Essential Knowledge and Skills (TEKS)

A.1.A: describe independent and dependent quantities in functional relationships;

Introduction to Functions

Linear Functions

A.1.C: describe functional relationships for given problem situations and write equations or inequalities to answer questions arising from the situations;

A.1.D: represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities; and

Cosine Function

Cubic Function Activity

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

General Form of a Rational Function

Introduction to Functions

Linear Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Polynomials and Linear Factors

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Rational Functions

Sine Function

Slope-Intercept Form of a Line - Activity A

Tangent Function

Using Algebraic Equations

Using Algebraic Expressions

Using Tables, Rules and Graphs

A.1.E: interpret and make decisions, predictions, and critical judgments from functional relationships.

A.2.A: identify and sketch the general forms of linear (y = x) and quadratic (y = x²) parent functions;

Linear Functions

Point-Slope Form of a Line - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

Slope-Intercept Form of a Line - Activity A

A.2.B: identify mathematical domains and ranges and determine reasonable domain and range values for given situations, both continuous and discrete;

A.2.D: collect and organize data, make and interpret scatterplots (including recognizing positive, negative, or no correlation for data approximating linear situations), and model, predict, and make decisions and critical judgments in problem situations.

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

A.3.A: use symbols to represent unknowns and variables; and

A.3.B: look for patterns and represent generalizations algebraically.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

A.4.A: find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations;

Dividing Polynomials Using Synthetic Division

Factoring Special Products

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

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

Solving Two-Step Equations

A.4.C: connect equation notation with function notation, such as y = x + 1 and f(x) = x + 1.

Point-Slope Form of a Line - Activity A

A.5.A: determine whether or not given situations can be represented by linear functions;

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

A.5.B: determine the domain and range for linear functions in given situations; and

Introduction to Functions

Linear Functions

Using Tables, Rules and Graphs

A.5.C: use, translate, and make connections among algebraic, tabular, graphical, or verbal descriptions of linear functions.

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

A.6.A: develop the concept of slope as rate of change and determine slopes from graphs, tables, and algebraic representations;

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Slope - Activity B

A.6.B: interpret the meaning of slope and intercepts in situations using data, symbolic representations, or graphs;

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

A.6.C: investigate, describe, and predict the effects of changes in m and b on the graph of y = mx + b;

Parabolas - Activity A

Roots of a Quadratic

Translating and Scaling Functions

A.6.D: graph and write equations of lines given characteristics such as two points, a point and a slope, or a slope and y-intercept;

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

Using Tables, Rules and Graphs

A.6.E: determine the intercepts of the graphs of linear functions and zeros of linear functions from graphs, tables, and algebraic representations;

Linear Functions

Point-Slope Form of a Line - Activity A

Polynomials and Linear Factors

Slope-Intercept Form of a Line - Activity A

Using Tables, Rules and Graphs

A.6.F: interpret and predict the effects of changing slope and y-intercept in applied situations; and

Defining a Line with Two Points

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

A.6.G: relate direct variation to linear functions and solve problems involving proportional change.

Direct Variation

Direct and Inverse Variation

Linear Functions

Point-Slope Form of a Line - Activity A

Similar Figures - Activity A

Similar Polygons

Slope-Intercept Form of a Line - Activity A

A.7.A: analyze situations involving linear functions and formulate linear equations or inequalities to solve problems;

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Using Tables, Rules and Graphs

A.7.B: investigate methods for solving linear equations and inequalities using concrete models, graphs, and the properties of equality, select a method, and solve the equations and inequalities; and

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

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

A.7.C: interpret and determine the reasonableness of solutions to linear equations and inequalities.

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

A.8.B: solve systems of linear equations using concrete models, graphs, tables, and algebraic methods; and

Modeling Linear Systems - Activity A

Solving Equations By Graphing Each Side

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

A.9.A: determine the domain and range for quadratic functions in given situations;

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

A.9.B: investigate, describe, and predict the effects of changes in a on the graph of y = ax² + c;

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

Parabolas - 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

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

Using Tables, Rules and Graphs

A.9.C: investigate, describe, and predict the effects of changes in c on the graph of y = ax² + c; and

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

Parabolas - 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

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

Using Tables, Rules and Graphs

A.9.D: analyze graphs of quadratic functions and draw conclusions.

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

A.10.A: solve quadratic equations using concrete models, tables, graphs, and algebraic methods; and

A.10.B: make connections among the solutions (roots) of quadratic equations, the zeros of their related functions, and the horizontal intercepts (x-intercepts) of the graph of the function.

