State Frameworks

G.1.a: Apply problem-solving skills to solve and verify the solutions for unknown measures in similar polygons.

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

G.1.c: Solve real-world or application problems that involve square roots and the Pythagorean Theorem.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Square Roots

G.2.a: Represent data from geometric and real-world contexts with expressions, formulas, tables, charts, graphs, relations, and functions.

Introduction to Functions

Linear Functions

G.2.b: Recognize and write the equation of a circle in standard form (x-h)_ + (y-k)_ = r_ and identify the center and radius.

G.2.c: Use slope to analyze and write equations for parallel and perpendicular lines.

Slope - Activity B

Using Algebraic Equations

G.2.d: Apply the Midpoint and Distance Formulas to solve application problems involving the coordinate plane.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

G.2.e: Determine the effects of rigid (translations, rotations, and reflections) and nonrigid (dilations) motions and compositions when performed on objects on the coordinate plane.

Dilations

Reflections

Rotations, Reflections and Translations

Translations

G.3.a: Use inductive reasoning to make conjectures and deductive reasoning to make valid conclusions.

Biconditional Statement

Conditional Statement

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

G.3.b: Develop and evaluate mathematical arguments and proofs to include paragraph, two-column, and flow chart forms.

Biconditional Statement

Conditional Statement

Proving Triangles Congruent

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

G.3.c: Identify, classify, and apply angle relationships formed by parallel lines cut by transversals.

Investigating Angle Theorems - Activity A

G.3.d: Use the properties of altitudes, medians, angle bisectors, and perpendicular bisectors of triangles to solve problems.

Concurrent Lines, Medians, and Altitudes

G.3.e: Classify triangles and apply postulates and theorems to test for triangle inequality, congruence, and similarity.

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

Triangle Inequalities

G.3.g: Describe and draw cross-sections of prisms, cylinders, pyramids, and cones.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

G.3.h: Graph a vector and determine the magnitude and direction of a given vector.

G.3.i: Given the pre-image or image, find figures obtained by applying reflections, translations, rotations, and dilations; describe and justify the method used.

Dilations

Reflections

Rotations, Reflections and Translations

Translations

G.4.b: Solve real-world applications and mathematical problems to find missing measurements in right triangles by applying special right triangle relationships, geometric means, or trigonometric functions.

Cosine Function

Similarity in Right Triangles

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

G.4.c: Solve real-world and mathematical problems involving the lateral area, surface area and volume of three-dimensional figures, including prisms, cylinders, cones, pyramids, and spheres.

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

G.4.e: Apply the relationships of sine, cosine, and tangent to problems involving right triangles.

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

Unit Circle

G.5.a: Apply multiple strategies and representations, including area models, to solve probability problems.

Binomial Probabilities

Geometric Probability - Activity A

AII.1.a: Diagram the relationship among the subsets of the complex number system.

Points in the Complex Plane - Activity A

AII.1.b: Compute with rational and radical expressions and complex numbers, expressing in simplest form.

Operations with Radical Expressions

Simplifying Radicals - Activity A

AII.1.e: Solve applications and problems in mathematical settings involving arithmetic and geometric sequences and series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

AII.1.h: Solve application problems involving exponential functions related to growth and decay.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

Simple and Compound Interest

AII.2.a: Solve compound and absolute value inequalities, graphing and writing solutions in interval notation.

Compound Inequalities

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

AII.2.b: Solve systems of absolute value and quadratic equations using a variety of solution methods including graphing.

Modeling Linear Systems - Activity A

AII.2.c: Given constraints, find the maximum and minimum value(s) of a system of linear inequalities and explain your reasoning.

Linear Programming - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

AII.2.d: Given the solution(s) to a quadratic equation, find a quadratic equation to fit the solution(s) and explain or justify the solution process.

AII.2.e: Use the discriminant to classify and predict the types of solutions of quadratic equations and justify the classification.

AII.2.f: Factor sums and differences of cubes and factor polynomials by grouping.

Factoring Special Products

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

Polynomials and Linear Factors

AII.2.l: Interpret the zeros and maximum or minimum value(s) of quadratic functions.

