadratic functions
Absolute value functions
Function transformations
9-12.F-BF.4: Find inverse functions.
9-12.F-BF.4: Find inverse functions.
9-12.F-BF.4.a: Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
9-12.F-BF.4.a: Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
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9-12.F-LE Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems.
Construct and compare linear, quadratic, and exponential models and solve problems.
9-12.F-LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
9-12.F-LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
9-12.F-TF Trigonometric Functions
Prove and apply trigonometric identities.
Prove and apply trigonometric identities.
9-12.F-TF.8: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to calculate trigonometric ratios.
9-12.F-TF.8: Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to calculate trigonometric ratios.
9-12.G
Geometry
9-12.G-CO Congruence
Prove geometric theorems.
Prove geometric theorems.
9-12.G-CO.9: Using methods of proof including direct, indirect, and counter examples to prove theorems about lines and angles.
Angles
Parallel lines
Perpendicular bisectors
9-12.G-CO.9: Using methods of proof including direct, indirect, and counter examples to prove theorems about lines and angles.
Angles
Parallel lines
Perpendicular bisectors
9-12.G-CO.10: Using methods of proof including direct, indirect, and counter examples to prove theorems about triangles.
Isosceles triangles
Angles in triangles
Segments in triangles
Centroids or orthocenters of triangles
9-12.G-CO.10: Using methods of proof including direct, indirect, and counter examples to prove theorems about triangles.
Isosceles triangles
Angles in triangles
Segments in triangles
Centroids or orthocenters of triangles
9-12.G-CO.11: Using methods of proof including direct, indirect, and counter examples to prove theorems about parallelograms.
9-12.G-CO.11: Using methods of proof including direct, indirect, and counter examples to prove theorems about parallelograms.
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9-12.G-SRT Similarity, Right Triangles, and Trigonometry
Understand similarity in terms of similarity transformations.
Understand similarity in terms of similarity transformations.
9-12.G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:
9-12.G-SRT.1: Verify experimentally the properties of dilations given by a center and a scale factor:
9-12.G-SRT.1.a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
9-12.G-SRT.1.a: A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
9-12.G-SRT.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
9-12.G-SRT.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
9-12.G-SRT.2: Given two figures, use the definition of similarity in terms of transformations to explain whether or not they are similar.
9-12.G-SRT.2: Given two figures, use the definition of similarity in terms of transformations to explain whether or not they are similar.
9-12.G-SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
9-12.G-SRT.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
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Prove theorems involving similarity.
Prove theorems involving similarity.
9-12.G-SRT.4: Prove theorems about triangles.
9-12.G-SRT.4: Prove theorems about triangles.
9-12.G-SRT.5: Apply congruence and similarity properties and prove relationships involving triangles and other geometric figures.
Congruent triangles
Proofs involving congruent triangles
Isosceles, equilateral, and right triangles
Similar triangles
Proofs involving similar triangles
9-12.G-SRT.5: Apply congruence and similarity properties and prove relationships involving triangles and other geometric figures.
Congruent triangles
Proofs involving congruent triangles
Isosceles, equilateral, and right triangles
Similar triangles
Proofs involving similar triangles
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Define trigonometric ratios and solve problems involving right triangles.
Define trigonometric ratios and solve problems involving right triangles.
9-12.G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
9-12.G-SRT.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
9-12.G-SRT.7: Explain and use the relationship between the sine and cosine of complementary angles.
9-12.G-SRT.7: Explain and use the relationship between the sine and cosine of complementary angles.
9-12.G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem
Trigonometric ratios
Solve a right triangle
9-12.G-SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Pythagorean Theorem
Trigonometric ratios
Solve a right triangle
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9-12.G-C Circles
Understand and apply theorems about circles.
Understand and apply theorems about circles.
9-12.G-C.1: Prove that all circles are similar.
9-12.G-C.1: Prove that all circles are similar.
9-12.G-C.2: Identify and describe relationships among inscribed angles, radii, and chords.
Central and inscribed angles
Chords, secants, and tangents
9-12.G-C.2: Identify and describe relationships among inscribed angles, radii, and chords.
Central and inscribed angles
Chords, secants, and tangents
9-12.G-C.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Constructions
Properties of angles
9-12.G-C.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Constructions
Properties of angles
9-12.G-C.4: Construct a tangent line from a point outside a given circle to the circle.
9-12.G-C.4: Construct a tangent line from a point outside a given circle to the circle.
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Find arc lengths and areas of sectors of circles.
Find arc lengths and areas of sectors of circles.
9-12.G-C.5: Use and apply the concepts of arc length and areas of sectors of circles. Determine or derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
9-12.G-C.5: Use and apply the concepts of arc length and areas of sectors of circles. Determine or derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
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9-12.G-GPE Expressing Geometric Properties with Equations
Translate between the geometric description and the equation for a conic section.
Translate between the geometric description and the equation for a conic section.
9-12.G-GPE.1: Determine or derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Complete the square
Write equations and graph circles
9-12.G-GPE.1: Determine or derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Complete the square
Write equations and graph circles
9-12.G-GPE.2: Determine or derive the equation of a parabola given a focus and directrix.
Find properties
Write equations
Graph parabolas
9-12.G-GPE.2: Determine or derive the equation of a parabola given a focus and directrix.
Find properties
Write equations
Graph parabolas
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Use coordinates to prove simple geometric theorems algebraically.
Use coordinates to prove simple geometric theorems algebraically.
9-12.G-GPE.4: Perform simple coordinate proofs. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
9-12.G-GPE.4: Perform simple coordinate proofs. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
9-12.G-GPE.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
9-12.G-GPE.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
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9-12.G-GMD Geometric Measurement and Dimension
Explain volume formulas and use them to solve problems.
Explain volume formulas and use them to solve problems.
9-12.G-GMD.1: Explain how to find the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
9-12.G-GMD.1: Explain how to find the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.
9-12.G-GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
9-12.G-GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
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9-12.S
Statistics and Probability
9-12.S-CP Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data.
Understand independence and conditional probability and use them to interpret data.
9-12.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").
9-12.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").
9-12.S-CP.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
9-12.S-CP.2: Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
9-12.S-CP.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
9-12.S-CP.3: Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
9-12.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.
9-12.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.
9-12.S-CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
9-12.S-CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
Use the rules of probability to compute probabilities of compound events in a uniform probability model.
9-12.S-CP.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
9-12.S-CP.6: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
9-12.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.
9-12.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.
9-12.S-CP.8: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
9-12.S-CP.8: Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
9-12.S-CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.
9-12.S-CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.
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9-12.S-MD Using Probability to Make Decisions
Use probability to evaluate outcomes of decisions.
Use probability to evaluate outcomes of decisions.
9-12.S-MD.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
9-12.S-MD.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
9-12.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).
9-12.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).