Curriculum Framework

I.1.1: Analyze and generalize mathematical patterns including sequences, series and recursive patterns.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

I.1.2: Analyze, interpret and translate among representations of patterns including tables, charts, graphs, matrices and vectors.

Arithmetic Sequences

Polynomials and Linear Factors

I.1.3: Study and employ mathematical models of patterns to make inferences, predictions and decisions.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Finding Patterns

Geometric Sequences

I.1.4: Explore patterns (graphic, numeric, etc.) characteristic of families of functions; explore structural patterns within systems of objects, operations or relations.

Arithmetic Sequences

Arithmetic and Geometric Sequences

Geometric Sequences

Introduction to Functions

I.2.1: Identify and describe the nature of change and begin to use the more formal language such as rate of change, continuity, limit, distribution and deviation.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

I.2.2: Develop a mathematical concept of function and recognize that functions display characteristic patterns of change (e.g., linear, quadratic, exponential).

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

I.2.3: Expand their understanding of function to include non-linear functions, composition of functions, inverses of functions, and piecewise- and recursively- defined functions.

Cosine Function

Sine Function

Tangent Function

Translating and Scaling Sine and Cosine Functions - Activity A

Unit Circle

I.2.4: Represent functions using symbolism such as matrices, vectors and functional representation (f(x)).

Linear Functions

Using Algebraic Equations

I.2.5: Differentiate and analyze classes of functions including linear, power, quadratic, exponential, circular and trigonometric functions, and realize that many different situations can be modeled by a particular type of function.

Cosine Function

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

Sine Function

Tangent Function

I.2.6: Increase their use of functions and mathematical models to solve problems in context.

Exponential Growth and Decay - Activity B

II.1.5: Study transformations of shapes using isometries, size transformations and coordinate mappings.

Dilations

Parabolas - Activity A

Reflections

Rotations, Reflections and Translations

Translations

II.1.6: Compare and analyze shapes and formally establish the relationships among them, including congruence, similarity, parallelism, perpendicularity and incidence.

Congruence in Right Triangles

Perimeters and Areas of Similar Figures

Proving Triangles Congruent

Similar Figures - Activity A

Similar Polygons

II.1.7: Use shape, shape properties and shape relationships to describe the physical world and to solve problems.

II.2.2: Locate and describe objects in terms of their orientation and relative position, including displacement (vectors), phase shift, maxima, minima and inflection points; give precise mathematical descriptions of symmetries.

Holiday Snowflake Designer

Translating and Scaling Functions

Translating and Scaling Sine and Cosine Functions - Activity A

II.2.3: Give precise mathematical descriptions of transformations and describe the effects of transformations on size, shape, position and orientation.

Dilations

Reflections

Rotations, Reflections and Translations

II.3.1: Select and use appropriate tools; make accurate measurements using both metric and common units, and measure angles in degrees and radians.

II.3.2: Continue to make and apply measurements of length, mass (weight), time, temperature, area, volume, angle; classify objects according to their dimensions.

Perimeter, Circumference, and Area - Activity B

Prisms and Cylinders - Activity A

Pyramids and Cones - Activity A

Special Quadrilaterals

II.3.3: Estimate measures with a specified degree of accuracy and evaluate measurements for accuracy, precision and tolerance.

II.3.4: Interpret measurements and explain how changes in one measure may affect other measures.

Distance-Time Graphs

Distance-Time and Velocity-Time Graphs

Prisms and Cylinders - Activity A

II.3.5: Use proportional reasoning and indirect measurements, including applications of trigonometric ratios, to measure inaccessible distances and to determine derived measures such as density.

Density Laboratory

Determining Density via Water Displacement

Estimating Population Size

Similar Figures - Activity A

Similar Polygons

III.1.1: Collect and explore data through observation, measurement, surveys, sampling techniques and simulations.

III.1.2: Organize data using tables, charts, graphs, spreadsheets and data bases.

III.1.3: Present data using the most appropriate representation and give a rationale for their choice; show how certain representations may skew the data or bias the presentation.

