Benchmarks for Excellent Student Thinking Standards
MA.912.NSO.1.2: Generate equivalent monomial algebraic expressions using the properties of exponents.
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
MA.912.NSO.1.3: Generate equivalent algebraic expressions involving radicals or rational exponents using the properties of exponents. Radicands are limited to monomial algebraic expressions.
Simplifying Radical Expressions
MA.912.NSO.1.4: Apply previous understanding of operations with rational numbers to add, subtract, multiply and divide numerical radicals.
Operations with Radical Expressions
Simplifying Radical Expressions
MA.912.NSO.1.5: Add, subtract, multiply and divide algebraic expressions involving radicals. Radicands are limited to monomial algebraic expressions.
Simplifying Radical Expressions
MA.912.NSO.1.6: Given an algebraic logarithmic expression, generate an equivalent algebraic expression using the properties of logarithms or exponents.
MA.912.NSO.2.1: Extend previous understanding of the real number system to include the complex number system. Add, subtract, multiply and divide complex numbers.
Points in the Complex Plane
Roots of a Quadratic
MA.912.NSO.2.2: Represent addition, subtraction, multiplication and conjugation of complex numbers geometrically on the complex plane.
MA.912.NSO.2.3: Calculate the distance and midpoint between two numbers on the complex coordinate plane.
MA.912.NSO.2.4: Solve mathematical and real-world problems involving complex numbers represented algebraically or on the coordinate plane.
Points in the Complex Plane
Roots of a Quadratic
MA.912.NSO.2.5: Represent complex numbers on the complex plane in rectangular and polar forms. Explain why the rectangular and polar forms of a given complex number represent the same number.
MA.912.NSO.2.6: Rewrite complex numbers to trigonometric form. Multiply complex numbers in trigonometric form.
MA.912.NSO.3.1: Apply appropriate notation and symbols to represent vectors in the plane as directed line segments. Determine the magnitude and direction of a vector in component form.
MA.912.NSO.3.2: Represent vectors in component form, linear form or trigonometric form. Rewrite vectors from one form to another.
MA.912.NSO.3.3: Solve mathematical and real-world problems involving velocity and other quantities that can be represented by vectors.
MA.912.NSO.3.4: Solve mathematical and real-world problems involving vectors in two dimensions using the dot product and vector projections.
MA.912.NSO.3.6: Add and subtract vectors algebraically or graphically.
MA.912.NSO.3.7: Given the magnitude and direction of two or more vectors, determine the magnitude and direction of their sum.
MA.912.NSO.3.8: Multiply a vector by a scalar algebraically or graphically.
MA.912.NSO.3.9: Compute the magnitude and direction of a vector scalar multiple.
MA.912.NSO.4.1: Given a mathematical or real-world context, represent and manipulate data using matrices.
Dilations
Solving Linear Systems (Matrices and Special Solutions)
Translations
MA.912.NSO.4.2: Given a mathematical or real-world context, represent and solve a system of two- or three-variable linear equations using matrices.
Solving Linear Systems (Matrices and Special Solutions)
MA.912.NSO.4.3: Solve mathematical and real-world problems involving addition, subtraction and multiplication of matrices.
Solving Linear Systems (Matrices and Special Solutions)
Translations
MA.912.NSO.4.4: Solve mathematical and real-world problems using the inverse and determinant of matrices.
Solving Linear Systems (Matrices and Special Solutions)
MA.912.AR.1.1: Identify and interpret parts of an expression that represent a quantity in terms of a mathematical or real-world context, including viewing one or more of its parts as a single entity.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Binomial Probabilities
Compound Interest
Geometric Sequences
Permutations and Combinations
MA.912.AR.1.2: Rearrange equations or formulas to isolate a quantity of interest.
Solving Formulas for any Variable
MA.912.AR.1.3: Add, subtract and multiply polynomial expressions with rational number coefficients.
Addition and Subtraction of Functions
Addition of Polynomials
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
MA.912.AR.1.5: Divide polynomial expressions using long division, synthetic division and algebraic manipulation.
Dividing Polynomials Using Synthetic Division
MA.912.AR.1.6: Solve mathematical and real-world problems involving addition, subtraction, multiplication or division of polynomials.
