Search Web Service Explorer

A new version of this service is available. The documentation here is for a previous version. Please refer to Current Search Web Service for new application development.

The Search Web Service explorer allows you to issue each of the available requests to the service and view the XML response using your web browser. Because XML is returned, we recommend using Internet Explorer 5 or later, Firefox or Netscape 7.1 or later.

This is service version DDSWS v1.0.

Service Base URL:   http://www.dlese.org/dds/services/ddsws1-0

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	GRADE LEVELS Primary (K-2) Intermediate (3-5) Middle (6-8) High (9-12) College (13-14) College (15-16) Graduate / Professional Informal General public SUBJECTS Agricultural science Atmospheric science Biology Chemistry Climatology Cryology Ecology Educational theory and practice Environmental science Forestry Geographical Sciences Human geography Physical geography Geological Sciences Geochemistry Geologic time Geology Geophysics Mineralogy or petrology Paleontology Structural geology History and philosophy of science Hydrology Mathematics Natural hazards Ocean Sciences Biological oceanography Chemical oceanography Physical oceanography Physics Policy issues Soil science Space science Technology RESOURCE TYPES For the classroom Classroom activity Computer activity Field activity Lab activity Assessment / Evaluation Case study Course Curriculum Field trip - virtual Guide for field trip Guide for instructor Lesson plan Module / Unit Presentation / Demo Problem set Project Syllabus Tutorial Visual Illustration - artistic Illustration - scientific Imagery - remotely sensed Map Photograph Video Visualization - scientific Webcast Text Glossary Index / Bibliography Ref. material Book Journal article Periodical Abstract / Summary Proceedings Proposal Report Thesis Policy / Procedure Audio Book Lecture Music Oral history Radio broadcast Sound Webcast Portal Commercial Educational Government Non-profit Services Ask an expert Clearinghouse Discussion / Forum Email lists Message board Search engine Dataset In-situ Modeled Remotely sensed Tools Calculation / Conversion Code Software CONTENT STANDARDS National Science Education Standards (NSES) K-4 Unifying concepts and processes Change, constancy, and measurement Evidence, models, and explanation Evolution and equilibrium Form and function Systems, order, and organization A - Science as inquiry Abilities necessary to do scientific inquiry Understanding about scientific inquiry B - Physical science Light, heat, electricity, and magnetism Position and motion of objects Properties of objects and materials C - Life science Characteristics of organisms Life cycles of organisms Organisms and environments D - Earth and space science Changes in earth and sky Objects in the sky Properties of earth materials E - Science and technology Abilities of technological design Abilities to distinguish between natural objects and objects made by humans Understanding about sci. / tech. F - Science in personal / social perspectives Changes in environments Characteristics / changes in populations Personal health Sci. / tech. in local challenges Types of resources G - History and nature of science Science as a human endeavor 5-8 Unifying concepts and processes Change, constancy, and measurement Evidence, models, and explanation Evolution and equilibrium Form and function Systems, order, and organization A - Science as inquiry Abilities necessary to do scientific inquiry Understanding about scientific inquiry B - Physical science Motion and forces Properties and changes of properties in matter Transfer of energy C - Life science Diversity and adaptations of organisms Population and ecosystems Regulation and behavior Reproduction and heredity Structure and function in living systems D - Earth and space science Earth in the solar system Earth's history Structure of the earth system E - Science and technology Abilities of technological design Understandings about sci. / tech. F - Science in personal / social perspectives Natural hazards Personal health Populations, resources, environments Risks and benefits Sci. / tech. in society G - History and nature of science History of science Nature of science Science as a human endeavor 9-12 Unifying concepts and processes Change, constancy, and measurement Evidence, models, and explanation Evolution and equilibrium Form and function Systems, order, and organization A - Science as inquiry Abilities necessary to do scientific inquiry Understandings about scientific inquiry B - Physical science Chemical reactions Conservation of energy and increase in disorder Interactions of energy and matter Motions and forces Structure and properties of matter Structure of atoms C - Life science Behavior of organisms Biological evolution Interdependence of organisms Matter, energy, and organization in living systems Molecular basis of heredity The cell D - Earth and space science Energy in the earth system Geochemical cycles Origin and evolution of the earth system Origin and evolution of the universe E - Science and technology Abilities of technological design Understandings about science and technology F - Science in personal / social perspectives Environmental quality Natural and human-induced hazards Natural resources Personal and community health Population growth Sci. / tech. in local, national, and global challenges G - History and nature of science Historical perspectives Nature of scientific knowledge Science as a human endeavor National Geography Standards Environment and society How human actions modify the physical env. How physical systems affect human systems The changes that occur in the meaning, use, distribution, and importance of resources Human systems How forces of cooperation and conflict among people influence the division and control of Earth's surface The characteristics, distribution, and migration of human populations on Earth's surface The characteristics, distributions, and complexity of Earth's cultural mosaics The patterns and networks of economic interdependence on Earth's surface The process, patterns, and functions of human settlement Physical systems The characteristics and spatial distribution of ecosystems on Earth's surface The physical processes that shape the patterns of Earth's surface Places and regions How culture and experience influence people's perception of places and regions That people create regions to interpret Earth's complexity The physical and human characteristics of places The uses of geography How to apply geography to interpret the past How to apply geography to interpret the present and plan for the future The world in spatial terms How to analyze the spatial organization of people, places, and environments on Earth's surface How to use maps and other geographic representations, tools, and technologies to acquire, process, and report information How to use mental maps to organize information about people, places, and environments Pre