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 *x*^{2}+*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 *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*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 *x*^{2}+*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 *x*^{2}+*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 *ax*^{2}+*bx*+*c*

Modeling the Factorization of *x*^{2}+*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 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 *x*^{2}+*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

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