### I: Patterns, Relationships and Functions

#### I.1: Students recognize similarities and generalize patterns, use patterns to create models and make predictions, describe the nature of patterns and relationships, and construct representations of mathematical relationships.

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

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

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

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

#### I.2: Students describe the relationships among variables, predict what will happen to one variable as another variable is changed, analyze natural variation and sources of variability, and compare patterns of change.

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.

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

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.

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

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.

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

### II: Geometry and Measurement

#### II.1: Students develop spatial sense, use shape as an analytic and descriptive tool, identify characteristics and define shapes, identify properties and describe relationships among shapes.

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

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

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

#### II.2: Students identify locations of objects, identify location relative to other objects, and describe the effects of transformations (e.g., sliding, flipping, turning, enlarging, reducing) on an object.

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.

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

#### II.3: Students compare attributes of two objects, or of one object with a standard (unit), and analyze situations to determine what measurement(s) should be made and to what level of precision.

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.

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.

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.

### III: Data Analysis and Statistics

#### III.1: Students collect and explore data, organize data into a useful form, and develop skill in representing and reading data displayed in different formats.

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.

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: Students examine data and describe characteristics of a distribution, relate data to the situation from which they arose, and use data to answer questions convincingly and persuasively.

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.

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: Students draw defensible inferences about unknown outcomes, make predictions, and identify the degree of confidence they have in their predictions.

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

### IV: Number Sense and Numeration

#### IV.1: Students experience counting and measuring activities to develop intuitive sense about numbers, develop understanding about properties of numbers, understand the need for and existence of different sets of numbers, and investigate properties of special numbers.

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

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.

#### IV.2: Students recognize that numbers are used in different ways such as counting, measuring, ordering and estimating, understand and produce multiple representations of a number, and translate among equivalent representations.

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

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.

#### IV.3: Students investigate relationships such as equality, inequality, inverses, factors and multiples, and represent and compare very large and very small numbers.

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

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

### V: Numerical and Algebraic Operations and Analytical Thinking

#### V.1: Students understand and use various types of operations (e.g., addition, subtraction, multiplication, division) to solve problems.

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: Students analyze problems to determine an appropriate process for solution, and use algebraic notations to model or represent problems. (Algebraic and Analytic Thinking)

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.

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.

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.

### VI: Probability and Discrete Mathematics

#### VI.1: Students develop an understanding of the notion of certainty and of probability as a measure of the degree of likelihood that can be assigned to a given event based on the knowledge available, and make critical judgments about claims that are made in probabilistic situations.

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

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

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

#### VI.2: Students investigate practical situations such as scheduling, routing, sequencing, networking, organizing and classifying, and analyze ideas like recurrence relations, induction, iteration, and algorithm design.

VI.2.1: Derive and use formulas for calculating 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.