MAFS.912.A-APR: Arithmetic with Polynomials and Rational Expressions

MAFS.912.A-APR.1: Perform arithmetic operations on polynomials

MAFS.912.A-APR.1.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

 Addition of Polynomials

MAFS.912.A-APR.2: Understand the relationship between zeros and factors of polynomials

MAFS.912.A-APR.2.2: Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

 Dividing Polynomials Using Synthetic Division
 Polynomials and Linear Factors

MAFS.912.A-APR.2.3: Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

 Polynomials and Linear Factors
 Quadratics in Factored Form

MAFS.912.A-APR.3: Use polynomial identities to solve problems

MAFS.912.A-APR.3.5: Know and apply the Binomial Theorem for the expansion of (x + y) to the n power in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal?s Triangle.

 Binomial Probabilities

MAFS.912.A-CED: Creating Equations

MAFS.912.A-CED.1: Create equations that describe numbers or relationships

MAFS.912.A-CED.1.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational, absolute, and exponential functions.

 Absolute Value Equations and Inequalities
 Arithmetic Sequences
 Compound Interest
 Exploring Linear Inequalities in One Variable
 Exponential Growth and Decay
 Geometric Sequences
 Modeling and Solving Two-Step Equations
 Quadratic Inequalities
 Solving Linear Inequalities in One Variable
 Solving Two-Step Equations

MAFS.912.A-CED.1.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

 2D Collisions
 Air Track
 Compound Interest
 Determining a Spring Constant
 Golf Range
 Points, Lines, and Equations
 Slope-Intercept Form of a Line

MAFS.912.A-CED.1.3: 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.

 Linear Programming

MAFS.912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

 Solving Formulas for any Variable

MAFS.912.A-REI: Reasoning with Equations and Inequalities

MAFS.912.A-REI.1: Understand solving equations as a process of reasoning and explain the reasoning

MAFS.912.A-REI.1.1: 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.

 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Formulas for any Variable

MAFS.912.A-REI.1.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

 Radical Functions

MAFS.912.A-REI.2: Solve equations and inequalities in one variable

MAFS.912.A-REI.2.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

 Exploring Linear Inequalities in One Variable
 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Linear Inequalities in One Variable

MAFS.912.A-REI.2.4: Solve quadratic equations in one variable.

MAFS.912.A-REI.2.4.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.

 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c
 Roots of a Quadratic

MAFS.912.A-REI.3: Solve systems of equations

MAFS.912.A-REI.3.5: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)

MAFS.912.A-REI.3.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

 Cat and Mouse (Modeling with Linear Systems)
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)

MAFS.912.A-REI.3.8: Represent a system of linear equations as a single matrix equation in a vector variable.

 Solving Linear Systems (Matrices and Special Solutions)

MAFS.912.A-REI.4: Represent and solve equations and inequalities graphically

MAFS.912.A-REI.4.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

 Circles
 Ellipses
 Hyperbolas
 Parabolas
 Points, Lines, and Equations

MAFS.912.A-REI.4.11: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

 Solving Equations by Graphing Each Side
 Solving Linear Systems (Slope-Intercept Form)

MAFS.912.A-REI.4.12: Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

 Linear Inequalities in Two Variables

MAFS.912.A-SSE: Seeing Structure in Expressions

MAFS.912.A-SSE.1: Interpret the structure of expressions

MAFS.912.A-SSE.1.1: Interpret expressions that represent a quantity in terms of its context.

MAFS.912.A-SSE.1.1.a: Interpret parts of an expression, such as terms, factors, and coefficients.

 Compound Interest
 Exponential Growth and Decay
 Unit Conversions

MAFS.912.A-SSE.1.1.b: Interpret complicated expressions by viewing one or more of their parts as a single entity.

 Compound Interest
 Exponential Growth and Decay
 Translating and Scaling Functions
 Using Algebraic Expressions

MAFS.912.A-SSE.1.2: Use the structure of an expression to identify ways to rewrite it.

 Equivalent Algebraic Expressions II
 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c
 Simplifying Algebraic Expressions I
 Simplifying Algebraic Expressions II
 Solving Algebraic Equations II

MAFS.912.A-SSE.2: Write expressions in equivalent forms to solve problems

MAFS.912.A-SSE.2.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

MAFS.912.A-SSE.2.3.a: Factor a quadratic expression to reveal the zeros of the function it defines.

 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c

MAFS.912.F-BF: Building Functions

MAFS.912.F-BF.1: Build a function that models a relationship between two quantities

MAFS.912.F-BF.1.1: Write a function that describes a relationship between two quantities.