K-2 Number and operations Understand numbers Count with understanding and recognize 'how many' in sets of objects Use multiple models to develop initial understandings of place value and the base-ten number system Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers Connect number words and numerals to the quantities they represent, using various physical models and representations Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2 Understand meanings of operations Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations Understand the effects of adding and subtracting whole numbers Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally Compute fluently and make reasonable estimates Develop and use strategies for whole-number computations, with a focus on addition and subtraction Develop fluency with basic number combinations for addition and subtraction Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators Algebra Understand patterns, relations, and functions Sort, classify, and order objects by size, number, and other properties Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another Analyze how both repeating and growing patterns are generated Represent and analyze mathematical situations Illustrate general principles and properties of operations, such as commutativity, using specific numbers Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations Use mathematical models to represent and understand quantitative relationships Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols Analyze change in various contexts Describe qualitative change, such as a student's growing taller Describe quantitative change, such as a student's growing two inches in one year Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes Describe attributes and parts of two- and three-dimensional shapes Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes Specify locations and describe spatial relationships Describe, name, and interpret relative positions in space and apply ideas about relative position Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance Find and name locations with simple relationships such as 'near to' and in coordinate systems such as maps Apply transformations and use symmetry to analyze mathematical situations Recognize and apply slides, flips, and turns Recognize and create shapes that have symmetry Use visualization, spatial reasoning, and geometric modeling to solve problems Create mental images of geometric shapes using spatial memory and spatial visualization Recognize and represent shapes from different perspectives Relate ideas in geometry to ideas in number and measurement Recognize geometric shapes and structures in the environment and specify their location Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement Recognize the attributes of length, volume, weight, area, and time Compare and order objects according to these attributes Understand how to measure using nonstandard and standard units Select an appropriate unit and tool for the attribute being measured Apply appropriate techniques, tools, and formulas to determine measurements Measure with multiple copies of units of the same size, such as paper clips laid end to end Use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick Use tools to measure Develop common referents for measures to make comparisons and estimates Data analysis and probability Formulate questions Pose questions and gather data about themselves and their surroundings Sort and classify objects according to their attributes and organize data about the objects Represent data using concrete objects, pictures, and graphs Select and use appropriate statistical methods to analyze data Describe parts of the data and the set of data as a whole to determine what the data show Develop and evaluate inferences and predictions that are based on data Discuss events related to students' experiences as likely or unlikely Understand and apply basic concepts of probability Understand and apply basic concepts of probability Problem solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Reasoning and proof Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof Communication Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others Connections Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics Representation Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena 3-5 Number and operations Understand numbers Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals Recognize equivalent representations for the same number and generate them by decomposing and composing numbers Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers Use models, benchmarks, and equivalent forms to judge the size of fractions Recognize and generate equivalent forms of commonly used fractions, decimals, and percents Explore numbers less than 0 by extending the number line and through familiar applications Describe classes of numbers according to characteristics such as the nature of their factors Understand meanings of operations Understand various meanings of multiplication and division Understand the effects of multiplying and dividing whole numbers Identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems Understand and use properties of operations, such as the distributivity of multiplication over addition Compute fluently and make reasonable estimates Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 x 50 Develop fluency in adding, subtracting, multiplying, and dividing whole numbers Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals Select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools Algebra Understand patterns, relations, and functions Describe, extend, and make generalizations about geometric and numeric patterns Represent and analyze patterns and functions, using words, tables, and graphs Represent and analyze mathematical situations Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers Represent the idea of a variable as an unknown quantity using a letter or a symbol Express mathematical relationships using equations Use mathematical models to represent and understand quantitative relationships Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions Analyze change in various contexts Investigate how a change in one variable relates to a change in a second variable Identify and describe situations with constant or varying rates of change and compare them Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes Explore congruence and similarity Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions Specify locations and describe spatial relationships Describe location and movement using common language and geometric vocabulary Make and use coordinate systems to specify locations and to describe paths Find the distance between points along horizontal and vertical lines of a coordinate system Apply transformations and use symmetry to analyze mathematical situations Predict and describe the results of sliding, flipping, and turning two-dimensional shapes Describe a motion