### FN1: Foundations I

FN1.1.1: demonstrate an understanding of the subsets, elements, properties, and operations of the rational number system;

FN1.1.3: order and compare rational numbers;

FN1.1.4: informally describe and model the concept of additive and multiplicative inverses (e.g., opposites, reciprocals) in real life problem situations;

FN1.1.5: apply number theory concepts (e.g., primes, composites, factors, divisibility ,and multiples) in mathematical problem situations;

FN1.1.6: use rational numbers to represent real-world applications (e.g., probability, proportionality);

FN1.1.8: select and apply an appropriate method (i.e., mental arithmetic, paper and pencil, or technology) for computing with rational numbers, and evaluate the reasonableness of results;

FN1.1.9: apply estimation strategies in computation and in problem solving.

FN1.2.1: recognize, extend, and create geometric, spatial, and numerical patterns;

FN1.2.3: communicate the meaning of variables in algebraic expressions and equations;

FN1.2.4: apply the concept of variable in simplifying algebraic expressions and solving equations;

FN1.3.1: apply geometric properties, formulas, and relationships to solve real-world problems;

FN1.3.3: demonstrate an understanding of the properties and construction of geometric figures, including angles, parallel lines, perpendicular lines, triangles, circles, and quadrilaterals;

FN1.4.1: apply appropriate techniques, tools, and formulas to determine measurements;

FN1.5.1: choose, construct, and analyze appropriate graphical representations for a data set including pie charts, histograms, stem and leaf plots, and scatterplots;

FN1.5.2: interpret a set of data using the appropriate measure of central tendency (mean, median, mode);

FN1.5.3: determine experimental and theoretical probabilities for simple experiments.

FN2.1.4: informally describe and model the concept of inverse (e.g., opposites, reciprocals, and squares and square roots);

FN2.1.7: apply number theory concepts (e.g., primes, factors, divisibility and multiples) in mathematical problem situations;

FN2.1.9: use real numbers to represent real-world applications (e.g., rate of change, probability, and proportionality);

FN2.1.11: communicate the concepts and strategies being used in estimation and computation;

FN2.2.1: recognize, extend, and create geometric, spatial, and numerical patterns;

FN2.2.2: analyze mathematical patterns related to algebra and geometry in real-world problem solving;

FN2.2.3: solve problems in number theory, geometry, probability and statistics, and measurement and estimation using algebraic thinking and symbolism (attention given to solving linear equations);

FN2.2.4: communicate the meaning of variables in algebraic expressions, equations, and inequalities;

FN2.2.5: interpret the results of algebraic procedures;

FN2.2.6: apply the concept of variable in simplifying algebraic expressions, solving equations, and solving inequalities;

FN2.3.1: analyze relationships among corresponding parts of similar or congruent geometric figures;

FN2.3.2: apply geometric properties, formulas, and relationships to solve real-world problems;

FN2.3.5: demonstrate an understanding of transformations of geometric figures;

FN2.3.6: apply the Pythagorean Theorem in problem solving;

FN2.4.2: use concepts of length and area, including surface area and volume, to estimate and solve real-world problems (e.g., parallelograms, triangles, right rectangular prisms, circles, right cylinders, spheres, and pyramids);

FN2.4.4: choose appropriate techniques and tools to measure quantities in order to meet specifications for precision and accuracy;

FN2.4.5: demonstrate an understanding of rates and other derived and indirect measurements (e.g., velocity, miles per hr, rpm, and cost per unit).

FN2.5.1: interpret a set of data using the appropriate measure of central tendency (mean, median, mode) and the appropriate measure of dispersion (e.g., quartiles, range);

FN2.5.2: choose, construct, and analyze appropriate graphical representations for a data set including pie charts, histograms, stem-and-leaf plots, scatterplots, and box plots;

FN2.5.4: apply theoretical and experimental probability to analyze the likelihood of an event;

FN2.5.5: use simulations to estimate probability;

FN2.5.7: apply counting principles of permutations and combinations using appropriate technology.