Addition and Subtraction of Functions
Addition of Polynomials
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
MA.912.AR.1.7: Rewrite a polynomial expression as a product of polynomials.
Factoring Special Products
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
MA.912.AR.2.1: Given a real-world context, write and solve one-variable multi-step linear equations.
Modeling and Solving Two-Step Equations
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations
MA.912.AR.2.2: Write a linear two-variable equation to represent relationships between quantities from a graph, a written description or a table of values within a mathematical or real-world context.
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line
MA.912.AR.2.3: Write a linear two-variable equation for a line that is parallel or perpendicular to a given line and goes through a given point.
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
MA.912.AR.2.4: Given a table, equation or written description of a linear function, graph that function, and determine and interpret its key features.
Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line
MA.912.AR.2.5: Solve and graph mathematical and real-world problems that are modeled with linear functions. Interpret key features and determine domain constraints in terms of the context.
Point-Slope Form of a Line
Solving Linear Systems (Matrices and Special Solutions)
Standard Form of a Line
MA.912.AR.2.6: Given a mathematical or real-world context, write and solve one-variable linear inequalities, including compound inequalities. Represent solutions algebraically or graphically.
Compound Inequalities
Exploring Linear Inequalities in One Variable
Solving Linear Inequalities in One Variable
MA.912.AR.2.7: Write two-variable linear inequalities to represent relationships between quantities from a graph or a written description within a mathematical or real-world context.
Linear Inequalities in Two Variables
MA.912.AR.2.8: Given a mathematical or real-world context, graph the solution set to a two-variable linear inequality.
Linear Inequalities in Two Variables
MA.912.AR.3.1: Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real number system.
Points in the Complex Plane
Quadratics in Factored Form
Roots of a Quadratic
MA.912.AR.3.2: Given a mathematical or real-world context, write and solve one-variable quadratic equations over the real and complex number systems.
Points in the Complex Plane
Roots of a Quadratic
MA.912.AR.3.3: Given a mathematical or real-world context, write and solve one-variable quadratic inequalities over the real number system. Represent solutions algebraically or graphically.
MA.912.AR.3.4: Write a quadratic function to represent the relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
MA.912.AR.3.5: Given the x-intercepts and another point on the graph of a quadratic function, write the equation for the function.
Quadratics in Factored Form
Quadratics in Polynomial Form
MA.912.AR.3.6: Given an expression or equation representing a quadratic function, determine the vertex and zeros and interpret them in terms of a real-world context.
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
MA.912.AR.3.7: Given a table, equation or written description of a quadratic function, graph that function, and determine and interpret its key features.
Quadratics in Factored Form
Quadratics in Polynomial Form
Quadratics in Vertex Form
Roots of a Quadratic
Zap It! Game
MA.912.AR.3.8: Solve and graph mathematical and real-world problems that are modeled with quadratic functions. Interpret key features and determine constraints in terms of the context.
MA.912.AR.3.9: Given a mathematical or real-world context, write two-variable quadratic inequalities to represent relationships between quantities from a graph or a written description.
MA.912.AR.3.10: Given a mathematical or real-world context, graph the solution set to a two-variable quadratic inequality.
MA.912.AR.4.1: Given a mathematical or real-world context, write and solve one-variable absolute value equations.
Absolute Value Equations and Inequalities
MA.912.AR.4.2: Given a mathematical or real-world context, write and solve one-variable absolute value inequalities. Represent solutions algebraically or graphically.
Absolute Value Equations and Inequalities
MA.912.AR.4.3: Given a table, equation or written description of an absolute value function, graph that function and determine its key features.
Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
MA.912.AR.4.4: Solve and graph mathematical and real-world problems that are modeled with absolute value functions. Interpret key features and determine domain constraints in terms of the context.
Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
MA.912.AR.5.1: Solve one-variable exponential equations using the properties of exponents.
MA.912.AR.5.2: Solve equations involving one-variable logarithms or exponents. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
MA.912.AR.5.3: Given a mathematical or real-world context, classify an exponential function as representing growth or decay.