or a series of motions that will show that two shapes are congruent Identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs Use visualization, spatial reasoning, and geometric modeling to solve problems Build and draw geometric objects Create and describe mental images of objects, patterns, and paths Identify and build a three-dimensional object from two-dimensional representations of that object Identify and draw a two-dimensional representation of a three-dimensional object Use geometric models to solve problems in other areas of mathematics, such as number and measurement Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement Understand that measurements are approximations and how differences in units affect precision Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way Apply appropriate techniques, tools, and formulas to determine measurements Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles Select and use benchmarks to estimate measurements Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms Develop strategies to determine the surface areas and volumes of rectangular solids Data analysis and probability Formulate questions Design investigations to address a question and consider how data-collection methods affect the nature of the data set Collect data using observations, surveys, and experiments Represent data using tables and graphs such as line plots, bar graphs, and line graphs Recognize the differences in representing categorical and numerical data Select and use appropriate statistical methods to analyze data Describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set Compare different representations of the same data and evaluate how well each representation shows important aspects of the data Develop and evaluate inferences and predictions that are based on data Propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions Understand and apply basic concepts of probability Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible Predict the probability of outcomes of simple experiments and test the predictions Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1 Problem solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Reasoning and proof Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof Communication Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others Use the language of mathematics to express mathematical ideas precisely Connections Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics Representation Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena 6-8 Number and operations Understand numbers Work flexibly with fractions, decimals, and percents to solve problems Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line Develop meaning for percents greater than 100 and less than 1 Understand and use ratios and proportions to represent quantitative relationships Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation Use factors, multiples, prime factorization, and relatively prime numbers to solve problems Develop meaning for integers and represent and compare quantities with them Understand meanings of operations Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems Compute fluently and make reasonable estimates Select appropriate methods and tools for computing with fractions and decimals from among mental computation, estimation, calculators or computers, and paper and pencil, depending on the situation, and apply the selected methods Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios Algebra Understand patterns, relations, and functions Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules Relate and compare different forms of representation for a relationship Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations Represent and analyze mathematical situations Develop an initial conceptual understanding of different uses of variables Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations Use mathematical models to represent and understand quantitative relationships Model and solve contextualized problems using various representations, such as graphs, tables, and equations Analyze change in various contexts Use graphs to analyze the nature of changes in quantities in linear relationships Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship Specify locations and describe spatial relationships Use coordinate geometry to represent and examine the properties of geometric shapes Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides Apply transformations and use symmetry to analyze mathematical situations Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling Examine the congruence, similarity, and line or rotational symmetry of objects using transformations Use visualization, spatial reasoning, and geometric modeling to solve problems Draw geometric objects with specified properties, such as side lengths or angle measures Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume Use visual tools such as networks to represent and solve problems Use geometric models to represent and explain numerical and algebraic relationships Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement Understand both metric and customary systems of measurement Understand relationships among units and convert from one unit to another within the same system Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume Apply appropriate techniques, tools, and formulas to determine measurements Use common benchmarks to select appropriate methods for estimating measurements Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders Solve problems involving scale factors, using ratio and proportion Solve simple problems involving rates and derived measurements for such attributes as velocity and density Data analysis and probability Formulate questions Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots Select and use appropriate statistical methods to analyze data Find, use, and interpret measures of center and spread, including mean and interquartile range Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots Develop and evaluate inferences and predictions that are based on data Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit Use conjectures to formulate new questions and plan new studies to answer them Understand and apply basic concepts of probability Understand and use appropriate terminology to describe complementary and mutually exclusive events Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models Problem solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Recognize reasoning and proof as fundamental aspects of mathematics Reasoning and proof Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof Communication Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others Use the language of mathematics to express mathematical ideas precisely Connections Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics Representation Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena 9-12 Number and operations Understand numbers Develop a deeper