A1: Algebra

A1.1: Solving Problems

A1.1.B: Solve problems that can be represented by linear functions, equations, and inequalities.

Linear Functions

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: Numbers, expressions, and operations

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: Characteristics and behaviors of functions

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: Linear functions, equations, and inequalities

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: Quadratic functions and equations

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.

Roots of a Quadratic

A1.6: Data and distributions

A1.6.C: Describe how linear transformations affect the center and spread of univariate data.

Mean, Median and Mode

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: Additional Key Content

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: Geometry

G.1: Logical arguments and proofs

G.1.D: Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

Conditional Statement

G.2: Lines and Angles

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: Two- and three-dimensional figures

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.

Parallelogram Conditions

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: Geometric transformations

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: Additional Key Content

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.

Triple Beam Balance

G.7: Reasoning, problem solving, and communication

G.7.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.

Biconditional Statement
Conditional Statement

A2: Algebra 2

A2.1: Solving Problems

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: Quadratic functions and equations

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: Exponential and logarithmic functions and equations

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: Additional functions and equations

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: Probability, data, and distributions

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: Additional Key Content

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: Mathematics 1

M1.1: Solving problems

M1.1.B: Solve problems that can be represented by linear functions, equations, and inequalities.

Linear Functions

M1.1.D: Solve problems that can be represented by exponential functions and equations.

Exponential Functions - Activity A

M1.2: Characteristics and behaviors of functions

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: Linear functions, equations, and relationships

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: Proportionality, similarity, and geometric reasoning

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: Data and distributions

M1.5.B: Describe how linear transformations affect the center and spread of univariate data.

Mean, Median and Mode

M1.6: Numbers, expressions, and operations

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: Additional Key Content

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: Reasoning, problem solving, and communication

M1.8.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.

Biconditional Statement
Conditional Statement

M2: Mathematics 2

M2.1: Modeling situations and solving problems

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: Quadratic functions, equations, and relationships

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.

Roots of a Quadratic

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: Conjectures and proofs

M2.3.C: Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

Conditional Statement

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.

Parallelogram Conditions

M2.4: Probability

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: Additional Key Content

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.

Triple Beam Balance

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: Reasoning, problem solving, and communication

M2.6.H: Use inductive reasoning to make conjectures, and use deductive reasoning to prove or disprove conjectures.

Biconditional Statement
Conditional Statement

M3: Mathematics 3

M3.1: Solving problems

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: Transformations and functions

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: Functions and modeling

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: Three-dimensional geometry

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: Algebraic properties

M3.6.C: Add, subtract, multiply, and divide polynomials.

Addition of Polynomials - Activity A

M3.7: Additional Key Content

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

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