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.
Addition of Polynomials - Activity A
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
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.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors
MAFS.912.A-APR.3: Use polynomial identities to solve problems
MAFS.912.A-APR.3.4: Prove polynomial identities and use them to describe numerical relationships.
Factoring Special Products
Modeling the Factorization of x2+bx+c
MAFS.912.A-CED: Creating Equations
MAFS.912.A-CED.1: Create equations that describe numbers or relationships
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.
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 - Activity A
System of Two Quadratic Inequalities
Systems of Linear Inequalities (Slope-intercept form) - Activity A
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 and Solving Two-Step Equations
Solving Formulas for any Variable
Solving Two-Step Equations
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.
Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Solving Two-Step Equations
System of Two Quadratic Inequalities
MAFS.912.A-REI.2.4: Solve quadratic equations in one variable.
MAFS.912.A-REI.2.4.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.
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
Roots of a Quadratic
Square Roots
MAFS.912.A-REI.3: Solve systems of equations
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.
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
MAFS.912.A-REI.3.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Solving Linear Systems by Graphing
Special Types of Solutions to Linear Systems
Systems of Linear Equations - Activity A
MAFS.912.A-REI.3.9: 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).
Systems of Linear Equations - Activity A
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).
Modeling and Solving Two-Step Equations
Solving Two-Step 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.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
General Form of a Rational Function
Logarithmic Functions - Activity A
Logarithmic Functions: Translating and Scaling
Quadratic and Absolute Value Functions
Rational Functions
Slope-Intercept Form of a Line - Activity B
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.
Inequalities Involving Absolute Values
Linear Inequalities in Two Variables - Activity A
Linear Programming - Activity A
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
System of Two Quadratic Inequalities
Systems of Linear Inequalities (Slope-intercept form) - Activity A
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.
Finding Factors with Area Models
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.
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
Quadratics in Factored Form
Roots of a Quadratic
MAFS.912.A-SSE.2.3.b: Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
Parabolas - Activity A
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
MAFS.912.A-SSE.2.3.c: Use the properties of exponents to transform expressions for exponential functions.
Multiplying Exponential Expressions
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.
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
MAFS.912.F-BF.1.1.b: Combine standard function types using arithmetic operations.
Addition and Subtraction of Polynomials
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
MAFS.912.F-BF.1.1.c: Compose functions.
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
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
Arithmetic and Geometric 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.
Translating and Scaling Functions
MAFS.912.F-BF.2.4: Find inverse functions.
MAFS.912.F-BF.2.4.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.
Function Machines 3 (Functions and Problem Solving)
Modeling and Solving Two-Step Equations
Solving Two-Step Equations
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.
Cosine Function
Fourth-Degree Polynomials - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions - Activity A
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
MAFS.912.F-BF.2.4.d: Produce an invertible function from a non-invertible function by restricting the domain.
Function Machines 3 (Functions and Problem Solving)
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.
Function Machines 3 (Functions and Problem Solving)
Logarithmic Functions - Activity A
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).
Cosine Function
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Functions Involving Square Roots
Introduction to Functions
Rational Functions
Sine Function
Tangent Function
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.
Linear Functions
Points, Lines, and Equations
MAFS.912.F-IF.1.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear 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.
Cosine Function
Fourth-Degree Polynomials - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Functions Involving Square Roots
Linear Functions
Points, Lines, and Equations
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Sine Function
Tangent Function
MAFS.912.F-IF.2.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Functions Involving Square Roots
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.
Direct and Inverse Variation
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations
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.
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B
MAFS.912.F-IF.3.7.b: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Function Machines 2 (Functions, Tables, and Graphs)
Functions Involving Square Roots
Quadratic and Absolute Value Functions
Radical Functions
Square Roots
MAFS.912.F-IF.3.7.c: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Function Machines 2 (Functions, Tables, and Graphs)
Polynomials and Linear Factors
MAFS.912.F-IF.3.7.d: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
Function Machines 2 (Functions, Tables, and Graphs)
General Form of a Rational Function
Polynomials and Linear Factors
Rational Functions
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.
Function Machines 2 (Functions, Tables, and Graphs)
Parabolas - Activity A
Polynomials and Linear Factors
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
MAFS.912.F-IF.3.8.b: Use the properties of exponents to interpret expressions for exponential functions.