MAFS.912.F-BF.1.1.a: Determine an explicit expression, a recursive process, or steps for calculation from a context.

 Arithmetic Sequences
 Geometric Sequences

MAFS.912.F-BF.1.2: Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

 Arithmetic Sequences
 Geometric Sequences

MAFS.912.F-BF.2: Build new functions from existing functions

MAFS.912.F-BF.2.3: 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. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

 Exponential Functions
 Logarithmic Functions
 Translating and Scaling Functions
 Translating and Scaling Sine and Cosine Functions
 Zap It! Game

MAFS.912.F-BF.2.4: Find inverse functions.

MAFS.912.F-BF.2.4.b: Verify by composition that one function is the inverse of another.

 Logarithmic Functions

MAFS.912.F-BF.2.4.c: Read values of an inverse function from a graph or a table, given that the function has an inverse.

 Logarithmic Functions

MAFS.912.F-BF.2.5: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

 Logarithmic Functions

MAFS.912.F-IF: Interpreting Functions

MAFS.912.F-IF.1: Understand the concept of a function and use function notation

MAFS.912.F-IF.1.1: 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).

 Introduction to Functions
 Points, Lines, and Equations

MAFS.912.F-IF.1.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

 Absolute Value with Linear Functions
 Translating and Scaling Functions

MAFS.912.F-IF.2: Interpret functions that arise in applications in terms of the context

MAFS.912.F-IF.2.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

 Distance-Time Graphs
 Distance-Time and Velocity-Time Graphs

MAFS.912.F-IF.2.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

 General Form of a Rational Function
 Introduction to Functions
 Radical Functions
 Rational Functions

MAFS.912.F-IF.2.6: 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.

 Distance-Time Graphs
 Distance-Time and Velocity-Time Graphs

MAFS.912.F-IF.3: Analyze functions using different representations

MAFS.912.F-IF.3.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

MAFS.912.F-IF.3.7.a: Graph linear and quadratic functions and show intercepts, maxima, and minima.

 Linear Functions
 Points, Lines, and Equations
 Quadratics in Factored Form
 Quadratics in Polynomial Form
 Quadratics in Vertex Form
 Slope-Intercept Form of a Line
 Zap It! Game

MAFS.912.F-IF.3.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

 Absolute Value with Linear Functions
 Radical Functions

MAFS.912.F-IF.3.7.c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

 Graphs of Polynomial Functions
 Polynomials and Linear Factors
 Quadratics in Factored Form
 Quadratics in Vertex Form
 Roots of a Quadratic
 Zap It! Game

MAFS.912.F-IF.3.7.d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

 General Form of a Rational Function
 Rational Functions

MAFS.912.F-IF.3.7.e: Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude, and using phase shift.

 Cosine Function
 Exponential Functions
 Exponential Growth and Decay
 Logarithmic Functions
 Logarithmic Functions: Translating and Scaling
 Sine Function
 Tangent Function

MAFS.912.F-IF.3.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

MAFS.912.F-IF.3.8.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.

 Factoring Special Products
 Modeling the Factorization of ax2+bx+c
 Modeling the Factorization of x2+bx+c

MAFS.912.F-IF.3.8.b: Use the properties of exponents to interpret expressions for exponential functions.

 Compound Interest
 Exponential Growth and Decay

MAFS.912.F-LE: Linear, Quadratic, and Exponential Models

MAFS.912.F-LE.1: Construct and compare linear, quadratic, and exponential models and solve problems

MAFS.912.F-LE.1.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

MAFS.912.F-LE.1.1.a: Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

 Compound Interest
 Linear Functions

MAFS.912.F-LE.1.1.b: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

 Arithmetic Sequences
 Compound Interest
 Distance-Time Graphs
 Distance-Time and Velocity-Time Graphs
 Linear Functions

MAFS.912.F-LE.1.1.c: Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

 Drug Dosage
 Exponential Growth and Decay
 Half-life

MAFS.912.F-LE.1.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

 Compound Interest
 Exponential Functions
 Exponential Growth and Decay
 Point-Slope Form of a Line
 Slope-Intercept Form of a Line

MAFS.912.F-LE.1.4: For exponential models, express as a logarithm the solution to ab to the ct power = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

 Compound Interest

MAFS.912.F-LE.2: Interpret expressions for functions in terms of the situation they model

MAFS.912.F-LE.2.5: Interpret the parameters in a linear or exponential function in terms of a context.