understanding of very large and very small numbers and of various representations of them Compare and contrast the properties of numbers and number systems, including the rational and real numbers, and understand complex numbers as solutions to quadratic equations that do not have real solutions Understand vectors and matrices as systems that have some of the properties of the real-number system Use number-theory arguments to justify relationships involving whole numbers Understand meanings of operations Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities Develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices Develop an understanding of permutations and combinations as counting techniques Compute fluently and make reasonable estimates Develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases Judge the reasonableness of numerical computations and their results Algebra Understand patterns, relations, and functions Generalize patterns using explicitly defined and recursively defined functions Understand relations and functions and select, convert flexibly among, and use various representations for them Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions Interpret representations of functions of two variables Represent and analyze mathematical situations Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluency, mentally or with paper and pencil in simple cases and using technology in all cases Use symbolic algebra to represent and explain mathematical relationships Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology Use mathematical models to represent and understand quantitative relationships Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts Draw reasonable conclusions about a situation being modeled Analyze change in various contexts Approximate and interpret rates of change from graphical and numerical data Geometry Analyze characteristics and properties of two- and three-dimensional geometric shapes Analyze properties and determine attributes of two- and three-dimensional objects Explore relationships (including congruence and similarity) among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others Use trigonometric relationships to determine lengths and angle measures Specify locations and describe spatial relationships Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates Apply transformations and use symmetry to analyze mathematical situations Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices Use various representations to help understand the effects of simple transformations and their compositions Use visualization, spatial reasoning, and geometric modeling to solve problems Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools Visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections Use vertex-edge graphs to model and solve problems Use geometric models to gain insights into, and answer questions in, other areas of mathematics Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture Measurement Understand measurable attributes of objects and the units, systems, and processes of measurement Make decisions about units and scales that are appropriate for problem situations involving measurement Apply appropriate techniques, tools, and formulas to determine measurements Analyze precision, accuracy, and approximate error in measurement situations Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders Apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations Use unit analysis to check measurement computations Data analysis and probability Formulate questions Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable Understand histograms, parallel box plots, and scatterplots and use them to display data Compute basic statistics and understand the distinction between a statistic and a parameter Select and use appropriate statistical methods to analyze data For univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools Display and discuss bivariate data where at least one variable is categorical Recognize how linear transformations of univariate data affect shape, center, and spread Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled Develop and evaluate inferences and predictions that are based on data Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions Understand how basic statistical techniques are used to monitor process characteristics in the workplace Understand and apply basic concepts of probability Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases Use simulations to construct empirical probability distributions Compute and interpret the expected value of random variables in simple cases Understand the concepts of conditional probability and independent events Understand how to compute the probability of a compound event Problem solving Build new mathematical knowledge through problem solving Solve problems that arise in mathematics and in other contexts Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Reasoning and proof Recognize reasoning and proof as fundamental aspects of mathematics Make and investigate mathematical conjectures Develop and evaluate mathematical arguments and proofs Select and use various types of reasoning and methods of proof Communication Organize and consolidate their mathematical thinking through communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Analyze and evaluate the mathematical thinking and strategies of others Use the language of mathematics to express mathematical ideas precisely Connections Recognize and use connections among mathematical ideas Understand how mathematical ideas interconnect and build on one another to produce a coherent whole Recognize and apply mathematics in contexts outside of mathematics Representation Create and use representations to organize, record, and communicate mathematical ideas Select, apply, and translate among mathematical representations to solve problems Use representations to model and interpret physical, social, and mathematical phenomena COLLECTIONS Alexandria Digital Library (ADL) Atmos Visualization Collection (AVC) BRIDGE NOAA Other Resources BRIDGE NOAA Resources BRIDGE Other Ocean Resources BRIDGE Ocean Resources COSEE Other Resources COSEE Resources Climate Change Collection Community Annotated Collection Coop Pgm Op Met Edu/Training (COMET) Curricular Resource Lib. 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Studio NAP Earth and Life Sciences New York Instructional Collection New York Standards Collection News and Opportunities Community Collection PRISMS Pedagogically Annotated Collection Realtime Atmospheric Data SIMPLE Science Other Resources SIMPLE Science Starting Point Stone Wall Initiative Teaching Boxes Teaching Box Resources Tips and Comments USGS Education Collection Visionlearning Collection XML FORMAT Record's native format (none indicated) adn adn-localized briefmeta dlese_anno dlese_anno-localized dlese_collect dlese_collect-localized news_opps news_opps-localized nsdl_dc oai_dc
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