Box-and-Whisker Plots

Histograms

Line Plots

Scatter Plots - Activity A

Stem-and-Leaf Plots

III.1.4: Identify what data are needed to answer a particular question or solve a given problem and design and implement strategies to obtain, organize and present those data.

III.2.1: Critically read data from tables, charts or graphs and explain the source of the data and what the data represent.

III.2.2: Describe the shape of a data distribution and determine measures of central tendency, variability and correlation.

Correlation

Line Plots

Mean, Median and Mode

Solving Using Trend Lines

III.2.4: Critically question the sources of data; the techniques used to collect, organize and present data; the inferences drawn from the data; and the sources of bias and measures taken to eliminate such bias.

III.3.5: Employ investigations, mathematical models, and simulations to make inferences and predictions to answer questions and solve problems.

IV.1.1: Develop an understanding of irrational, real and complex numbers.

Points in the Complex Plane - Activity A

IV.1.2: Use the (a+bi) and polar forms of complex numbers.

IV.1.3: Develop an understanding of the properties of the real and complex number systems and of the properties of special numbers including pi, i, e, and conjugates.

Points in the Complex Plane - Activity A

IV.2.1: Give decimal representations of rational and irrational numbers and coordinate and vector representations of complex numbers.

Points in the Complex Plane - Activity A

IV.2.5: Select appropriate representations for numbers, including representations of rational and irrational numbers and coordinate and vector representations of complex numbers, in order to simplify and solve problems.

Points in the Complex Plane - Activity A

IV.3.1: Compare and order real numbers and compare rational approximations to exact values.

Comparing and Ordering Decimals

Comparing and Ordering Fractions

Comparing and Ordering Rational Numbers

IV.3.2: Express numerical comparisons as ratios and rates.

Beam to Moon (Ratios and Proportions)

Estimating Population Size

Part:Part and Part:Whole Ratios

Polling: Neighborhood

V.1.2: Compute with real numbers, complex numbers, algebraic expressions, matrices and vectors using technology and, for simple instances, with paper- and-pencil algorithms.

V.2.1: Identify important variables in a context, symbolize them and express their relationships algebraically.

V.2.2: Represent algebraic concepts and relationships with matrices, spreadsheets, diagrams, graphs, tables, physical models, vectors, equations and inequalities; and translate among the various representations.

Introduction to Functions

Linear Functions

Linear Inequalities in Two Variables - Activity A

Using Tables, Rules and Graphs

Vectors

V.2.3: Solve linear equations and inequalities algebraically and non-linear equations using graphing, symbol-manipulating or spreadsheet technology; and solve linear and non-linear systems using appropriate methods.

Modeling One-Step Equations - Activity A

Modeling and Solving Two-Step Equations

Solving Equations By Graphing Each Side

Solving Linear Inequalities using Addition and Subtraction

Solving Linear Inequalities using Multiplication and Division

Solving Two-Step Equations

V.2.5: Explore problems that reflect the contemporary uses of mathematics in significant contexts and use the power of technology and algebraic and analytic reasoning to experience the ways mathematics is used in society.

Biconditional Statement

Conditional Statement

VI.1.2: Give a mathematical definition of probability and determine the probabilities of more complex events, and generate and interpret probability distributions.

Binomial Probabilities

Geometric Probability - Activity A

VI.1.3: Analyze events to determine their dependence or independence and calculate probabilities of compound events.

Binomial Probabilities

Compound Independent Events

Compound Independent and Dependent Events

Independent and Dependent Events

VI.1.4: Use sampling and simulations to determine empirical probabilities and, when appropriate, compare them to the corresponding theoretical probabilities; understand and apply the law of large numbers.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Polling: City

Probability Simulations

Theoretical and Experimental Probability

VI.1.5: Conduct probability experiments and simulations, to model and solve problems, including compound events.

Compound Independent Events

Compound Independent and Dependent Events

Geometric Probability - Activity A

Independent and Dependent Events

Probability Simulations

VI.2.1: Derive and use formulas for calculating permutations and combinations.

Binomial Probabilities

Permutations

Permutations and Combinations

Correlation last revised: 11/13/2008

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