 Arithmetic Sequences
 Compound Interest
 Distance-Time Graphs
 Distance-Time and Velocity-Time Graphs
 Exponential Growth and Decay

MAFS.912.F-TF: Trigonometric Functions

MAFS.912.F-TF.2: Model periodic phenomena with trigonometric functions

MAFS.912.F-TF.2.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

 Sound Beats and Sine Waves

MAFS.912.F-TF.3: Prove and apply trigonometric identities

MAFS.912.F-TF.3.9: Prove the addition and subtraction, half-angle, and double-angle formulas for sine, cosine, and tangent and use these formulas to solve problems.

 Simplifying Trigonometric Expressions
 Sum and Difference Identities for Sine and Cosine

MAFS.912.G-C: Circles

MAFS.912.G-C.1: Understand and apply theorems about circles

MAFS.912.G-C.1.2: Identify and describe relationships among inscribed angles, radii, and chords.

 Inscribed Angles

MAFS.912.G-C.2: Find arc lengths and areas of sectors of circles

MAFS.912.G-C.2.5: 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.

 Chords and Arcs

MAFS.912.G-CO: Congruence

MAFS.912.G-CO.1: Experiment with transformations in the plane

MAFS.912.G-CO.1.1: Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

 Circles
 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines

MAFS.912.G-CO.1.2: Represent transformations in the plane using, e.g., transparencies and geometry software; 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).

 Dilations
 Reflections
 Rotations, Reflections, and Translations
 Translations

MAFS.912.G-CO.1.4: Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

 Dilations
 Reflections
 Rotations, Reflections, and Translations
 Translations

MAFS.912.G-CO.1.5: 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.

 Dilations
 Reflections
 Rotations, Reflections, and Translations
 Translations

MAFS.912.G-CO.2: Understand congruence in terms of rigid motions

MAFS.912.G-CO.2.6: Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

 Proving Triangles Congruent
 Reflections
 Rotations, Reflections, and Translations
 Translations

MAFS.912.G-CO.2.8: Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.

 Proving Triangles Congruent

MAFS.912.G-CO.3: Prove geometric theorems

MAFS.912.G-CO.3.9: Prove theorems about lines and angles; use theorems about lines and angles to solve problems.

 Investigating Angle Theorems

MAFS.912.G-CO.3.10: Prove theorems about triangles; use theorems about triangles to solve problems.

 Pythagorean Theorem
 Triangle Angle Sum
 Triangle Inequalities

MAFS.912.G-CO.3.11: Prove theorems about parallelograms; use theorems about parallelograms to solve problems.

 Parallelogram Conditions
 Special Parallelograms

MAFS.912.G-CO.4: Make geometric constructions

MAFS.912.G-CO.4.12: Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines

MAFS.912.G-GPE: Expressing Geometric Properties with Equations

MAFS.912.G-GPE.1: Translate between the geometric description and the equation for a conic section

MAFS.912.G-GPE.1.1: 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.

 Circles
 Distance Formula
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard

MAFS.912.G-GPE.1.2: Derive the equation of a parabola given a focus and directrix.

 Parabolas

MAFS.912.G-GPE.1.3: Derive the equations of ellipses and hyperbolas given the foci and directrices.

 Ellipses
 Hyperbolas

MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically

MAFS.912.G-GPE.2.7: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

 Distance Formula

MAFS.912.G-GMD: Geometric Measurement and Dimension

MAFS.912.G-GMD.1: Explain volume formulas and use them to solve problems

MAFS.912.G-GMD.1.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

 Circumference and Area of Circles
 Prisms and Cylinders
 Pyramids and Cones

MAFS.912.G-GMD.1.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

 Prisms and Cylinders
 Pyramids and Cones

MAFS.912.G-SRT: Similarity, Right Triangles, and Trigonometry

MAFS.912.G-SRT.1: Understand similarity in terms of similarity transformations

MAFS.912.G-SRT.1.1: Verify experimentally the properties of dilations given by a center and a scale factor:

MAFS.912.G-SRT.1.1.b: The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

 Dilations
 Similar Figures

MAFS.912.G-SRT.1.2: Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

 Similar Figures

MAFS.912.G-SRT.2: Prove theorems involving similarity

MAFS.912.G-SRT.2.4: Prove theorems about triangles.

 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Similar Figures

MAFS.912.G-SRT.2.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

 Dilations
 Perimeters and Areas of Similar Figures
 Similarity in Right Triangles

MAFS.912.G-SRT.3: Define trigonometric ratios and solve problems involving right triangles

MAFS.912.G-SRT.3.6: 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.

 Sine, Cosine, and Tangent Ratios

MAFS.912.G-SRT.3.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

 Distance Formula
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine, Cosine, and Tangent Ratios

MAFS.912.N-CN: The Complex Number System

MAFS.912.N-CN.1: Perform arithmetic operations with complex numbers.