MA.912.AR.5.4: Write an exponential function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions
MA.912.AR.5.5: Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percent rate of change in terms of a real-world context.
MA.912.AR.5.6: Given a table, equation or written description of an exponential function, graph that function and determine its key features.
Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions
MA.912.AR.5.7: Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine domain constraints in terms of the context.
Exponential Functions
Exponential Growth and Decay
Introduction to Exponential Functions
MA.912.AR.5.8: Given a table, equation or written description of a logarithmic function, graph that function and determine its key features.
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
MA.912.AR.5.9: Solve and graph mathematical and real-world problems that are modeled with logarithmic functions. Interpret key features and determine constraints in terms of the context.
Logarithmic Functions
Logarithmic Functions: Translating and Scaling
MA.912.AR.6.1: Given a mathematical or real-world context, when suitable factorization is possible, solve one-variable polynomial equations of degree 3 or higher over the real and complex number systems.
Polynomials and Linear Factors
MA.912.AR.6.2: Explain and apply the Remainder Theorem.
Dividing Polynomials Using Synthetic Division
MA.912.AR.6.3: Given a table, equation or written description of a polynomial function of degree 3 or higher, graph that function and determine its key features.
Graphs of Polynomial Functions
Polynomials and Linear Factors
MA.912.AR.6.4: Sketch a rough graph of a polynomial function of degree 3 or higher using zeros, multiplicity and knowledge of end behavior.
Graphs of Polynomial Functions
MA.912.AR.6.5: Solve and graph mathematical and real-world problems that are modeled with polynomial functions of degree 3 or higher. Interpret key features in terms of the context.
Graphs of Polynomial Functions
Polynomials and Linear Factors
MA.912.AR.7.1: Solve one-variable radical equations. Interpret solutions as viable in terms of context and identify any extraneous solutions.
MA.912.AR.7.2: Given a table, equation or written description of a square root or cube root function, graph that function and determine its key features.
MA.912.AR.7.3: Solve and graph mathematical and real-world problems that are modeled with square root or cube root functions. Interpret key features in context.
MA.912.AR.8.1: Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
MA.912.AR.8.2: Given a table, equation or written description of a rational function, graph that function and determine its key features.
General Form of a Rational Function
Rational Functions
MA.912.AR.8.3: Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features in terms of the context.
General Form of a Rational Function
Rational Functions
MA.912.AR.9.1: Given a mathematical or real-world context, write and solve a system of two-variable linear equations algebraically or graphically.
Cat and Mouse (Modeling with Linear Systems)
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
MA.912.AR.9.4: Graph the solution set of a system of two-variable linear inequalities.
Systems of Linear Inequalities (Slope-intercept form)
MA.912.AR.9.5: Given a real-world context, represent constraints as systems of linear equations or inequalities. Interpret solutions to problems as viable or nonviable options.
Cat and Mouse (Modeling with Linear Systems)
Linear Programming
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)
Systems of Linear Inequalities (Slope-intercept form)
MA.912.AR.9.7: Solve real-world problems involving linear programming.
MA.912.AR.9.9: Graph and solve mathematical and real-world problems that are modeled with piecewise functions. Interpret key features and determine constraints in terms of the context.
Absolute Value Equations and Inequalities
Absolute Value with Linear Functions
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
MA.912.AR.10.1: Given a mathematical or real-world context, write and solve problems involving arithmetic sequences.
Arithmetic Sequences
Arithmetic and Geometric Sequences
MA.912.AR.10.2: Given a mathematical or real-world context, write and solve problems involving geometric sequences.
Arithmetic and Geometric Sequences
Geometric Sequences
MA.912.AR.10.5: Given a mathematical or real-world context, write a sequence using function notation, defined explicitly or recursively, to represent relationships between quantities from a written description.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
MA.912.AR.10.6: Given a mathematical or real-world context, find the domain of a given sequence defined recursively or explicitly.
MA.912.F.1.1: Given an equation or graph that defines a function, determine the function type. Given an input-output table, determine a function type that could represent it.
