Priority Academic Student Skills

AI.1.1: Equations and Formulas

AI.1.1.a: Translate word phrases and sentences into expressions and equations and vice versa.

Using Algebraic Equations

Using Algebraic Expressions

AI.1.1.b: Solve literal equations involving several variables for one variable in terms of the others.

Solving Formulas for any Variable

AI.1.1.c: Use the formulas from measurable attributes of geometric models (perimeter, circumference, area and volume), science, and statistics to solve problems within an algebraic context.

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

AI.1.1.d: Solve two-step and three-step problems using concepts such as rules of exponents, rate, distance, ratio and proportion, and percent.

Compound Independent Events

Compound Independent and Dependent Events

Distance Formula - Activity A

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Dividing Exponential Expressions

Estimating Population Size

Exponents and Power Rules

Geoboard: The Pythagorean Theorem

Geometric Probability - Activity A

Independent and Dependent Events

Multiplying Exponential Expressions

Part:Part and Part:Whole Ratios

Perimeters and Areas of Similar Figures

Polling: Neighborhood

Probability Simulations

Pythagorean Theorem - Activity A

Similar Figures - Activity A

Similar Polygons

Theoretical and Experimental Probability

AI.1.2: Expressions

AI.1.2.a: Simplify and evaluate linear, absolute value, rational and radical expressions.

Dividing Exponential Expressions

Exponents and Power Rules

Simplifying Radicals - Activity A

Solving Equations By Graphing Each Side

AI.1.2.b: Simplify polynomials by adding, subtracting or multiplying.

Addition of Polynomials - Activity A

AI.1.2.c: Factor polynomial expressions.

Factoring Special Products

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

AI.2.1: Relations and Functions

AI.2.1.a: Distinguish between linear and nonlinear data.

Cosine Function

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Functions Involving Square Roots

General Form of a Rational Function

Linear Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Point-Slope Form of a Line - Activity A

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

Unit Circle

Using Tables, Rules and Graphs

AI.2.1.b: Distinguish between relations and functions.

Introduction to Functions

Linear Functions

AI.2.1.c: Identify dependent and independent variables, domain and range.

Functions Involving Square Roots

Introduction to Functions

AI.2.1.d: Evaluate a function using tables, equations or graphs.

Cosine Function

Cubic Function Activity

Describing Data Using Statistics

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

General Form of a Rational Function

Linear Functions

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Point-Slope Form of a Line - Activity A

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

AI.2.2: Linear Equations and Graphs

AI.2.2.a: Solve linear equations by graphing or using properties of equality.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Point-Slope Form of a Line - Activity A

Solving Equations By Graphing Each Side

Solving Formulas for any Variable

Solving Two-Step Equations

AI.2.2.b: Recognize the parent graph of the functions y = k, y = x, y = |x|, and predict the effects of transformations on the parent graph.

Inequalities Involving Absolute Values

Linear Functions

Quadratic and Absolute Value Functions

Reflections of a Linear Function

Translating and Scaling Functions

Using Tables, Rules and Graphs

AI.2.2.c: Slope

AI.2.2.c.I: Calculate the slope of a line using a graph, an equation, two points or a set of data 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

Using Algebraic Equations

AI.2.2.c.II: Use the slope to differentiate between lines that are parallel, perpendicular, horizontal, or vertical.

Construct Parallel and Perpendicular Lines

Point-Slope Form of a Line - Activity A

Slope - Activity B

AI.2.2.c.III: Interpret the slope and intercepts within the context of everyday life (e.g., telephone charges based on base rate [y-intercept] plus rate per minute [slope]).

Direct Variation

Direct and Inverse Variation

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Modeling Linear Systems - Activity A

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

AI.2.2.d: Develop the equation of a line and graph linear relationships given the following: slope and y-intercept, slope and one point on the line, two points on the line, x-intercept and y-intercept, a set of data points.

Defining a Line with Two Points

Modeling Linear Systems - Activity A

Point-Slope Form of a Line - Activity A

Slope - Activity B

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

AI.2.2.e: Match appropriate equations to a graph, table, or situation and vice versa.

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

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 Tables, Rules and Graphs

AI.2.3: Linear Inequalities and Graphs

AI.2.3.a: Solve linear inequalities by graphing or using properties of inequalities.

Inequalities Involving Absolute Values

Linear Inequalities in Two Variables - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

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

AI.2.3.b: Match appropriate inequalities (with 1 or 2 variables) to a graph, table, or situation and vice versa.