Multiplying Exponential Expressions
MAFS.912.F-IF.3.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Cosine Function
Fourth-Degree Polynomials - Activity A
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Functions Involving Square Roots
Introduction to Functions
Linear Functions
Logarithmic Functions - Activity A
Points, Lines, and Equations
Polynomials and Linear Factors
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions
Sine Function
Tangent Function
Using Algebraic Equations
Using Algebraic Expressions
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.
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Points, Lines, and Equations
Slope-Intercept Form of a Line - Activity B
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).
Arithmetic Sequences
Arithmetic and Geometric Sequences
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Geometric Sequences
Linear Functions
Points, Lines, and Equations
Slope-Intercept Form of a Line - Activity B
MAFS.912.F-LE.1.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Function Machines 2 (Functions, Tables, and Graphs)
Introduction to Exponential Functions
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.
Function Machines 2 (Functions, Tables, and Graphs)
Slope-Intercept Form of a Line - Activity B
MAFS.912.F-TF: Trigonometric Functions
MAFS.912.F-TF.1: Extend the domain of trigonometric functions using the unit circle
MAFS.912.F-TF.1.2: 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.
Cosine Function
Sine Function
Tangent Function
Unit Circle
MAFS.912.F-TF.1.3: Use special triangles to determine geometrically the values of sine, cosine, tangent for pi/3, pi/4 and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi–x, pi+x, and 2pi–x in terms of their values for x, where x is any real number.
Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Function
Tangent Ratio
Unit Circle
MAFS.912.F-TF.1.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Cosine Function
Sine Function
Tangent Function
Unit Circle
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.
Cosine Function
Sine Function
Tangent Function
MAFS.912.F-TF.2.6: Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
Cosine Function
Sine Function
Tangent Function
MAFS.912.F-TF.3: Prove and apply trigonometric identities
MAFS.912.F-TF.3.8: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to calculate trigonometric ratios.
Simplifying Trigonometric Expressions
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
MAFS.912.G-C: Circles
MAFS.912.G-C.1: Understand and apply theorems about circles
MAFS.912.G-C.1.1: Prove that all circles are similar.
Perimeters and Areas of Similar Figures
MAFS.912.G-C.1.2: Identify and describe relationships among inscribed angles, radii, and chords.
Chords and Arcs
Inscribed Angles
MAFS.912.G-C.1.3: Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Segment and Angle Bisectors
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.
Area of Triangles
Chords and Arcs
Inscribed Angles
MAFS.912.G-CO: Congruence
MAFS.912.G-CO.1: Experiment with transformations in the plane
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).
Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
MAFS.912.G-CO.1.3: Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Reflections
Rotations, Reflections and Translations
Segment and Angle Bisectors
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.
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.
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.
Dilations
Reflections
Rotations, Reflections and Translations
MAFS.912.G-CO.2.7: 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.
Congruence in Right Triangles
Dilations
Proving Triangles Congruent
Reflections
Rotations, Reflections and Translations
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-CO.4.13: Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Classifying Triangles
Isosceles and Equilateral Triangles
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.
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.
Ellipse - Activity A
Hyperbola - Activity A
MAFS.912.G-GPE.2: Use coordinates to prove simple geometric theorems algebraically
MAFS.912.G-GPE.2.4: Use coordinates to prove simple geometric theorems algebraically.
Simplifying Trigonometric Expressions
MAFS.912.G-GPE.2.5: Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Constructing Parallel and Perpendicular Lines
Slope - Activity B
MAFS.912.G-GPE.2.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
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.
Area of Parallelograms
Distance Formula - Activity A
Perimeter and Area of Rectangles
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard
Segment and Angle Bisectors
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.
Circles: Circumference and Area
Prisms and Cylinders - Activity A
MAFS.912.G-GMD.1.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Prisms and Cylinders - Activity A
MAFS.912.G-MG: Modeling with Geometry
MAFS.912.G-MG.1: Apply geometric concepts in modeling situations
MAFS.912.G-MG.1.1: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Special Parallelograms
MAFS.912.G-MG.1.2: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
Area of Triangles
Prisms and Cylinders - Activity A
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.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.
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
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
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.
Dilations
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
MAFS.912.G-SRT.1.3: Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
MAFS.912.G-SRT.2: Prove theorems involving similarity
MAFS.912.G-SRT.2.4: Prove theorems about triangles.
Perimeters and Areas of Similar Figures
Segment and Angle Bisectors
MAFS.912.G-SRT.2.5: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
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 and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
MAFS.912.G-SRT.3.7: Explain and use the relationship between the sine and cosine of complementary angles.