MAFS.912.N-CN.1.1: 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.

 Points in the Complex Plane

MAFS.912.N-CN.1.2: Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

 Points in the Complex Plane

MAFS.912.N-CN.1.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

 Points in the Complex Plane

MAFS.912.N-CN.2: Represent complex numbers and their operations on the complex plane.

MAFS.912.N-CN.2.4: Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

 Points in the Complex Plane

MAFS.912.N-CN.3: Use complex numbers in polynomial identities and equations.

MAFS.912.N-CN.3.7: Solve quadratic equations with real coefficients that have complex solutions.

 Roots of a Quadratic

MAFS.912.N-RN: The Real Number System

MAFS.912.N-RN.1: Extend the properties of exponents to rational exponents.

MAFS.912.N-RN.1.1: 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.

 Exponents and Power Rules

MAFS.912.N-VM: Vector and Matrix Quantities

MAFS.912.N-VM.1: Represent and model with vector quantities.

MAFS.912.N-VM.1.1: 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).

 Vectors

MAFS.912.N-VM.1.2: Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

 Vectors

MAFS.912.N-VM.1.3: Solve problems involving velocity and other quantities that can be represented by vectors.

 2D Collisions
 Golf Range

MAFS.912.N-VM.2: Perform operations on vectors.

MAFS.912.N-VM.2.4: Add and subtract vectors.

MAFS.912.N-VM.2.4.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.

 Adding Vectors
 Vectors

MAFS.912.N-VM.2.4.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.

 Adding Vectors
 Vectors

MAFS.912.N-VM.2.5: Multiply a vector by a scalar.

MAFS.912.N-VM.2.5.a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(v subscript x, v subscript y) = (cv subscript x, cv subscript y).

 Dilations

MAFS.912.S-CP: Conditional Probability and the Rules of Probability

MAFS.912.S-CP.1: Understand independence and conditional probability and use them to interpret data

MAFS.912.S-CP.1.1: 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').

 Independent and Dependent Events
 Probability Simulations
 Theoretical and Experimental Probability

MAFS.912.S-CP.1.2: 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.

 Independent and Dependent Events

MAFS.912.S-CP.1.3: 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.

 Independent and Dependent Events

MAFS.912.S-CP.2: Use the rules of probability to compute probabilities of compound events in a uniform probability model

MAFS.912.S-CP.2.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

 Binomial Probabilities
 Permutations and Combinations

MAFS.912.S-ID: Interpreting Categorical and Quantitative Data

MAFS.912.S-ID.1: Summarize, represent, and interpret data on a single count or measurement variable

MAFS.912.S-ID.1.1: Represent data with plots on the real number line (dot plots, histograms, and box plots).

 Box-and-Whisker Plots
 Histograms
 Mean, Median, and Mode

MAFS.912.S-ID.1.2: 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.

 Box-and-Whisker Plots
 Describing Data Using Statistics
 Real-Time Histogram
 Sight vs. Sound Reactions

MAFS.912.S-ID.1.3: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

 Mean, Median, and Mode
 Reaction Time 2 (Graphs and Statistics)

MAFS.912.S-ID.2: Summarize, represent, and interpret data on two categorical and quantitative variables

MAFS.912.S-ID.2.6: Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

MAFS.912.S-ID.2.6.a: Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Zap It! Game

MAFS.912.S-ID.2.6.b: Informally assess the fit of a function by plotting and analyzing residuals.

 Least-Squares Best Fit Lines

MAFS.912.S-ID.2.6.c: Fit a linear function for a scatter plot that suggests a linear association.

 Least-Squares Best Fit Lines

MAFS.912.S-ID.3: Interpret linear models

MAFS.912.S-ID.3.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

 Cat and Mouse (Modeling with Linear Systems)

MAFS.912.S-ID.3.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.

 Correlation

MAFS.912.S-IC: Making Inferences and Justifying Conclusions

MAFS.912.S-IC.2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies

MAFS.912.S-IC.2.4: 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.

 Estimating Population Size
 Polling: City
 Polling: Neighborhood

MAFS.912.S-IC.2.5: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

 Real-Time Histogram
 Sight vs. Sound Reactions

MAFS.912.S-MD: Using Probability to Make Decisions

MAFS.912.S-MD.1: Calculate expected values and use them to solve problems

MAFS.912.S-MD.1.3: Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

 Independent and Dependent Events
 Probability Simulations
 Theoretical and Experimental Probability

MAFS.912.S-MD.1.4: Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.

 Geometric Probability
 Independent and Dependent Events
 Probability Simulations
 Theoretical and Experimental Probability

Correlation last revised: 4/4/2018

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.