Absolute Value with Linear Functions
Exponential Functions
Graphs of Polynomial Functions
Introduction to Exponential Functions
Point-Slope Form of a Line
Radical Functions
Slope-Intercept Form of a Line
Standard Form of a Line
Translating and Scaling Functions
MA.912.F.1.2: Given a function represented in function notation, evaluate the function for an input in its domain. For a real-world context, interpret the output.
Absolute Value with Linear Functions
Exponential Functions
Points, Lines, and Equations
Quadratics in Polynomial Form
Radical Functions
MA.912.F.1.3: Calculate and interpret the average rate of change of a real-world situation represented graphically, algebraically or in a table over a specified interval.
Cat and Mouse (Modeling with Linear Systems)
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Slope
MA.912.F.1.4: Demonstrate understanding of the concept of limit and estimate limits from graphs and tables of values, as related to the concept of the derivative of a function.
Graphs of Derivative Functions
MA.912.F.1.5: Compare key features of linear and nonlinear functions each represented in the same way, such as algebraically, graphically, in tables or written descriptions.
Graphs of Polynomial Functions
MA.912.F.1.6: Compare key features of two functions each represented in a different way such as algebraically, graphically, in tables or written descriptions.
Direct and Inverse Variation
Logarithmic Functions
MA.912.F.1.7: Determine whether a linear, quadratic or exponential function best models a given real-world situation.
MA.912.F.1.8: Determine whether a function is even, odd or neither when represented algebraically, graphically or in a table.
Graphs of Polynomial Functions
MA.912.F.2.1: Identify the effect on the graph or table of a given function after replacing f(x) by f(x) + k, kf(x) and f(x + k) for specific values of k.
Absolute Value with Linear Functions
Point-Slope Form of a Line
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game
MA.912.F.2.2: Identify the effect on the graph of a given function of two or more transformations defined by adding a real number to the x- or y-values or multiplying the x- or y-values by a real number.
Absolute Value with Linear Functions
Point-Slope Form of a Line
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game
MA.912.F.2.3: Given the graph or table of f(x) and the graph or table of f(x) + k, kf(x), f(kx) and f(x + k), state the type of transformation and find the value of the real number k.
Absolute Value with Linear Functions
Point-Slope Form of a Line
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game
MA.912.F.2.4: Given the graph or table of values of two or more transformations of a function, state the type of transformation and find the values of the real number that defines the transformation.
Absolute Value with Linear Functions
Point-Slope Form of a Line
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions
Zap It! Game
MA.912.F.2.5: Given two or more transformations and a function, create the table or graph of the transformed function.
Absolute Value with Linear Functions
Point-Slope Form of a Line
Quadratics in Polynomial Form
Quadratics in Vertex Form
Slope-Intercept Form of a Line
Translating and Scaling Functions
MA.912.F.2.6: Given a graph or table of values of two or more transformations of a function, write the equation of the transformed function.
Point-Slope Form of a Line
Translating and Scaling Functions
MA.912.F.3.1: Given a mathematical or real-world context, combine two functions, limited to linear and quadratic, using arithmetic operations. When appropriate, include domain restrictions for the new function.
Addition and Subtraction of Functions
Solving Linear Systems (Standard Form)
MA.912.F.3.2: Given a mathematical or real-world context, combine two or more functions, limited to linear, quadratic, exponential and polynomial, using arithmetic operations. When appropriate, include domain restrictions for the new function.
Addition and Subtraction of Functions
Solving Linear Systems (Standard Form)
MA.912.F.3.3: Solve mathematical and real-world problems involving functions that have been combined using arithmetic operations.
Addition and Subtraction of Functions
Solving Linear Systems (Standard Form)
MA.912.F.3.6: Determine whether an inverse function exists by analyzing tables, graphs and equations.
Logarithmic Functions
Radical Functions
MA.912.F.3.7: Represent the inverse of a function algebraically, graphically or in a table. Use composition of functions to verify that one function is the inverse of the other.
Logarithmic Functions
Radical Functions
MA.912.F.3.9: Solve mathematical and real-world problems involving inverse functions.
Logarithmic Functions
Radical Functions
MA.912.FL.1.1: Compare simple, compound and continuously compounded interest over time.