Cosine Function
Sine Function
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Unit Circle
MAFS.912.G-SRT.3.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Cosine Function
Distance Formula - Activity A
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard
Sine Function
Sine and Cosine Ratios - Activity A
Tangent Function
MAFS.912.G-SRT.4: Apply trigonometry to general triangles
MAFS.912.G-SRT.4.11: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
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 - Activity A
MAFS.912.N-CN.1.3: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Absolute Value of a Complex Number
Points in the Complex Plane - Activity A
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.
Complex Numbers in Polar Form
Points in the Complex Plane - Activity A
MAFS.912.N-CN.2.5: Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.
Points in the Complex Plane - Activity A
MAFS.912.N-CN.2.6: Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
Absolute Value of a Complex Number
Distance Formula - Activity A
Points in the Complex Plane - Activity A
Pythagorean Theorem with a Geoboard
MAFS.912.N-CN.3: Use complex numbers in polynomial identities and equations.
MAFS.912.N-CN.3.8: Extend polynomial identities to the complex numbers.
Modeling the Factorization of x2+bx+c
Points in the Complex Plane - Activity A
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.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.2.4.c: Understand vector subtraction v – w 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 perform vector subtraction component-wise.
MAFS.912.N-VM.3: Perform operations on matrices and use matrices in applications.
MAFS.912.N-VM.3.11: Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
Dilations
Reflections
Rotations, Reflections and Translations
MAFS.912.N-VM.3.12: Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Area of Triangles
Dilations
Real Number Line - Activity B
Reflections
Rotations, Reflections and Translations
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.1.2: 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.
Compound Independent Events
Compound 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.
Probability Simulations
Theoretical and Experimental Probability
MAFS.912.S-CP.1.4: 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.
Box-and-Whisker Plots
Compound Independent Events
Compound Independent and Dependent Events
Describing Data Using Statistics
Histograms
Scatter Plots - Activity A
Stem-and-Leaf Plots
MAFS.912.S-CP.1.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Compound Independent Events
Compound 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.2.6: 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.
MAFS.912.S-CP.2.9: Use permutations and combinations to compute probabilities of compound events and solve problems.
Compound Independent Events
Compound Independent and Dependent Events
Permutations
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
Describing Data Using Statistics
Histograms
Populations and Samples
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
Mean, Median and Mode
Populations and Samples
Real-Time Histogram
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).
Describing Data Using Statistics
Mean, Median and Mode
MAFS.912.S-ID.1.4: 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, and tables to estimate areas under the normal curve.
MAFS.912.S-ID.2: Summarize, represent, and interpret data on two categorical and quantitative variables
MAFS.912.S-ID.2.5: 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.
Correlation
Solving Using Trend Lines
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.
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines
MAFS.912.S-ID.2.6.b: Informally assess the fit of a function by plotting and analyzing residuals.
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines
MAFS.912.S-ID.2.6.c: Fit a linear function for a scatter plot that suggests a linear association.
Correlation
Lines of Best Fit Using Least Squares - Activity A
Scatter Plots - Activity A
Solving Using Trend 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.
Points, Lines, and Equations
Slope-Intercept Form of a Line - Activity B
MAFS.912.S-ID.3.8: Compute (using technology) and interpret the correlation coefficient of a linear fit.
MAFS.912.S-ID.3.9: Distinguish between correlation and causation.
MAFS.912.S-IC: Making Inferences and Justifying Conclusions
MAFS.912.S-IC.1: Understand and evaluate random processes underlying statistical experiments
MAFS.912.S-IC.1.1: Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Polling: City
Polling: Neighborhood
MAFS.912.S-IC.2: Make inferences and justify conclusions from sample surveys, experiments, and observational studies
MAFS.912.S-IC.2.3: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
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.
Polling: Neighborhood
Probability Simulations
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.
Populations and Samples
Probability Simulations
MAFS.912.S-IC.2.6: Evaluate reports based on data.
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.1.1: 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.
Box-and-Whisker Plots
Describing Data Using Statistics
Histograms
Scatter Plots - Activity A
Stem-and-Leaf Plots
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.
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 - Activity A
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.
Binomial Probabilities
Geometric Probability - Activity A
MAFS.912.S-MD.2.6: Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Probability Simulations
Theoretical and Experimental Probability
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: 8/7/2014