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

Inequalities Involving Absolute Values

Introduction to Functions

Linear Functions

Linear Inequalities in Two Variables - Activity A

Linear Programming - Activity A

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

Slope-Intercept Form of a Line - Activity A

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Tangent Function

Using Tables, Rules and Graphs

AI.2.4: Solve a system of linear equations by graphing, substitution or elimination.

Modeling Linear Systems - Activity A

Solving Linear Systems by Graphing

Special Types of Solutions to Linear Systems

Systems of Linear Equations - Activity A

AI.2.5: Nonlinear Functions

AI.2.5.a: Match exponential and quadratic functions to a table, graph or situation and vice versa.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Exponential Functions - Activity A

Introduction to Functions

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

Using Tables, Rules and Graphs

AI.2.5.b: Solve quadratic equations by graphing, factoring, or using the quadratic formula.

Factoring Special Products

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

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

Roots of a Quadratic

AI.3.1: Data Analysis

AI.3.1.a: Translate from one representation of data to another and understand that the data can be represented using a variety of tables, graphs, or symbols and that different modes of representation often convey different messages.

Describing Data Using Statistics

AI.3.1.c: Solve two-step and three-step problems using concepts such as probability and measures of central tendency.

Binomial Probabilities

Describing Data Using Statistics

Mean, Median and Mode

AI.3.2: Collect data involving two variables and display on a scatter plot; interpret results using a linear model/equation and identify whether the model/equation is a line best fit for the data.

Correlation

Lines of Best Fit Using Least Squares - Activity A

Solving Using Trend Lines

G.1.1: Identify and use logical reasoning skills (inductive and deductive) to make and test conjectures, formulate counter examples, and follow logical arguments.

G.1.3: Compare the properties of Euclidean geometry to non-Euclidean geometries (for example, elliptical geometry, as shown on the surface of a globe, does not uphold the parallel postulate).

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

G.2.1: Use geometric tools (for example, protractor, compass, straight edge) to construct a variety of figures.

Construct Parallel and Perpendicular Lines

Constructing Congruent Segments and Angles

G.2.2: Line and Angle Relationships

G.2.2.a: Use the angle relationships formed by parallel lines cut by a transversal to solve problems.

Investigating Angle Theorems - Activity A

G.2.2.b: Use the angle relationships formed by two lines cut by a transversal to determine if the two lines are parallel and verify, using algebraic and deductive proofs.

Biconditional Statement

Conditional Statement

Investigating Angle Theorems - Activity A

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

G.2.2.c: Use relationships between pairs of angles (for example, adjacent, complementary, vertical) to solve problems.

Investigating Angle Theorems - Activity A

G.2.3: Polygons and Other Plane Figures

G.2.3.a: Identify, describe, and analyze polygons (for example, convex, concave, regular, pentagonal, hexagonal, n-gonal).

Classifying Quadrilaterals - Activity B

Classifying Triangles

Parallelogram Conditions

Special Quadrilaterals

G.2.3.b: Apply the interior and exterior angle sum of convex polygons to solve problems, and verify using algebraic and deductive proofs.

Biconditional Statement

Conditional Statement

Polygon Angle Sum - Activity A

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

Triangle Angle Sum - Activity A

G.2.3.c: Develop and apply the properties of quadrilaterals to solve problems (for example, rectangles, parallelograms, rhombi, trapezoids, kites).

Classifying Quadrilaterals - Activity B

Parallelogram Conditions

Special Quadrilaterals

G.2.3.d: Use properties of 2-dimensional figures and side length, perimeter or circumference, and area to determine unknown values and correctly identify the appropriate unit of measure of each.

Circle: Circumference and Area

Minimize Perimeter

Perimeter, Circumference, and Area - Activity B

Rectangle: Perimeter and Area

G.2.4: Similarity

G.2.4.a: Determine and verify the relationships of similarity of triangles, using algebraic and deductive proofs.

Biconditional Statement

Conditional Statement

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

G.2.4.b: Use ratios of similar 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

Circle: Circumference and Area

Part:Part and Part:Whole Ratios

Perimeter, Circumference, and Area - Activity B

Perimeters and Areas of Similar Figures

Rectangle: Perimeter and Area

Similar Figures - Activity A

Similar Polygons

G.2.5: Congruence

G.2.5.a: Determine and verify the relationships of congruency of triangles, using algebraic and deductive proofs.

