Standards
A1.1.B: Solve problems that can be represented by linear functions, equations, and inequalities.
A1.1.C: Solve problems that can be represented by a system of two linear equations or inequalities.
Systems of Linear Inequalities (Slope-intercept form) - Activity A
A1.1.D: Solve problems that can be represented by quadratic functions and equations.
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
A1.1.E: Solve problems that can be represented by exponential functions and equations.
Exponential Functions - Activity A
A1.2.B: Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.
Using Tables, Rules and Graphs
A1.2.C: Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions.
Dividing Exponential Expressions
Multiplying Exponential Expressions
Square Roots
A1.2.E: Use algebraic properties to factor and combine like terms in polynomials.
Modeling the Factorization of x2+bx+c
A1.2.F: Add, subtract, multiply, and divide polynomials.
Addition of Polynomials - Activity A
A1.3.A: Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.
Introduction to Functions
Linear Functions
A1.3.B: Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs
A1.4.A: Write and solve linear equations and inequalities in one variable.
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Using Algebraic Equations
Using Algebraic Expressions
A1.4.B: Write and graph an equation for a line given the slope and the yintercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.
Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs
A1.4.C: Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.
Linear Functions
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
A1.4.D: Write and solve systems of two linear equations and inequalities in two variables.
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A
A1.4.E: Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent.
Linear Functions
Quadratic and Absolute Value Functions
Roots of a Quadratic
Using Tables, Rules and Graphs
A1.5.A: Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations.
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Using Algebraic Equations
Using Algebraic Expressions
Using Tables, Rules and Graphs
A1.5.B: Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.
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
A1.5.C: Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers.
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
A1.5.D: Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.
A1.6.C: Describe how linear transformations affect the center and spread of univariate data.
A1.6.D: Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.
Linear Functions
Slope - Activity B
A1.6.E: Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative.
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines
A1.7.A: Sketch the graph for an exponential function of the form y = abn where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.
Exponential Functions - Activity A
A1.7.C: Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
G.1.D: Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.
G.2.B: Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal
Investigating Angle Theorems - Activity A
G.2.C: Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines.
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
G.3.B: Determine and prove triangle congruence, triangle similarity, and other properties of triangles.
Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
G.3.E: Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
G.3.F: Know, prove, and apply basic theorems about parallelograms.
G.3.H: Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles.
Chords and Arcs
Inscribing Angles
G.3.I: Explain and perform constructions related to the circle.
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
G.5.A: Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axes or the line y = x.
Reflections
Rotations, Reflections and Translations
Translations
G.5.C: Given two congruent or similar figures in a coordinate plane, describe a composition of translations, reflections, rotations, and dilations that superimposes one figure on the other.
Dilations
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
Translations
G.5.D: Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.
Holiday Snowflake Designer
Reflections
Rotations, Reflections and Translations
G.6.C: Apply formulas for surface area and volume of three-dimensional figures to solve problems.
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
G.6.D: Predict and verify the effect that changing one, two, or three linear dimensions has on perimeter, area, volume, or surface area of two- and three-dimensional figures.
Prisms and Cylinders - Activity A
G.6.E: Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.
G.7.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.
Biconditional Statement
Conditional Statement
A2.1.C: Solve problems that can be represented by quadratic functions, equations, and inequalities.
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
A2.1.D: Solve problems that can be represented by exponential and logarithmic functions and equations.
Exponential Functions - Activity A
Logarithmic Functions - Activity A
A2.1.F: Solve problems involving combinations and permutations.
Permutations
Permutations and Combinations
A2.3.A: Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.
Modeling the Factorization of x2+bx+c
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
A2.3.B: Determine the number and nature of the roots of a quadratic function.
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
A2.3.C: Solve quadratic equations and inequalities, including equations with complex roots.
Quadratic Inequalities - Activity A
Roots of a Quadratic
A2.4.A: Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.
Exponential Functions - Activity A
Logarithmic Functions - Activity A
A2.4.B: Graph an exponential function of the form f(x) = abx and its inverse logarithmic function.
Exponential Functions - Activity A
Logarithmic Functions - Activity A
A2.5.A: Construct new functions using the transformations f(x - h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s).