### AL1: Algebra I

AL1.1.5: apply number theory concepts (e.g., primes, factors, divisibility and multiples) in mathematical problem solving;

AL1.1.7: use real numbers to represent real-world applications (e.g., slope, rate of change, probability, and proportionality);

AL1.1.8: use a variety of notations appropriately (e.g. exponential, functional, square root);

AL1.2.1: recognize, analyze, extend, and create a variety of patterns;

AL1.2.3: solve linear systems using a variety of techniques;

AL1.2.4: communicate the meaning of variables in algebraic expressions, equations, and inequalities;

AL1.2.5: identify and represent a variety of functions;

AL1.2.6: apply and interpret rates of change from graphical and numerical data;

AL1.2.7: analyze graphs to describe the behavior of functions;

AL1.2.8: interpret results of algebraic procedures;

AL1.2.9: apply the concept of variable in simplifying algebraic expressions, solving equations, and solving inequalities;

AL1.2.11: model real-world phenomena using functions and graphs;

AL1.2.12: articulate and apply algebraic properties in symbolic manipulation;

AL1.2.13: analyze relationships which can and which cannot be represented by a function;

AL1.2.14: graph inequalities and interpret graphs of inequalities;

AL1.2.15: describe the domain and range of functions and articulate restrictions imposed either by the operations or by the real-life situations which the functions represent;

AL1.2.16: describe the transformation of the graph that occurs when coefficients and/or constants of the corresponding linear equations are changed.

AL1.3.1: apply geometric properties, formulas, and relationships to solve real-world problems;

AL1.3.3: apply right triangle relationships including the Pythagorean Theorem and the distance formula;

AL1.4.1: use concepts of length, area, and volume to estimate and solve real-world problems;

AL1.4.2: apply and communicate measurement concepts and relationships in algebraic and geometric problem-solving situations;

AL1.4.4: make decisions about units, scales, and measurement tools that are appropriate for problem situations involving measurement;

AL1.5.3: interpret a set of data using the appropriate measure of central tendency;

AL1.5.4: choose, construct, and analyze appropriate graphical representations for a data set;

AL1.5.5: understand the concept of random sampling;

AL1.5.6: apply counting principles of permutations and combinations using appropriate technology;

AL1.5.7: model situations to determine theoretical and experimental probabilities.

### GEO: Geometry

GEO.2.1: recognize, extend, and create geometric, spatial, and numerical patterns;

GEO.2.2: analyze mathematical patterns related to algebra and geometry in real-world problem solving;

GEO.2.3: solve problems connecting geometry with number theory, probability and statistics, and measurement and estimation using algebraic thinking and symbolism;

GEO.2.5: apply ratio and proportion to problems involving similar figures.

GEO.3.1: analyze relationships among corresponding parts of similar or congruent geometric figures;

GEO.3.2: apply geometric properties of solids, polygons, and circles to solve real-world problems;

GEO.3.3: justify conclusions and solve problems using deductive reasoning;

GEO.3.6: demonstrate an understanding of transformations of geometric figures (i.e., translations, rotations, dilations, and reflections);

GEO.3.7: apply right triangle relationships including the Pythagorean Theorem, the distance formula, and trigonometric ratios;

GEO.3.9: apply reflexive, transitive, and symmetric properties when appropriate;

GEO.3.10: demonstrate understanding of geometric properties of congruence, similarity, perpendicularity, and parallelism;

GEO.3.11: recognize and articulate relationships among families of geometric figures (e.g., quadrilaterals, prisms);

GEO.3.12: use logic and proof to establish the validity of conjectures and theorems.

GEO.4.1: use concepts of length, area, and volume to estimate and solve real-world problems;

GEO.4.3: choose appropriate techniques and tools to measure quantities in order to meet specifications for precision, accuracy, and tolerance.

GEO.5.1: apply geometric representations to calculate theoretical probability;

GEO.5.2: use data analysis to investigate geometric relationships.

### TGE: Technical Geometry

TGE.2.1: recognize, extend, and create geometric, spatial, and numerical patterns;

TGE.2.2: analyze mathematical patterns related to algebra and geometry in real-world problem solving;

TGE.2.3: solve problems connecting geometry with number theory, probability and statistics, and measurement and estimation using algebraic thinking and symbolism;

TGE.2.5: apply ratio and proportion to problems involving similar figures.

TGE.3.1: analyze relationships among corresponding parts of similar or congruent geometric figures;

TGE.3.2: apply geometric properties of solids, polygons, and circles to solve real-world problems;

TGE.3.3: justify conclusions and solve problems using deductive reasoning;

TGE.3.6: demonstrate an understanding of transformations of geometric figures (i.e., translations, rotations, dilations, and reflections);

TGE.3.7: apply right triangle relationships including the Pythagorean Theorem, the distance formula, and trigonometric ratios;

TGE.3.9: apply reflexive, transitive, and symmetric properties when appropriate;

TGE.3.10: demonstrate understanding of geometric properties of congruence, similarity, perpendicularity, and parallelism;

TGE.3.11: recognize and articulate relationships among families of geometric figures (e.g., quadrilaterals, prisms);

TGE.3.12: use logic and proof to establish the validity of conjectures and theorems.