MA.912.FL.1.2: Solve problems involving simple, compound and continuously compounded interest, including determining the present value and future value of money.
MA.912.FL.1.4: Explain the relationship between compound interest and exponential growth and the relationship between continuously compounded interest and exponential growth.
MA.912.FL.1.6: Solve problems involving potential profit and actual cost.
MA.912.FL.2.2: Calculate the finance charges and total amount due on a bill using various forms of credit.
MA.912.FL.2.7: Solve problems involving student, personal and car loans, including finding the total amount to be paid, adjustable rates and refinancing options.
MA.912.FL.2.12: Compare interest rate calculations and annual percentage rate calculations, and distinguish between the two rates.
MA.912.GR.1.1: Prove relationships and theorems about lines and angles. Solve mathematical and real-world problems involving postulates, relationships and theorems of lines and angles.
Concurrent Lines, Medians, and Altitudes
Investigating Angle Theorems
Parallel, Intersecting, and Skew Lines
MA.912.GR.1.2: Prove triangle congruence or similarity using Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle and Hypotenuse-Leg.
Congruence in Right Triangles
Proving Triangles Congruent
Similarity in Right Triangles
MA.912.GR.1.3: Prove relationships and theorems about triangles. Solve mathematical and real-world problems involving postulates, relationships and theorems of triangles.
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Segment and Angle Bisectors
Triangle Angle Sum
Triangle Inequalities
MA.912.GR.1.4: Prove relationships and theorems about parallelograms. Solve mathematical and real-world problems involving postulates, relationships and theorems of parallelograms.
Parallelogram Conditions
Polygon Angle Sum
Special Parallelograms
MA.912.GR.1.5: Prove relationships and theorems about trapezoids. Solve mathematical and real-world problems involving postulates, relationships and theorems of trapezoids.
MA.912.GR.1.6: Solve mathematical and real-world problems involving congruence or similarity in two-dimensional figures.
Congruence in Right Triangles
Similar Figures
Similarity in Right Triangles
MA.912.GR.2.1: Given a preimage and image, describe the transformation and represent the transformation algebraically using coordinates.
Dilations
Rotations, Reflections, and Translations
Translations
MA.912.GR.2.2: Identify transformations that do or do not preserve distance.
Dilations
Rotations, Reflections, and Translations
Translations
MA.912.GR.2.3: Specify a sequence of transformations that will map a given figure onto itself or onto another congruent or similar figure.
Rotations, Reflections, and Translations
MA.912.GR.2.5: Apply rigid transformations to map one figure onto another to justify that the two figures are congruent.
Reflections
Rotations, Reflections, and Translations
Translations
MA.912.GR.2.6: Justify the criteria for triangle congruence using the definition of congruence in terms of rigid transformations.
Reflections
Rotations, Reflections, and Translations
Translations
MA.912.GR.2.7: Apply an appropriate transformation to map one figure onto another to justify that the two figures are similar.
MA.912.GR.2.8: Justify the criteria for triangle similarity using the definition of similarity in terms of non-rigid transformations.
MA.912.GR.3.1: Given a mathematical or real-world context, use coordinate geometry to classify or justify definitions, properties and theorems involving circles, triangles or quadrilaterals.
MA.912.GR.3.2: Solve geometric problems involving circles, triangles and quadrilaterals on the coordinate plane.
MA.912.GR.3.3: Solve mathematical and real-world problems on the coordinate plane that involve finding the coordinates of a point on a line segment including the midpoint.
MA.912.GR.3.4: Solve mathematical and real-world problems on the coordinate plane involving perimeter or area of polygons.
MA.912.GR.4.1: Identify the shapes of two-dimensional cross-sections of three-dimensional figures.
MA.912.GR.4.2: Identify three-dimensional objects generated by rotations of two-dimensional figures.
Prisms and Cylinders
Pyramids and Cones
MA.912.GR.4.3: Determine how changes in dimensions affect the area of two-dimensional figures and the surface area or volume of three-dimensional figures.
Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures
Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones
MA.912.GR.4.4: Solve mathematical and real-world problems involving the area of two-dimensional figures.
Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles
MA.912.GR.4.5: Solve mathematical and real-world problems involving the volume of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
Prisms and Cylinders
Pyramids and Cones
MA.912.GR.4.6: Solve mathematical and real-world problems involving the surface area of three-dimensional figures limited to cylinders, pyramids, prisms, cones and spheres.
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones
MA.912.GR.5.1: Construct a copy of a segment or an angle.
Constructing Congruent Segments and Angles
MA.912.GR.5.2: Construct the bisector of a segment or an angle, including the perpendicular bisector of a line segment.
Constructing Parallel and Perpendicular Lines
MA.912.GR.6.1: Solve mathematical and real-world problems involving the length of a secant, tangent, segment or chord in a given circle.
MA.912.GR.6.2: Solve mathematical and real-world problems involving the measures of arcs and related angles, limited to central, inscribed and intersections of a chord, secants or tangents.
Chords and Arcs
Inscribed Angles
MA.912.GR.6.3: Solve mathematical problems involving triangles and quadrilaterals inscribed in a circle.
MA.912.GR.6.4: Solve mathematical and real-world problems involving the arc length and area of a sector in a given circle.
MA.912.GR.6.5: Apply transformations to prove that all circles are similar.
MA.912.GR.7.1: Identify the conic resulting from the cross-section of cones.
Circles
Ellipses
Hyperbolas
Parabolas
MA.912.GR.7.2: Given a mathematical or real-world context, derive and create the equation of a circle using key features.
MA.912.GR.7.3: Graph and solve mathematical and real-world problems that are modeled with an equation of a circle. Determine and interpret key features in terms of the context.
MA.912.GR.7.4: Given a mathematical or real-world context, derive and create the equation of a parabola using key features.
MA.912.GR.7.5: Graph and solve mathematical and real-world problems that are modeled with an equation of a parabola. Determine and interpret key features in terms of the context.
MA.912.GR.7.6: Given a mathematical or real-world context, derive and create the equation of an ellipse using key features.
MA.912.GR.7.7: Graph and solve mathematical and real-world problems that are modeled with an equation of an ellipse. Determine and interpret key features in terms of the context.
MA.912.GR.7.8: Given a mathematical or real-world context, derive and create the equation of a hyperbola using key features.
MA.912.GR.7.9: Graph and solve mathematical and real-world problems that are modeled with an equation of a hyperbola. Determine and interpret key features in terms of the context.
MA.912.T.1.1: Define trigonometric ratios for acute angles in right triangles.
Sine, Cosine, and Tangent Ratios
MA.912.T.1.2: Solve mathematical and real-world problems involving right triangles using trigonometric ratios and the Pythagorean Theorem.
Cosine Function
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function
MA.912.T.1.5: Prove Pythagorean Identities. Apply Pythagorean Identities to calculate trigonometric ratios and to solve problems.
Cosine Function
Simplifying Trigonometric Expressions
Sine Function
MA.912.T.1.6: Prove the Double-Angle, Half-Angle, Angle Sum and Difference formulas for sine, cosine, and tangent. Apply these formulas to solve problems.
Sum and Difference Identities for Sine and Cosine
MA.912.T.1.7: Simplify expressions using trigonometric identities.
Simplifying Trigonometric Expressions
MA.912.T.1.8: Solve trigonometric equations within a mathematical or real-world context, applying inverse functions and using technology when appropriate.
Sine, Cosine, and Tangent Ratios
MA.912.T.2.1: Define the trigonometric functions for any angle using right triangles drawn in the unit circle. Determine the values of sine, cosine and tangent of pi/3, pi/4 and pi/6 and their multiples using special triangles.
Cosine Function
Sine Function
Tangent Function
MA.912.T.2.2: Define and determine the sine, cosine, tangent, cosecant, secant and cotangent of angles using the unit circle.
Cosine Function
Sine Function
Tangent Function
MA.912.T.2.3: Given angles measured in radians or degrees, calculate the values of the six trigonometric functions.
Cosine Function
Sine Function
Tangent Function
MA.912.T.3.1: Describe and demonstrate the connections between right triangle ratios and trigonometric functions.