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
A2.5.B: Plot points, sketch, and describe the graphs of functions of the form f (x) = a times the square root of x - c + d , and solve related equations.
Functions Involving Square Roots
Radical Functions
A2.5.C: Plot points, sketch, and describe the graphs of functions of the form (x) = a/x + b, f(x) = a/x² + b, and f(x) = a/(bx + c), and solve related equations.
General Form of a Rational Function
Rational Functions
A2.5.D: Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors
A2.6.A: Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
A2.6.B: Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B.
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
A2.6.C: Compute permutations and combinations, and use the results to calculate probabilities.
Binomial Probabilities
Permutations
Permutations and Combinations
A2.6.E: Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions.
Exponential Functions - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
A2.7.B: Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
M1.1.B: Solve problems that can be represented by linear functions, equations, and inequalities.
M1.1.D: Solve problems that can be represented by exponential functions and equations.
Exponential Functions - Activity A
M1.2.A: Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables.
Introduction to Functions
Linear Functions
M1.2.B: Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations.
Introduction to Functions
Linear Functions
Using Tables, Rules and Graphs
M1.2.D: Plot points, sketch, and describe the graphs of functions of the form f(x) = a/x + b.
General Form of a Rational Function
Rational Functions
M1.3.A: Write and solve linear equations and inequalities in one variable.
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Using Algebraic Equations
Using Algebraic Expressions
M1.3.B: Describe how changes in the parameters of linear functions and functions containing an absolute value of a linear expression affect their graphs and the relationships they represent.
Linear Functions
Quadratic and Absolute Value Functions
Roots of a Quadratic
Using Tables, Rules and Graphs
M1.3.C: Identify and interpret the slope and intercepts of a linear function, including equations for parallel and perpendicular lines.
Linear Functions
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
M1.3.D: Write and graph an equation for a line given the slope and the y-intercept, the slope and a point on the line, or two points on the line, and translate between forms of linear equations.
Defining a Line with Two Points
Point-Slope Form of a Line - Activity A
Slope - Activity B
Slope-Intercept Form of a Line - Activity A
Standard Form of a Line
Using Tables, Rules and Graphs
M1.3.E: Write and solve systems of two linear equations and inequalities in two variables.
Solving Linear Inequalities using Addition and Subtraction
Solving Linear Inequalities using Multiplication and Division
Systems of Linear Inequalities (Slope-intercept form) - Activity A
M1.3.F: Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions.
Linear Functions
Slope - Activity B
M1.3.G: Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative.
Correlation
Scatter Plots - Activity A
Solving Using Trend Lines
M1.4.D: Determine and prove triangle similarity.
Biconditional Statement
Conditional Statement
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons
M1.4.F: Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal.
Investigating Angle Theorems - Activity A
M1.4.G: Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines.
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
M1.5.B: Describe how linear transformations affect the center and spread of univariate data.
M1.6.C: Recognize the multiple uses of variables, determine all possible values of variables that satisfy prescribed conditions, and evaluate algebraic expressions that involve variables.
Using Tables, Rules and Graphs
M1.7.A: Sketch the graph for an exponential function of the form y = ab to the n power where n is an integer, describe the effects that changes in the parameters a and b have on the graph, and answer questions that arise in situations modeled by exponential functions.
Exponential Functions - Activity A
M1.7.C: Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions.
Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Square Roots
M1.7.D: Express arithmetic and geometric sequences in both explicit and recursive forms, translate between the two forms, explain how rate of change is represented in each form, and use the forms to find specific terms in the sequence.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
M1.8.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.
Biconditional Statement
Conditional Statement
M2.1.C: Solve problems that can be represented by quadratic functions, equations, and inequalities.
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
M2.1.D: Solve problems that can be represented by exponential functions and equations.
Exponential Functions - Activity A
M2.1.E: Solve problems involving combinations and permutations.
Permutations
Permutations and Combinations
M2.2.A: Represent a quadratic function with a symbolic expression, as a graph, in a table, and with a description, and make connections among the representations.
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Using Tables, Rules and Graphs
M2.2.B: Sketch the graph of a quadratic function, describe the effects that changes in the parameters have on the graph, and interpret the x-intercepts as solutions to a quadratic equation.