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

AII.3.a: Determine and justify whether the inverse of a relation or a function exists.

AII.3.b: Classify functions based on sketches of their graphs.

Cosine Function

Point-Slope Form of a Line - Activity A

Sine Function

Slope-Intercept Form of a Line - Activity A

Tangent Function

AII.3.c: Sketch and describe transformations of quadratic and absolute value functions.

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Reflections of a Quadratic Function

Roots of a Quadratic

Translating and Scaling Functions

AII.3.d: Represent complex numbers and the sum of complex numbers in a complex coordinate plane.

Complex Numbers in Polar Form

Points in the Complex Plane - Activity A

AII.3.e: Identify and sketch the essential graphs of the four conic sections: circle, parabola, ellipse, and hyperbola.

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

AII.4.b: Describe the level of accuracy of measurements in real-world situations by using absolute value inequalities.

Inequalities Involving Absolute Values

AII.5.a: Through the use of technology, use scatter plots and linear and quadratic regression analysis to determine an appropriate function to model real-life data.

Correlation

Lines of Best Fit Using Least Squares - Activity A

Solving Using Trend Lines

AII.5.b: Solve simple combinations.

Binomial Probabilities

Permutations and Combinations

AII.5.d: Identify the difference between permutations and combinations and use them to solve real-world problems.

Binomial Probabilities

Permutations

Permutations and Combinations

AA.1.e: Solve application problems involving e and exponential functions related to growth and decay.

Exponential Functions - Activity A

AA.2.a: Find the sum, difference, product, and quotient of functions, noting any restrictions on the domain.

Addition and Subtraction of Polynomials

AA.2.c: Describe patterns found in Pascal's Triangle and explain the relationship to the Binomial Theorem.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

AA.2.d: Write and graph the equations of conic sections.

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

AA.2.e: Solve linear-quadratic and quadratic-quadratic systems of equations and inequalities.

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Systems of Linear Inequalities (Slope-intercept form) - Activity A

AA.3.a: Describe and explain the conic sections resulting from cutting a cone.

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

Pyramids and Cones - Activity A

Surface and Lateral Area of Pyramids and Cones

AA.3.b: Explain and perform the geometric constructions of conic sections.

Circles

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

AA.4.a: Use technology and regression analysis to determine appropriate quadratic and cubic functions modeling real-life data.

Cubic Function Activity

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

T.1.a: Perform conversions across measurement systems including degree to radian measurements of angles, radian measurements to degree measurements of angles, polar to rectangular coordinates, rectangular to polar coordinates, rectangular to trigonometric forms of complex numbers, and trigonometric to rectangular forms of complex numbers.

Complex Numbers in Polar Form

Points in Polar Coordinates

T.1.b: Determine the product and quotient of complex numbers in trigonometric form.

T.1.c: Apply De Moivre's theorem to determine the nth roots of a complex number given in polar form.

T.1.d: Explain the addition formulas for sine and cosine and use them to prove (or simplify) other trigonometric functions.

Cosine Function

Sine Function

Sine, Cosine and Tangent

Sum and Difference Identities for Sine and Cosine

Tangent Function

Unit Circle

T.2.a: Recognize and draw different notations for vectors to represent a quantity.

T.2.b: Analyze properties of vectors and the effects of these properties on operations with vectors.

T.3.a: Determine the domain and range of trigonometric functions.

Cosine Function

Sine Function

Tangent Function

T.3.b: Identify and apply trigonometric identities.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

T.3.c: Verify identities analytically and with technology.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

T.3.d: Solve trigonometric equations in real-world situations or mathematical settings.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

T.4.a: Use the unit circle to solve real-world applications and problems in mathematical settings.

Cosine Function

Sine Function

Tangent Function

Unit Circle

T.4.b: Apply the six trigonometric functions in relation to a right triangle to solve real-world applications and problems in mathematical settings.

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

T.4.c: Find exact values of trigonometric functions of special angles in the unit circle.

Cosine Function

Sine Function

Tangent Function

Unit Circle

T.4.d: Recognize, sketch, and interpret graphs of the six trigonometric functions and include restrictions on their domain.

