Mathematics Florida Standards
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.
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.
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.
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.
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.A-SSE.2.3.c: Use the properties of exponents to transform expressions for exponential functions.
Dividing Exponential Expressions
Exponents and Power Rules
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
MAFS.912.G-GPE.1.3: Derive the equations of ellipses and hyperbolas given the foci and directrices.
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.
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.
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.
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.
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.
MAFS.912.N-CN.1.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
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.
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.
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.
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).
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.
MAFS.912.N-VM.1.3: Solve problems involving velocity and other quantities that can be represented by vectors.
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.
MAFS.912.N-VM.2.4.b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
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).
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.
MAFS.912.S-ID.2.6.c: Fit a linear function for a scatter plot that suggests a linear association.
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.
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.1.2: Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
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
Lucky Duck (Expected Value)
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
Lucky Duck (Expected Value)
Probability Simulations
Theoretical and Experimental Probability
MAFS.912.S-MD.2: Use probability to evaluate outcomes of decisions
MAFS.912.S-MD.2.5: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
MAFS.912.S-MD.2.5.a: Find the expected payoff for a game of chance.
MAFS.912.S-MD.2.5.b: Evaluate and compare strategies on the basis of expected values.
MAFS.912.S-MD.2.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
MAFS.912.S-MD.2.7: Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Correlation last revised: 9/16/2020