TGE.4.1: use concepts of length, area, and volume to estimate and solve real-world problems;

TGE.4.3: choose appropriate techniques and tools to measure quantities in order to meet specifications for precision, accuracy, and tolerance.

TGE.5.1: apply geometric representations to calculate theoretical probability;

TGE.5.2: use data analysis to investigate geometric relationships.

### AL2: Algebra II

AL2.1.6: use a variety of notations appropriately (e.g. logarithmic, factorial, sigma, delta, radical);

AL2.2.3: solve linear systems using a variety of techniques, including matrices;

AL2.2.4: communicate the meaning of variables in algebraic expressions, equations, and inequalities;

AL2.2.7: identify and represent a variety of functions (e.g. linear, quadratic, cubic);

AL2.2.8: identify, describe, and articulate the characteristics and the parameters of a parent function;

AL2.2.9: interpret results of algebraic procedures;

AL2.2.10: apply the concept of variable in simplifying algebraic expressions, solving equations, and solving inequalities;

AL2.2.12: model real-world phenomena using functions and graphs;

AL2.2.13: describe the domain and range of functions and articulate restrictions imposed either by the operations or by the real-life situations which the functions represent;

AL2.2.14: use linear programming to solve real-world problems.

AL2.3.1: apply geometric properties, formulas, and relationships to solve real-world problems;

AL2.3.2: justify conclusions using deductive reasoning;

AL2.3.5: perform a given transformation and predict the results of the transformation.

AL2.4.2: apply appropriate techniques, tools, and formulas to determine measurements.

AL2.5.1: understand concept of randomness in sampling;

AL2.5.3: apply counting principles of permutations and combinations using appropriate technology;

AL2.5.4: apply theoretical and experimental probability to analyze the likelihood of an event;

AL2.5.5: collect, represent, and describe linear and nonlinear data sets developed from real world;

AL2.5.7: make inferences about a data set using appropriate measures of central tendency and dispersion;

AL2.5.10: analyze the probability of dependent events and of independent events;

AL2.5.11: use simulations to estimate probability;

AL2.5.12: choose, construct, and analyze appropriate graphical representations for a data set;

### IM1: Integrated Mathematics I

IM1.1.1: demonstrate an understanding of the elements, subsets, properties, and operations of rational numbers;

IM1.1.2: demonstrate understanding of positive integer exponents and perform operations with expressions involving exponents;

IM1.1.9: use a variety of notations appropriately (e.g., exponential, functional, square root);

IM1.2.1: communicate the meaning of variables in algebraic expressions, equations, and inequalities;

IM1.2.2: identify dependent and independent variables in real-world situations;

IM1.2.3: apply the concept of variable in simplifying algebraic expressions, solving equations, and solving inequalities;

IM1.2.4: represent the solution set linear equations and inequalities in one variable symbolically, graphically, and verbally;

IM1.2.7: represent functions with equations, graphs, tables, and words;

IM1.2.9: solve real-world problems represented by linear functions and interpret the slope and intercepts;

IM1.2.10: solve systems of two equations in two unknowns using a variety of techniques;

IM1.2.11: recognize and extend numerical, geometric, and spatial patterns;

IM1.2.12: describe the domain and range of functions imposed either by operations or by real-life situations that the functions represent;

IM1.2.13: describe the transformation of the graph that occurs when coefficients and/or constants of the corresponding linear equation are changed;

IM1.2.14: generalize numerical, geometric patterns verbally and symbolically.

IM1.3.2: apply properties of special pairs of angles (e.g. supplementary, complementary, vertical, and adjacent);

IM1.3.3: articulate relationships of angles formed when parallel lines are cut by a transversal;

IM1.3.4: apply the concept of slope to parallel and perpendicular lines;

IM1.3.5: solve real world problems involving length, perimeter, and circumference;

IM1.3.6: apply the properties of congruence and similarity to solve problems;

IM1.3.7: apply the Pythagorean Theorem and the distance formula;

IM1.4.1: choose appropriate techniques and tools to measure quantities in order to meet specifications for precision and accuracy;

IM1.4.2: use concepts of length, area, and volume to estimate and solve real- world problems;

IM1.5.2: choose, construct, and analyze appropriate graphical representations for a data set;

IM1.5.3: interpret data using the appropriate measure of central tendency for the data set;

IM1.5.4: determine the measures of dispersion of a data set including range and quartiles;

IM1.5.5: apply basic counting principles, introducing factorial notation; apply experimental and theoretical probability with simulations where appropriate;

IM1.5.6: make predictions from a linear data set using a line of best fit.