Point-Slope Form of a Line - Activity A

Roots of a Quadratic

Slope-Intercept Form of a Line - Activity A

A.11.A: use patterns to generate the laws of exponents and apply them in problem-solving situations;

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

A.11.B: analyze data and represent situations involving inverse variation using concrete models, tables, graphs, or algebraic methods; and

A.11.C: analyze data and represent situations involving exponential growth and decay using concrete models, tables, graphs, or algebraic methods.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

2A.1.A: identify the mathematical domains and ranges of functions and determine reasonable domain and range values for continuous and discrete situations; and

Functions Involving Square Roots

Introduction to Functions

2A.1.B: collect and organize data, make and interpret scatterplots, fit the graph of a function to the data, interpret the results, and proceed to model, predict, and make decisions and critical judgments.

Correlation

Scatter Plots - Activity A

Solving Using Trend Lines

2A.2.A: use tools including factoring and properties of exponents to simplify expressions and to transform and solve equations; and

Dividing Exponential Expressions

Exponents and Power Rules

Multiplying Exponential Expressions

2A.2.B: use complex numbers to describe the solutions of quadratic equations.

2A.3.A: analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;

Linear Programming - Activity A

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

2A.3.B: use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities; and

Linear Programming - Activity A

Modeling Linear Systems - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

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

2A.3.C: interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.

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

2A.4.A: identify and sketch graphs of parent functions, including linear (f(x) = x), quadratic (f(x) = x²), exponential (f(x) = a to the x power), and logarithmic (f(x) = log of a(x)) functions, absolute value of x (f(x) = |x|), square root of x (f(x) = square root of x), and reciprocal of x (f(x) = 1/x);

Exponential Functions - Activity A

Functions Involving Square Roots

Linear Functions

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

Roots of a Quadratic

2A.4.B: extend parent functions with parameters such as a in f(x) = a/x and describe the effects of the parameter changes on the graph of parent functions; and

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

Parabolas - 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

Sine Function

Tangent Function

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

Using Tables, Rules and Graphs

2A.5.A: describe a conic section as the intersection of a plane and a cone;

Pyramids and Cones - Activity A

Surface and Lateral Area of Pyramids and Cones

2A.5.B: sketch graphs of conic sections to relate simple parameter changes in the equation to corresponding changes in the graph;

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

Quadratics in Factored Form

Roots of a Quadratic

Translating and Scaling Functions

2A.5.C: identify symmetries from graphs of conic sections;

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

Quadratics in Factored Form

2A.5.D: identify the conic section from a given equation; and

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

2A.6.A: determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;

Parabolas - Activity A

Quadratic Inequalities - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

2A.6.B: relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; and

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

Using Algebraic Equations

2A.6.C: determine a quadratic function from its roots or a graph.

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

2A.7.B: use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of y = a(x - h)² + k form of a function in applied and purely mathematical situations.

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

Translating and Scaling Functions

2A.8.A: analyze situations involving quadratic functions and formulate quadratic equations or inequalities to solve problems;

Parabolas - Activity A

Quadratic Inequalities - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

2A.8.B: analyze and interpret the solutions of quadratic equations using discriminants and solve quadratic equations using the quadratic formula;

2A.8.D: solve quadratic equations and inequalities using graphs, tables, and algebraic methods.

Quadratic Inequalities - Activity A

Roots of a Quadratic

Using Tables, Rules and Graphs

2A.9.A: use the parent function to investigate, describe, and predict the effects of parameter changes on the graphs of square root functions and describe limitations on the domains and ranges;

Functions Involving Square Roots

Radical Functions

Translating and Scaling Functions

2A.9.B: relate representations of square root functions, such as algebraic, tabular, graphical, and verbal descriptions;

Functions Involving Square Roots

Radical Functions

Using Algebraic Equations

2A.9.C: determine the reasonable domain and range values of square root functions, as well as interpret and determine the reasonableness of solutions to square root equations and inequalities;

Functions Involving Square Roots

Radical Functions

2A.9.D: determine solutions of square root equations using graphs, tables, and algebraic methods;

Defining a Line with Two Points

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

Using Tables, Rules and Graphs

2A.9.E: determine solutions of square root inequalities using graphs and tables;

Functions Involving Square Roots

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

Radical Functions

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

2A.9.F: analyze situations modeled by square root functions, formulate equations or inequalities, select a method, and solve problems; and

Functions Involving Square Roots

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Radical Functions

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

2A.9.G: connect inverses of square root functions with quadratic functions.