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
M2.2.C: Translate between the standard form of a quadratic function, the vertex form, and the factored form; graph and interpret the meaning of each form.
Modeling the Factorization of x2+bx+c
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
M2.2.D: Solve quadratic equations that can be factored as (ax + b)(cx + d) where a, b, c, and d are integers.
Modeling the Factorization of ax2+bx+c
Modeling the Factorization of x2+bx+c
M2.2.E: Determine the number and nature of the roots of a quadratic function.
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
M2.2.F: Solve quadratic equations that have real roots by completing the square and by using the quadratic formula.
M2.2.G: Solve quadratic equations and inequalities, including equations with complex roots.
Quadratic Inequalities - Activity A
Roots of a Quadratic
M2.2.H: Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions.
Exponential Functions - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
M2.3.C: Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.
M2.3.F: Determine and prove triangle congruence and other properties of triangles.
Congruence in Right Triangles
Proving Triangles Congruent
M2.3.H: Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.
Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio
M2.3.J: Know, prove, and apply basic theorems about parallelograms.
M2.4.A: Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
M2.4.B: Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B.
Compound Independent Events
Compound Independent and Dependent Events
Independent and Dependent Events
M2.4.C: Compute permutations and combinations, and use the results to calculate probabilities.
Binomial Probabilities
Permutations
Permutations and Combinations
M2.5.A: Use algebraic properties to factor and combine like terms in polynomials.
Modeling the Factorization of x2+bx+c
M2.5.B: Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.
M2.5.D: Find the terms and partial sums of arithmetic and geometric series and the infinite sum for geometric series.
Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
M2.6.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.
Biconditional Statement
Conditional Statement
M3.1.C: Solve problems that can be represented by quadratic functions, equations, and inequalities.
Quadratic Inequalities - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
M3.1.D: Solve problems that can be represented by exponential and logarithmic functions and equations.
Exponential Functions - Activity A
Logarithmic Functions - Activity A
M3.2.A: Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axes or the line y = x.
Reflections
Rotations, Reflections and Translations
Translations
M3.2.C: Given two congruent or similar figures in a coordinate plane, describe a composition of translations, reflections, rotations, and dilations that superimposes one figure on the other.
Dilations
Perimeters and Areas of Similar Figures
Reflections
Rotations, Reflections and Translations
Similar Figures - Activity A
Similar Polygons
Translations
M3.2.D: Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.
Holiday Snowflake Designer
Reflections
Rotations, Reflections and Translations
M3.2.E: Construct new functions using the transformations f(x - h), f(x) + k, cf(x), and by adding and subtracting functions, and describe the effect on the original graph(s).
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions - Activity A
M3.3.A: Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.
Exponential Functions - Activity A
Logarithmic Functions - Activity A
M3.3.B: Graph an exponential function of the form f(x) = ab to the x power and its inverse logarithmic function.
Exponential Functions - Activity A
Logarithmic Functions - Activity A
M3.3.D: Plot points, sketch, and describe the graphs of functions of the form f (x) = a times the square root of x - c + d, and solve related equations.
Functions Involving Square Roots
Radical Functions
M3.3.E: Plot points, sketch, and describe the graphs of functions of the form f(x) = a/x² + b and f(x) = a/(bx + c), and solve related equations.
General Form of a Rational Function
Rational Functions
M3.3.F: Plot points, sketch, and describe the graphs of cubic polynomial functions of the form f(x) = ax³ + d as an example of higher order polynomials and solve related equations.
Cubic Function Activity
Fourth-Degree Polynomials - Activity A
Polynomials and Linear Factors
M3.5.D: Apply formulas for surface area and volume of three-dimensional figures to solve problems.
Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
M3.5.E: Predict and verify the effect that changing one, two, or three linear dimensions has on perimeter, area, volume, or surface area of two- and three-dimensional figures.
Prisms and Cylinders - Activity A
M3.6.C: Add, subtract, multiply, and divide polynomials.
Addition of Polynomials - Activity A
M3.7.A: Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles.
Chords and Arcs
Inscribing Angles
Tangent Ratio
M3.7.C: Explain and perform constructions related to the circle.
Construct Parallel and Perpendicular Lines
Constructing Congruent Segments and Angles
Correlation last revised: 12/10/2009