Cosine Function

Sine Function

Tangent Function

Unit Circle

T.4.e: Model and apply right triangle formulas, Law of Sines, and Law of Cosines to problem-solving situations.

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Ratio

T.4.f: Use the graph of polar coordinates and associated equations to model real-world applications and mathematical situations.

Complex Numbers in Polar Form

Points in Polar Coordinates

T.5.a: Find arc length and sector area of a circle.

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

T.5.b: Using graphs of functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C), interpret A, B, C in terms of amplitude, frequency, period, and phase shift.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

T.5.c: Given one angle and the measures of two adjacent sides, determine the area of a triangle and explain the process used.

Isosceles and Equilateral Triangles

Triangle Angle Sum - Activity A

PC.1.a: Express sequences and series using recursive and explicit formulas.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

PC.1.b: Evaluate and apply formulas for arithmetic and geometric sequences and series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

PC.1.d: Evaluate and apply infinite geometric series.

Arithmetic and Geometric Sequences

Geometric Sequences

PC.2.a: Determine characteristics of graphs of parent functions (domain/range, increasing/decreasing intervals, intercepts, symmetry, end behavior, and asymptotic behavior).

Exponential Functions - Activity A

Functions Involving Square Roots

Introduction to Functions

Logarithmic Functions: Translating and Scaling

Tangent Function

PC.2.b: Determine horizontal, vertical, and slant asymptotes and holes of rational functions and explain how each was found.

General Form of a Rational Function

Rational Functions

PC.2.c: Determine the domain and range of functions, including piece-wise functions.

Functions Involving Square Roots

PC.2.d: Determine the end behavior of polynomial functions.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

PC.2.f: Solve exponential and logarithmic equations to include real-world applications.

PC.2.h: Find the zeros of polynomial functions by synthetic division and the Factor Theorem.

Cubic Function Activity

Dividing Polynomials Using Synthetic Division

Fourth-Degree Polynomials - Activity A

Polynomials and Linear Factors

PC.2.i: Graph and solve quadratic inequalities.

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Quadratic Inequalities - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

PC.2.j: Decompose a rational function into partial fractions.

General Form of a Rational Function

Rational Functions

PC.3.a: Describe the attributes of graphs and the general equations of parent functions (linear, quadratic, cubic, absolute value, rational, exponential, logarithmic, square root, cube root, and greatest integer).

Exponential Functions - Activity A

Functions Involving Square Roots

General Form of a Rational Function

Linear Functions

Logarithmic Functions - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Roots of a Quadratic

PC.3.b: Explain the effects of changing the parameters in transformations of functions.

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

PC.3.c: Predict the shapes of graphs of exponential, logarithmic, rational, and piece-wise functions, and verify the prediction with and without technology.

Exponential Functions - Activity A

General Form of a Rational Function

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Rational Functions

PC.3.d: Relate symmetry of the behavior of even and odd functions.

PC.4.a: Use regression methods available through technology to determine appropriate exponential and logarithmic functions that model real-life data.

Exponential Functions - Activity A

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

PC.4.b: Use regression methods available through technology to determine appropriate cubic functions that model real-life data.

Cubic Function Activity

Polynomials and Linear Factors

DM.2.a: Define sentence (proposition), and use logic to determine if the sentence is true or false.

DM.2.c: Define a conditional statement using truth tables.

DM.2.e: Define a sequence recursively and explicitly.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

DM.2.f: Find the explicit formula for a recursively-defined sequence using iteration.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

DM.2.g: Use mathematical induction to verify explicit formulas for arithmetic, geometric, and other sequences and/or series.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

DM.3.a: Construct a logic circuit from a Boolean expression to determine output.

Biconditional Statement

Conditional Statement

DM.3.b: Construct a Boolean expression given a logic circuit.

Biconditional Statement

Conditional Statement

DM.3.c: Construct a logic circuit and Boolean expression given an input/output table.

Biconditional Statement

Conditional Statement

Linear Functions

Using Tables, Rules and Graphs

DM.4.c: Create and use simulations for probability models.