Sine, Cosine, and Tangent Ratios
MA.912.T.3.2: On the coordinate plane, 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
Tangent Function
MA.912.T.3.3: Given a mathematical or real-world context, choose sine, cosine or tangent trigonometric functions to model periodic phenomena with specified amplitude, frequency, horizontal shift and midline.
Sine Function
Sound Beats and Sine Waves
Translating and Scaling Sine and Cosine Functions
MA.912.T.3.4: Given a table, equation or written description of a trigonometric function, graph that function and determine key features.
Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions
MA.912.T.3.5: Graph and solve mathematical and real-world problems that are modeled with trigonometric functions. Interpret key features and determine domain constraints in terms of the context.
Cosine Function
Sine Function
Sound Beats and Sine Waves
Tangent Function
Translating and Scaling Sine and Cosine Functions
MA.912.T.3.7: Solve mathematical and real-world problems involving applications of trigonometric functions using graphing technology when appropriate.
Cosine Function
Sine Function
Sound Beats and Sine Waves
Tangent Function
Translating and Scaling Sine and Cosine Functions
MA.912.T.4.1: Define polar coordinates and relate polar coordinates to Cartesian coordinates with and without the use of technology.
MA.912.DP.1.1: Given a set of data, select an appropriate method to represent the data, depending on whether it is numerical or categorical data and on whether it is univariate or bivariate.
Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Histograms
Polling: City
Polling: Neighborhood
Solving Using Trend Lines
Stem-and-Leaf Plots
Trends in Scatter Plots
MA.912.DP.1.2: Interpret data distributions represented in various ways. State whether the data is numerical or categorical, whether it is univariate or bivariate and interpret the different components and quantities in the display.
Box-and-Whisker Plots
Correlation
Describing Data Using Statistics
Histograms
Polling: City
Polling: Neighborhood
Stem-and-Leaf Plots
Trends in Scatter Plots
MA.912.DP.1.3: Explain the difference between correlation and causation in the contexts of both numerical and categorical data.
MA.912.DP.1.4: Estimate a population total, mean or percentage using data from a sample survey; develop a margin of error through the use of simulation.
Polling: City
Polling: Neighborhood
Populations and Samples
MA.912.DP.1.5: Interpret the margin of error of a mean or percentage from a data set. Interpret the confidence level corresponding to the margin of error.
MA.912.DP.2.1: For two or more sets of numerical univariate data, calculate and compare the appropriate measures of center and measures of variability, accounting for possible effects of outliers. Interpret any notable features of the shape of the data distribution.
Box-and-Whisker Plots
Populations and Samples
MA.912.DP.2.2: 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 technology, empirical rules or tables to estimate areas under the normal curve.
Polling: City
Populations and Samples
MA.912.DP.2.3: Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and y-intercept of the model. Use the model to solve real-world problems in terms of the context of the data.
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
MA.912.DP.2.4: Given a scatter plot that represents bivariate numerical data, assess the fit of a given linear function by plotting and analyzing residuals.
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
MA.912.DP.2.5: Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real-world context.
Least-Squares Best Fit Lines
Solving Using Trend Lines
Trends in Scatter Plots
MA.912.DP.2.6: Compute the correlation coefficient of a linear model using technology. Interpret the strength and direction of the correlation coefficient.
MA.912.DP.3.5: Solve real-world problems involving univariate and bivariate categorical data.
Polling: City
Polling: Neighborhood
MA.912.DP.4.2: Determine if events A and B are independent by calculating the product of their probabilities.
Independent and Dependent Events
MA.912.DP.4.3: Calculate the conditional probability of two events and interpret the result in terms of its context.
Independent and Dependent Events
MA.912.DP.4.4: Interpret the independence of two events using conditional probability.
Independent and Dependent Events
MA.912.DP.4.6: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Independent and Dependent Events
MA.912.DP.4.8: Apply the general multiplication rule for probability, taking into consideration whether the events are independent, and interpret the result in terms of the context.
Independent and Dependent Events
MA.912.DP.4.9: Given a mathematical or real-world situation, calculate the appropriate permutation or combination.
MA.912.DP.4.10: Compute probabilities of compound events. Solve mathematical and real-world problems using permutations and combinations.