Functions Involving Square Roots

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Radical Functions

Roots of a Quadratic

2A.10.A: use quotients of polynomials to describe the graphs of rational functions, predict the effects of parameter changes, describe limitations on the domains and ranges, and examine asymptotic behavior;

General Form of a Rational Function

Rational Functions

Translating and Scaling Functions

2A.10.B: analyze various representations of rational functions with respect to problem situations;

General Form of a Rational Function

Rational Functions

Using Algebraic Equations

2A.10.C: determine the reasonable domain and range values of rational functions, as well as interpret and determine the reasonableness of solutions to rational equations and inequalities;

General Form of a Rational Function

Rational Functions

2A.10.D: determine the solutions of rational equations using graphs, tables, and algebraic methods;

Using Tables, Rules and Graphs

2A.10.F: analyze a situation modeled by a rational function, formulate an equation or inequality composed of a linear or quadratic function, and solve the problem; and

General Form of a Rational Function

Linear Functions

Quadratic Inequalities - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Rational Functions

Roots of a Quadratic

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

2A.10.G: use functions to model and make predictions in problem situations involving direct and inverse variation.

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

2A.11.A: develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses;

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

2A.11.B: use the parent functions to investigate, describe, and predict the effects of parameter changes on the graphs of exponential and logarithmic functions, describe limitations on the domains and ranges, and examine asymptotic behavior;

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

2A.11.C: determine the reasonable domain and range values of exponential and logarithmic functions, as well as interpret and determine the reasonableness of solutions to exponential and logarithmic equations and inequalities;

Exponential Functions - Activity A

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

2A.11.D: determine solutions of exponential and logarithmic equations using graphs, tables, and algebraic methods;

Using Tables, Rules and Graphs

2A.11.E: determine solutions of exponential and logarithmic inequalities using graphs and tables; and

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

2A.11.F: analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

G.1.A: develop an awareness of the structure of a mathematical system, connecting definitions, postulates, logical reasoning, and theorems;

Biconditional Statement

Conditional Statement

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

G.2.A: use constructions to explore attributes of geometric figures and to make conjectures about geometric relationships; and

Classifying Quadrilaterals - Activity B

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

G.2.B: make conjectures about angles, lines, polygons, circles, and three-dimensional figures and determine the validity of the conjectures, choosing from a variety of approaches such as coordinate, transformational, or axiomatic.

G.3.A: determine the validity of a conditional statement, its converse, inverse, and contrapositive;

G.3.B: construct and justify statements about geometric figures and their properties;

Classifying Quadrilaterals - Activity B

Classifying Triangles

Parallelogram Conditions

Special Quadrilaterals

G.3.E: use deductive reasoning to prove a statement.

Biconditional Statement

Conditional Statement

G.5.A: use numeric and geometric patterns to develop algebraic expressions representing geometric properties;

Arithmetic and Geometric Sequences

Classifying Triangles

Ellipse - Activity A

Finding Patterns

Geometric Sequences

Hyperbola - Activity A

G.5.B: use numeric and geometric patterns to make generalizations about geometric properties, including properties of polygons, ratios in similar figures and solids, and angle relationships in polygons and circles;

Arithmetic and Geometric Sequences

Classifying Triangles

Finding Patterns

Geometric Sequences

G.5.D: identify and apply patterns from right triangles to solve meaningful problems, including special right triangles (45-45-90 and 30-60-90) and triangles whose sides are Pythagorean triples.

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

G.6.A: describe and draw the intersection of a given plane with various three-dimensional geometric figures;

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

G.6.B: use nets to represent and construct three-dimensional geometric figures; and

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.6.C: use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems.

3D and Orthographic Views - Activity A

G.7.A: use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures;

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

G.7.B: use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons; and

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

G.7.C: derive and use formulas involving length, slope, and midpoint.

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Slope - Activity B

G.8.A: find areas of regular polygons, circles, and composite figures;

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

G.8.B: find areas of sectors and arc lengths of circles using proportional reasoning;

Circle: Circumference and Area

Perimeter, Circumference, and Area - Activity B

G.8.C: derive, extend, and use the Pythagorean Theorem; and

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

G.8.D: find surface areas and volumes of prisms, pyramids, spheres, cones, cylinders, and composites of these figures in problem situations.

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.9.A: formulate and test conjectures about the properties of parallel and perpendicular lines based on explorations and concrete models;

Construct Parallel and Perpendicular Lines

G.9.C: formulate and test conjectures about the properties and attributes of circles and the lines that intersect them based on explorations and concrete models; and

Defining a Line with Two Points

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

G.10.A: use congruence transformations to make conjectures and justify properties of geometric figures including figures represented on a coordinate plane; and

Classifying Quadrilaterals - Activity B

Constructing Congruent Segments and Angles

Dilations

Parallelogram Conditions

Reflections

Rotations, Reflections and Translations

Special Quadrilaterals

G.10.B: justify and apply triangle congruence relationships.