### IM2: Integrated Mathematics II

IM2.2.1: solve systems of three equations and three unknowns using a variety of techniques including inverse matrices with technology;

IM2.2.2: describe the domain and range of a function;

IM2.2.5: solve quadratic equations and inequalities using appropriate methods;

IM2.2.7: graph absolute value functions and quadratic functions with emphasis on transformations;

IM2.2.8: solve real-world problems modeled by absolute value or quadratic functions;

IM2.2.9: recognize the conic sections from given information;

IM2.2.10: recognize, extend, and create numerical, geometric, and spatial patterns;

IM2.3.1: demonstrate an understanding of geometric transformations (i.e. reflection, translation, rotation, and dilation);

IM2.3.2: apply deductive reasoning using postulates and theorems to prove conclusions from given hypotheses;

IM2.3.4: apply right triangle properties, including geometric mean, The Pythagorean Theorem, special right triangles, and the trigonometric ratios;

IM2.3.5: derive the distance formula for the distance between two points in a rectangular coordinate system;

IM2.3.6: apply concepts related to similar and congruent triangles;

IM2.3.7: apply properties of circles, arcs, chords, tangents, or secants to solve problems;

IM2.3.8: apply the distance and midpoint formulas in solving problems;

IM2.3.9: solve real-world problems involving area with two- and three- dimensional shapes;

IM2.3.10: use coordinates to describe position in two and three dimensions.

IM2.4.1: choose appropriate techniques and tools to measure quantities in order to meet specifications for tolerance;

IM2.4.3: use concepts of length, area, and volume to estimate and solve real-world problems;

IM2.4.7: apply geometric properties in constructions using a variety of tools (e.g. paper folding, geometric software, reflections tools).

IM2.5.2: use simulations to demonstrate probability experiments;

IM2.5.5: determine the probability of an event;

### IM3: Integrated Mathematics III

IM3.1.2: demonstrate an understanding of the elements, subsets, and properties of the complex number system.

IM3.2.1: perform operations on functions, including composition, and determine the effects of the composition on the domain and range;

IM3.2.3: identify and describe the characteristics of families of functions;

IM3.2.4: articulate the results of varying parameters of a parent function;

IM3.2.6: solve absolute value equations and inequalities;

IM3.2.7: graph polynomial, exponential, and logarithmic and rational functions;

IM3.2.9: solve real-world problems modeled by polynomial, exponential, logarithmic, and periodic functions;

IM3.2.10: solve problems involving linear programming;

IM3.2.11: demonstrate an understanding of recursive and explicit definitions of functions and sequences;

IM3.2.13: apply sigma notation with arithmetic and geometric series;

IM3.2.14: represent a sequence using a list, graph, symbols, and words;

IM3.2.15: determine an equation of a conic section from its graph.

IM3.3.1: apply and justify properties of quadrilaterals and circles;

IM3.3.2: solve real world problems involving volume of geometric solids;

IM3.3.3: demonstrate an understanding of the Platonic Solids;

IM3.3.5: apply transformational matrices to transform geometric figures in a rectangular coordinate system.

IM3.4.1: use concepts of length, area, and volume to estimate and solve real-world problems;

IM3.5.2: use z-scores to compare normally distributed data sets;

IM3.5.3: use a variety of techniques to determine equations of best fit for nonlinear data sets;

IM3.5.6: determine binomial probabilities using appropriate methods;

### AAT: Advanced Algebra and Trigonometry

AAT.1.1: represent situations that involve variable quantities with expressions, equations, inequalities, and matrices;

AAT.1.2: use appropriate methods and technologies to represent and characterize the solutions for a variety of equations, inequalities, and systems of equations and systems of inequalities;

AAT.1.3: demonstrate understanding of sequences and series.

AAT.2.2: connect trigonometric and circular functions;

AAT.2.3: interpret trigonometric functions represented graphically.

### DMS: Discrete Mathematics with Statistics and Probability

DMS.1.2: apply inductive and deductive reasoning to discrete problem situations;

DMS.1.1: use discrete structures to represent problem situations;

DMS.3.2: select and use appropriate representations to summarize data;

### PRC: PreCalculus

PRC.2.1: represent a variety of functions graphically;

PRC.2.2: use a variety of methods to analyze and interpret functions;

PRC.2.3: determine the slope and equations of lines tangent to curves;

PRC.2.4: apply functions in problem situations.