MA.912.DP.5.1: Distinguish between a population parameter and a sample statistic.
Polling: City
Populations and Samples
MA.912.DP.5.2: Explain how random sampling produces data that is representative of a population.
Polling: City
Polling: Neighborhood
Populations and Samples
MA.912.DP.5.3: Compare and contrast sampling methods.
Polling: City
Polling: Neighborhood
MA.912.DP.5.4: Generate multiple samples or simulated samples of the same size to measure the variation in estimates or predictions.
Polling: City
Polling: Neighborhood
Populations and Samples
MA.912.DP.5.6: Determine the appropriate design, survey, experiment or observational study, based on the purpose. Articulate the types of questions appropriate for each type of design.
Polling: City
Polling: Neighborhood
Populations and Samples
MA.912.DP.5.7: Compare and contrast surveys, experiments and observational studies.
Polling: Neighborhood
Populations and Samples
MA.912.DP.5.8: Explain how randomization relates to sample surveys, experiments and observational studies.
Polling: City
Polling: Neighborhood
Populations and Samples
MA.912.DP.5.9: Draw inferences about two populations using data and statistical analysis from two random samples.
MA.912.DP.5.10: Compare two treatments from an experiment using data from a randomized experiment.
MA.912.DP.5.11: Determine whether differences between parameters are significant using simulations.
MA.912.DP.5.12: Evaluate reports based on data from diverse media, print and digital resources by interpreting graphs and tables; evaluating data-based arguments; determining whether a valid sampling method was used; or interpreting provided statistics.
MA.912.DP.6.2: Develop a probability distribution for a discrete random variable using theoretical probabilities. Find the expected value and interpret it as the mean of the discrete distribution.
MA.912.DP.6.3: Develop a probability distribution for a discrete random variable using empirically assigned probabilities. Find the expected value and interpret it as the mean of the discrete distribution.
MA.912.DP.6.4: Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. Evaluate and compare strategies on the basis of the calculated expected values.
MA.912.DP.6.5: Apply probabilities to make decisions which are equally likely, such as drawing from lots or using a random number generator.
MA.912.DP.6.6: Analyze decisions that were made and solve problems using probability concepts and strategies.
MA.912.LT.1.1: Apply recursive and iterative thinking to solve problems.
Arithmetic Sequences
Geometric Sequences
MA.912.LT.1.2: Solve problems and find explicit formulas for recurrence relations using finite differences.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
MA.912.LT.4.3: Identify and accurately interpret “if…then,” “if and only if,” “all” and “not” statements. Find the converse, inverse and contrapositive of a statement.
Biconditional Statements
Conditional Statements
MA.912.C.1.11: Identify the types of discontinuities for a given function.
General Form of a Rational Function
MA.912.C.2.1: Apply and interpret derivatives geometrically and numerically.
Graphs of Derivative Functions
MA.912.C.2.2: Interpret the derivative as an instantaneous rate of change or as the slope of the tangent line.
Graphs of Derivative Functions
MA.912.C.2.10: Find second derivatives and derivatives of higher order.
Graphs of Derivative Functions
MA.912.C.3.1: Find the slope of a curve at a point, including points at which there are vertical tangent lines and no tangent lines.
Graphs of Derivative Functions
MA.912.C.3.3: Determine where a function is decreasing and increasing using its derivative.
Graphs of Derivative Functions
MA.912.C.3.4: Find local and absolute maximum and minimum points of a function.
Graphs of Derivative Functions
MA.912.C.3.5: Determine the concavity and points of inflection of a function using its second derivative.
Graphs of Derivative Functions
MA.912.C.3.6: Sketch graphs by using first and second derivatives. Compare the corresponding characteristics of the graphs of f, f prime and f double prime.
Graphs of Derivative Functions
MA.912.C.3.8: Find average and instantaneous rates of change. Explain the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed and acceleration.
Graphs of Derivative Functions
MA.912.C.4.1: Find approximate values of integrals by using rectangle approximations.
MA.912.C.4.2: Calculate the values of Riemann sums over equal subdivisions using left, right and midpoint evaluation points.
Correlation last revised: 9/15/2020