Biconditional Statement

Conditional Statement

Congruence in Right Triangles

Proving Triangles Congruent

G.2.5.b: Use the relationships of congruency of 2-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference, and area.

Circle: Circumference and Area

Congruence in Right Triangles

Constructing Congruent Segments and Angles

Perimeter, Circumference, and Area - Activity B

Proving Triangles Congruent

G.2.6: Circles

G.2.6.b: Find angle measures and segment lengths using the relationships among radii, chords, secants, and tangents of a circle.

G.3.1: Use the Pythagorean Theorem and its converse to find missing side lengths and to determine acute, right, and obtuse triangles, and verify using algebraic and deductive proofs.

Biconditional Statement

Conditional Statement

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Pythagorean Theorem - Activity A

Pythagorean Theorem - Activity B

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

Triangle Angle Sum - Activity A

G.3.2: Apply the 45-45-90 and 30-60-90 right triangle relationships to solve problems, and verify using algebraic and deductive proofs.

Biconditional Statement

Conditional Statement

Simplifying Trigonometric Expressions

Sum and Difference Identities for Sine and Cosine

G.3.3: Express the trigonometric functions as ratios and use sine, cosine, and tangent ratios to solve real-world problems.

Cosine Function

Estimating Population Size

Part:Part and Part:Whole Ratios

Perimeters and Areas of Similar Figures

Polling: Neighborhood

Similar Figures - Activity A

Similar Polygons

Sine Function

Sine and Cosine Ratios - Activity A

Sine, Cosine and Tangent

Tangent Function

Tangent Ratio

Unit Circle

G.4.1: Polyhedra and Other Solids

G.4.1.a: Identify, describe, and analyze polyhedra (for example, regular, decahedral).

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

G.4.1.b: Use properties of 3-dimensional figures; side lengths, perimeter or circumference, and area of a face; and volume, lateral area, and surface area to determine unknown values and correctly identify the appropriate unit of measure of each.

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

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

G.4.2: Similarity and Congruence

G.4.2.a: Use ratios of similar 3-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume.

Circle: Circumference and Area

Estimating Population Size

Geometric Probability - Activity A

Part:Part and Part:Whole Ratios

Perimeter, Circumference, and Area - Activity B

Perimeters and Areas of Similar Figures

Similar Figures - Activity A

Similar Polygons

G.4.2.b: Use the relationships of congruency of 3-dimensional figures to determine unknown values, such as angles, side lengths, perimeter or circumference of a face, area of a face, and volume.

Circle: Circumference and Area

Congruence in Right Triangles

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Proving Triangles Congruent

Pyramids and Cones - Activity A

G.4.3: Create a model of a 3-dimensional figure from a 2-dimensional drawing and make a 2-dimensional representation of a 3-dimensional object (for example, nets, blueprints, perspective drawings).

3D and Orthographic Views - Activity A

Surface and Lateral Area of Prisms and Cylinders

Surface and Lateral Area of Pyramids and Cones

G.5.1: Use coordinate geometry to find the distance between two points; the midpoint of a segment; and to calculate the slopes of parallel, perpendicular, horizontal, and vertical lines.

Construct Parallel and Perpendicular Lines

Distance Formula - Activity A

Geoboard: The Pythagorean Theorem

Point-Slope Form of a Line - Activity A

Pythagorean Theorem - Activity A

Slope - Activity B

G.5.2: Properties of Figures

G.5.2.a: Given a set of points determine the type of figure formed based on its properties.

G.5.2.b: Use transformations (reflection, rotation, translation) on geometric figures to solve problems within coordinate geometry.

Dilations

Reflections

Rotations, Reflections and Translations

Translations

AII.1.1: Rational Exponents

AII.1.1.b: Add, subtract, multiply, divide, and simplify radical expressions and expressions containing rational exponents.

Operations with Radical Expressions

Simplifying Radicals - Activity A

AII.1.2: Polynomial and Rational Expressions

AII.1.2.a: Divide polynomial expressions by lower degree polynomials.

Dividing Polynomials Using Synthetic Division

AII.1.3: Complex Numbers

AII.1.3.a: Recognize that to solve certain problems and equations, number systems need to be extended from real numbers to complex numbers.

Points in the Complex Plane - Activity A

AII.2.1: Functions and Function Notation

AII.2.1.a: Recognize the parent graphs of polynomial, exponential, and logarithmic functions and predict the effects of transformations on the parent graphs, using various methods and tools which may include graphing calculators.