PRC.3.3: solve trigonometric equations and inequalities algebraically or graphically;

PRC.3.4: interpret transformations of trigonometric functions.

PRC.4.1: represent sequences and series;

### STA: Statistics

STA.2.1: select and use appropriate displays to represent and summarize the data collected in statistical studies or experiments;

### CAL: Calculus

CAL.1.3: represent a variety of functions graphically;

### TMA: Technical Mathematics

TMA.1.4: informally describe and model the concept of inverse (e.g., opposites, reciprocals, and squares and square roots);

TMA.1.6: apply number theory concepts (e.g., primes, factors, divisibility and multiples) in mathematical problem situations;

TMA.1.8: use real numbers to represent real-world applications (e.g., rate of change, probability, and proportionality);

TMA.2.1: analyze, extend, and create mathematical patterns related to algebra in real-world problem solving;

TMA.2.2: communicate the meaning of variables in algebraic expressions and equation;

TMA.2.3: apply and interpret rates of change from numerical data;

TMA.2.4: apply the concept of variable to simplify algebraic expressions and solve equations;

TMA.2.5: model real-world phenomenon using graphs.

TMA.3.1: analyze and apply concepts and properties in the construction of lines, angles, and vertices when solving work-related problems;

TMA.3.3: synthesize and apply geometrical concepts, properties, and formulas of three-dimensional shapes when solving work-related problems.

TMA.4.1: select and use appropriate tools of measurement to determine length, area, angular measurement and volume with in given tolerances (i.e. vernier caliper, micrometer, machinist rule, graduated cylinders, protractors as well as rulers);

TMA.4.2: use measurements of length, area, angular measurement and volume to estimate and solve real-world problems;

TMA.4.4: demonstrate an understanding of rates and other derived and indirect measurements.

TMA.5.1: read graphs, charts, and tables;

TMA.5.4: choose, construct, and analyze appropriate graphical representations for a data set;

TMA.5.5: interpret a set of data using the appropriate measure of central tendency;

TMA.5.6: interpolate readings on a graph as well as extrapolate to estimate values;

### TAL: Technical Algebra

TAL.1.5: apply number theory concepts (, primes, factors, divisibility and multiples) in mathematical problem solving;

TAL.1.7: use real numbers to represent real-world applications (, slope, rate of change, probability, and proportionality);

TAL.1.8: use a variety of notations appropriately (exponential, functional, square root);

TAL.2.1: recognize, analyze, extend, and create a variety of patterns;

TAL.2.3: communicate the meaning of variables in algebraic expressions, equations, and inequalities;

TAL.2.4: identify and represent a variety of functions using technology;

TAL.2.5: apply and interpret rates of change from graphical and numerical data

TAL.2.6: analyze graphs to describe the behavior of functions;

TAL.2.7: interpret results of algebraic procedures;

TAL.2.8: apply the concept of variable in simplifying algebraic expressions, solving equations, and solving inequalities;

TAL.2.10: model real-world phenomena using functions and graphs;

TAL.2.11: articulate and apply algebraic properties in symbolic manipulation;

TAL.2.12: analyze relationships which can and which cannot be represented by a function;

TAL.2.13: graph inequalities and interpret graphs of inequalities;

TAL.2.14: describe the domain and range of functions and articulate restrictions imposed either by the operations or by the real-life situations which the functions represent;

TAL.2.15: describe the transformation of the graph that occurs when coefficients and/or constants of the corresponding linear equations are changed.

TAL.3.1: apply geometric properties, formulas, and relationships to solve real-world problems;

TAL.3.3: apply right triangle relationships including the Pythagorean Theorem and the distance formula;

TAL.3.4: find and represent solutions of quadratic equations geometrically.

TAL.4.1: use concepts of length, area, and volume to estimate and solve real-world problems;

TAL.4.4: make decisions about units, scales, and measurement tools that are appropriate for problem situations involving measurement;

TAL.5.1: collect, represent, and describe linear and nonlinear data sets developed from the real world;

TAL.5.2: interpret a set of data using the appropriate measure of central tendency;

TAL.5.3: choose, construct, and analyze appropriate graphical representations for a data set;

TAL.5.4: understand the concept of random sampling;

TAL.5.5: apply counting principles of permutations and combinations using appropriate technology;

TAL.5.6: model situations to determine theoretical and experimental probabilities.

Correlation last revised: 11/14/2008

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