Congruence in Right Triangles

Proving Triangles Congruent

G.11.A: use and extend similarity properties and transformations to explore and justify conjectures about geometric figures;

Classifying Quadrilaterals - Activity B

Dilations

Perimeters and Areas of Similar Figures

Reflections

Rotations, Reflections and Translations

Similar Figures - Activity A

Similar Polygons

G.11.B: use ratios to solve problems involving similar figures;

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

G.11.C: develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods; and

Cosine Function

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

G.11.D: describe the effect on perimeter, area, and volume when one or more dimensions of a figure are changed and apply this idea in solving problems.

Area of Parallelograms - Activity A

Circle: Circumference and Area

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Rectangle: Perimeter and Area

P.1.A: describe parent functions symbolically and graphically, including f(x) = x to the n power, f(x) = 1n x, f(x) = loga x, f(x) = 1/x, f(x) = e to the x power, f(x) = |x|, f(x) = a to the x power, f(x) = sin x, f(x) = arcsin x, etc.;

Cosine Function

Exponential Functions - Activity A

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

P.1.B: determine the domain and range of functions using graphs, tables, and symbols;

Functions Involving Square Roots

Introduction to Functions

P.1.D: recognize and use connections among significant values of a function (zeros, maximum values, minimum values, etc.), points on the graph of a function, and the symbolic representation of a function; and

Polynomials and Linear Factors

Roots of a Quadratic

P.2.A: apply basic transformations, including a • f(x), f(x) + d, f(x - c), f(b • x), and compositions with absolute value functions, including |f(x)|, and f(|x|), to the parent functions;

Inequalities Involving Absolute Values

Quadratic and Absolute Value Functions

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

P.2.C: investigate identities graphically and verify them symbolically, including logarithmic properties, trigonometric identities, and exponential properties.

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

P.3.A: investigate properties of trigonometric and polynomial functions;

Cosine Function

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

Sine Function

Tangent Function

P.3.B: use functions such as logarithmic, exponential, trigonometric, polynomial, etc. to model real-life data;

Cosine Function

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Sine Function

Tangent Function

P.3.C: use regression to determine the appropriateness of a linear function to model real-life data (including using technology to determine the correlation coefficient);

Correlation

Linear Functions

Solving Using Trend Lines

P.3.D: use properties of functions to analyze and solve problems and make predictions; and

Exponential Functions - Activity A

Logarithmic Functions: Translating and Scaling

P.3.E: solve problems from physical situations using trigonometry, including the use of Law of Sines, Law of Cosines, and area formulas and incorporate radian measure where needed.

P.4.A: represent patterns using arithmetic and geometric sequences and series;

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

P.4.B: use arithmetic, geometric, and other sequences and series to solve real-life problems;

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

P.5.A: use conic sections to model motion, such as the graph of velocity vs. position of a pendulum and motions of planets;

P.6.A: use the concept of vectors to model situations defined by magnitude and direction; and

P.6.B: analyze and solve vector problems generated by real-life situations.

M.2.A: interpret information from various graphs, including line graphs, bar graphs, circle graphs, histograms, scatterplots, line plots, stem and leaf plots, and box and whisker plots to draw conclusions from the data;

Box-and-Whisker Plots

Scatter Plots - Activity A

Stem-and-Leaf Plots

M.2.B: analyze numerical data using measures of central tendency, variability, and correlation in order to make inferences;

M.2.D: use regression methods available through technology to describe various models for data such as linear, quadratic, exponential, etc., select the most appropriate model, and use the model to interpret information.

Exponential Functions - Activity A

Linear Functions

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

M.4.A: compare theoretical and empirical probability; and

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Polling: City

Probability Simulations

Theoretical and Experimental Probability

M.5.A: use rates, linear functions, and direct variation to solve problems involving personal finance and budgeting, including compensations and deductions;

Direct Variation

Direct and Inverse Variation

Linear Functions

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

M.7.A: analyze types of savings options involving simple and compound interest and compare relative advantages of these options;

Exponential Functions - Activity A

Simple and Compound Interest

M.8.B: use trigonometric ratios and functions available through technology to calculate distances and model periodic motion; and

Cosine Function

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

M.8.C: use direct and inverse variation to describe physical laws such as Hook's, Newton's, and Boyle's laws.

Determining a Spring Constant

Direct Variation

Direct and Inverse Variation

M.9.A: use geometric transformations, symmetry, and perspective drawings to describe mathematical patterns and structure in art and architecture; and

Dilations

Holiday Snowflake Designer

Reflections

Rotations, Reflections and Translations

M.9.B: use geometric transformations, proportions, and periodic motion to describe mathematical patterns and structure in music.

Dilations

Polling: Neighborhood

Reflections

Rotations, Reflections and Translations

Similar Figures - Activity A

Similar Polygons

Correlation last revised: 10/30/2009

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