Cubic Function Activity

Exponential Functions - Activity A

Fourth-Degree Polynomials - Activity A

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Translating and Scaling Functions

AII.2.1.b: Add, subtract, multiply, and divide functions using function notation.

Addition and Subtraction of Polynomials

AII.2.1.d: Use algebraic, interval, and set notations to specify the domain and range of functions of various types.

Functions Involving Square Roots

AII.2.2: Systems of Equations

AII.2.2.a: Model a situation that can be described by a system of equations or inequalities and use the model to answer questions about the situation.

Linear Programming - Activity A

Modeling Linear Systems - Activity A

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

AII.2.2.b: Solve systems of linear equations and inequalities using various methods and tools which may include substitution, elimination, matrices, graphing, and graphing calculators.

Linear Programming - Activity A

Modeling Linear Systems - Activity A

Special Types of Solutions to Linear Systems

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

AII.2.3: Quadratic Equations and Functions

AII.2.3.a: Solve quadratic equations by graphing, factoring, completing the square and quadratic formula.

Factoring Special Products

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

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

Roots of a Quadratic

AII.2.3.b: Graph a quadratic function and identify the x- and y-intercepts and maximum or minimum value, using various methods and tools which may include a graphing calculator.

Defining a Line with Two Points

Parabolas - Activity A

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Solving Equations By Graphing Each Side

Standard Form of a Line

AII.2.3.c: Model a situation that can be described by a quadratic function and use the model to answer questions about the situation.

Parabolas - Activity A

Quadratic and Absolute Value Functions

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

Roots of a Quadratic

AII.2.4: Identify, graph, and write the equations of the conic sections (circle, ellipse, parabola, and hyperbola).

Circles

Ellipse - Activity A

Hyperbola - Activity A

Parabolas - Activity A

AII.2.5: Exponential and Logarithmic Functions

AII.2.5.a: Graph exponential and logarithmic functions.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

AII.2.5.b: Apply the inverse relationship between exponential and logarithmic functions to convert from one form to another.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

AII.2.5.c: Model a situation that can be described by an exponential or logarithmic function and use the model to answer questions about the situation.

Exponential Functions - Activity A

Exponential Growth and Decay - Activity B

Half-life

Logarithmic Functions - Activity A

Logarithmic Functions: Translating and Scaling

Simple and Compound Interest

AII.2.6: Polynomial Equations and Functions

AII.2.6.a: Solve polynomial equations using various methods and tools which may include factoring and synthetic division.

Dividing Polynomials Using Synthetic Division

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

AII.2.6.b: Sketch the graph of a polynomial function.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

Polynomials and Linear Factors

Quadratics in Factored Form

Quadratics in Polynomial Form - Activity A

AII.2.6.c: Given the graph of a polynomial function, identify the x- and y-intercepts, relative maximums and relative minimums, using various methods and tools which may include a graphing calculator.

Cubic Function Activity

Defining a Line with Two Points

Fourth-Degree Polynomials - Activity A

Parabolas - Activity A

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

Standard Form of a Line

AII.2.6.d: Model a situation that can be described by a polynomial function and use the model to answer questions about the situation.

Cubic Function Activity

Fourth-Degree Polynomials - Activity A

AII.2.7: Rational Equations and Functions

AII.2.7.c: Given the graph of a rational function, identify the x- and y-intercepts, asymptotes, using various methods and tools which may include a graphing calculator.

Parabolas - Activity A

Point-Slope Form of a Line - Activity A

Slope-Intercept Form of a Line - Activity A

AII.3.1: Analysis of Collected Data Involving Two Variables

AII.3.1.a: Display data on a scatter plot.

Scatter Plots - Activity A

Solving Using Trend Lines

AII.3.2: Measures of Central Tendency and Variability

AII.3.2.a: Analyze and synthesize data from a sample using appropriate measures of central tendency (mean, median, mode, weighted average).

Describing Data Using Statistics

Mean, Median and Mode

AII.3.2.b: Analyze and synthesize data from a sample using appropriate measures of variability (range, variance, standard deviation).

Describing Data Using Statistics

AII.3.3: Identify and use arithmetic and geometric sequences and series to solve problems.

Arithmetic and Geometric Sequences

Geometric Sequences

Correlation last revised: 12/4/2009

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