Binomial Probabilities

Geometric Probability - Activity A

Probability Simulations

C.2.a: Predict and explain the characteristics and behavior of functions and their graphs (domain, range, increasing/decreasing intervals, intercepts, symmetry, and end behavior).

Cosine Function

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Functions Involving Square Roots

General Form of a Rational Function

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Sine Function

Tangent Function

C.2.b: Investigate, describe, and determine asymptotic behavior using tables, graphs, and analytical methods.

General Form of a Rational Function

Rational Functions

Tangent Function

C.2.c: Determine and justify the continuity and discontinuity of functions.

Exponential Functions - Activity A

Functions Involving Square Roots

C.8.a: Apply integration to solve problems of area.

Perimeter, Circumference, and Area - Activity B

C.9.a: Interpret the concept of definite integral as a limit of Riemann sums over equal subdivisions.

S.1.a: Describe the comparison of center and spread within groups and between or across group variation.

Describing Data Using Statistics

Mean, Median and Mode

S.1.b: Interpret and apply the concept of the Law of Large Numbers.

Geometric Probability - Activity A

Polling: City

S.1.c: Apply the counting principles, including permutations and combinations.

Binomial Probabilities

Permutations

Permutations and Combinations

S.1.d: Construct and interpret sample spaces, events, and tree diagrams.

Binomial Probabilities

Permutations

Permutations and Combinations

S.1.e: Identify types of events, including mutually exclusive, independent, and complements.

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

S.1.f: Calculate geometric probability using two-dimensional models, and explain the processes used.

Geometric Probability - Activity A

S.1.g: Create simulations and experiments that correlate to theoretical probability.

Binomial Probabilities

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Probability Simulations

Theoretical and Experimental Probability

S.1.h: Use Markov Chains to calculate probability by constructing matrix models.

S.1.i: Apply the concept of a random variable to generate and interpret probability distributions.

S.2.a: Analyze and describe outliers and shape of the data including linearity and correlation across graphs and data sets.

Correlation

Roots of a Quadratic

Solving Using Trend Lines

S.2.b: Calculate mean, median, mode, standard deviation, z-scores, t-scores, quartiles, and ranges, and explain their applications.

Box-and-Whisker Plots

Describing Data Using Statistics

Mean, Median and Mode

S.2.d: Use algebraic concepts and methods to determine mathematical models of best fit.

S.3.a: Organize data using graphs that are appropriate to the data set, including frequency distributions, stacked line and bar graphs, stem-and-leaf plots, scatter plot, frequency polygon, and histograms.

Histograms

Populations and Samples

Scatter Plots - Activity A

Stem-and-Leaf Plots

S.3.b: Determine and justify the graph type that best represents a given set of data.

Describing Data Using Statistics

S.4.a: Make inferences and predictions from charts, tables, and graphs that summarize data.

S.4.b: Determine the most appropriate measure to describe a data set, including mean, median, mode, standard deviation, and variance.

Describing Data Using Statistics

Line Plots

Mean, Median and Mode

S.4.d: Explain and defend regression models using correlation coefficients and residuals.

S.5.c: Analyze sources of bias and sampling error(s) in studies.

S.5.d: Compare and contrast sampling methods, including simple random sampling, stratified random sampling, and cluster sampling with regard to benefits and trade-offs.

SMT.2.a: Identify and apply appropriate algebraic formulas to personal finance situations.

SMT.2.b: Apply linear programming to business decisions.

Linear Programming - Activity A

IE.1.b: Convert decimal to binary numbers and binary to decimal numbers.

IE.2.a: Write mass and energy balance equations to solve for some unknown value.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Two-Step Equations

IE.2.b: Find voltage, current, resistance, and solve power in series, parallel, and complex electric circuit theory problems using simultaneous equations generated from Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law (i.e., 3 equations and 3 unknowns).

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

IE.2.c: Graph a "Line of Best Fit" from given lab data and determine the degree of linearity (R_ value), slope of the line, and equation of the line.

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Correlation last revised: 3/26/2010

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