csNational_Science_Education_Standards_(NSES)NSES represents the National Science Education StandardsNSESfalsefalsefalsetruefalse1K-4Pertains to content for kindergarten through 4th gradefalsefalsefalsetruefalse2Unifying_concepts_and_processesEmpahsizes conceptual and procedural schemes that unify science disciplinesfalsefalsefalsetruefalse3NSES:K-4:Unifying Concepts and Processes Standards:Change, constancy, and measurement01sfalsefalsefalsefalsefalse3NSES:K-4:Unifying Concepts and Processes Standards:Evidence, models, and explanation01tfalsefalsefalsefalsefalse3NSES:K-4:Unifying Concepts and Processes Standards:Evolution and equilibrium01ufalsefalsefalsefalsefalse3NSES:K-4:Unifying Concepts and Processes Standards:Form and function01vfalsefalsefalsefalsefalse3NSES:K-4:Unifying Concepts and Processes Standards:Systems, order, and organization01wfalsefalsefalsefalsetrue3A_-_Science_as_inquiryThe combination of the processes of science, scientific knowledge and reasoning to understand sciencefalsefalsefalsetruefalse3NSES:K-4:Content Standard A Science as Inquiry Standards:Abilities necessary to do scientific inquiry018falsefalsefalsefalsefalse3NSES:K-4:Content Standard A Science as Inquiry Standards:Understanding about scientific inquiry019falsefalsefalsefalsetrue3B_-_Physical_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of physical sciencefalsefalsefalsetruefalse3NSES:K-4:Content Standard B Physical Science Standards:Light, heat, electricity, and magnetism01afalsefalsefalsefalsefalse3NSES:K-4:Content Standard B Physical Science Standards:Position and motion of objects01bfalsefalsefalsefalsefalse3NSES:K-4:Content Standard B Physical Science Standards:Properties of objects and materials01cfalsefalsefalsefalsetrue3C_-_Life_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of life sciencefalsefalsefalsetruefalse3NSES:K-4:Content Standard C Life Science Standards:Characteristics of organisms01dfalsefalsefalsefalsefalse3NSES:K-4:Content Standard C Life Science Standards:Life cycles of organisms01efalsefalsefalsefalsefalse3NSES:K-4:Content Standard C Life Science Standards:Organisms and environments01ffalsefalsefalsefalsetrue3D_-_Earth_and_space_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of Earth and space sciencefalsefalsefalsetruefalse3NSES:K-4:Content Standard D Earth and Space Science Standards:Changes in earth and sky01gfalsefalsefalsefalsefalse3NSES:K-4:Content Standard D Earth and Space Science Standards:Objects in the sky01hfalsefalsefalsefalsefalse3NSES:K-4:Content Standard D Earth and Space Science Standards:Properties of earth materials01ifalsefalsefalsefalsetrue3E_-_Science_and_technologyEstablish connections between the natural and designed worlds and provide opportunities to develop decision-making abilitiesfalsefalsefalsetruefalse3NSES:K-4:Content Standard E Science and Technology Standards:Abilities of technological design01jfalsefalsefalsefalsefalse3NSES:K-4:Content Standard E Science and Technology Standards:Abilities to distinguish between natural objects and objects made by humans01kfalsefalsefalsefalsefalse3NSES:K-4:Content Standard E Science and Technology Standards:Understanding about science and technology01lfalsefalsefalsefalsetrue3F_-_Science_in_personal_/_social_perspectivesDevelop decision-making skills in relation to personal social issuesfalsefalsefalsetruefalse3NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Changes in environments01mfalsefalsefalsefalsefalse3NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Characteristics and changes in populations01nfalsefalsefalsefalsefalse3NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Personal health01ofalsefalsefalsefalsefalse3NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Science and technology in local challenges01pfalsefalsefalsefalsefalse3NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Types of resources01qfalsefalsefalsefalsetrue3G_-_History_and_nature_of_scienceEmphasizes the clarification of different aspects of scientific inquiry, the human aspects of science, and the role that science has played in the development of various culturesfalsefalsefalsetruetrue3NSES:K-4:Content Standard G History and Nature of Science Standards:Science as a human endeavor01rfalsefalsefalsefalsetrue35-8Pertains to content for 5th through 8th gradefalsefalsefalsetruefalse2Unifying_concepts_and_processesEmpahsizes conceptual and procedural schemes that unify science disciplinesfalsefalsefalsetruefalse3NSES:5-8:Unifying Concepts and Processes Standards:Change, constancy, and measurement005falsefalsefalsefalsefalse3NSES:5-8:Unifying Concepts and Processes Standards:Evidence, models, and explanation006falsefalsefalsefalsefalse3NSES:5-8:Unifying Concepts and Processes Standards:Evolution and equilibrium007falsefalsefalsefalsefalse3NSES:5-8:Unifying Concepts and Processes Standards:Form and function008falsefalsefalsefalsefalse3NSES:5-8:Unifying Concepts and Processes Standards:Systems, order, and organization009falsefalsefalsefalsetrue3A_-_Science_as_inquiryThe combination of the processes of science, scientific knowledge and reasoning to understand sciencefalsefalsefalsetruefalse3NSES:5-8:Content Standard A Science as Inquiry Standards:Abilities necessary to do scientific inquiry0ifalsefalsefalsefalsefalse3NSES:5-8:Content Standard A Science as Inquiry Standards:Understanding about scientific inquiry0jfalsefalsefalsefalsetrue3B_-_Physical_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of physical sciencefalsefalsefalsetruefalse3NSES:5-8:Content Standard B Physical Science Standards:Motion and forces0kfalsefalsefalsefalsefalse3NSES:5-8:Content Standard B Physical Science Standards:Properties and changes of properties in matter0lfalsefalsefalsefalsefalse3NSES:5-8:Content Standard B Physical Science Standards:Transfer of energy0mfalsefalsefalsefalsetrue3C_-_Life_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of life sciencefalsefalsefalsetruefalse3NSES:5-8:Content Standard C Life Science Standards:Diversity and adaptations of organisms0nfalsefalsefalsefalsefalse3NSES:5-8:Content Standard C Life Science Standards:Population and ecosystems0ofalsefalsefalsefalsefalse3NSES:5-8:Content Standard C Life Science Standards:Regulation and behavior0pfalsefalsefalsefalsefalse3NSES:5-8:Content Standard C Life Science Standards:Reproduction and heredity0qfalsefalsefalsefalsefalse3NSES:5-8:Content Standard C Life Science Standards:Structure and function in living systems0rfalsefalsefalsefalsetrue3D_-_Earth_and_space_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of Earth and space sciencefalsefalsefalsetruefalse3NSES:5-8:Content Standard D Earth and Space Science Standards:Earth in the solar system0sfalsefalsefalsefalsefalse3NSES:5-8:Content Standard D Earth and Space Science Standards:Earth's history0tfalsefalsefalsefalsefalse3NSES:5-8:Content Standard D Earth and Space Science Standards:Structure of the earth system0ufalsefalsefalsefalsetrue3E_-_Science_and_technologyEstablish connections between the natural and designed worlds and provide opportunities to develop decision-making abilitiesfalsefalsefalsetruefalse3NSES:5-8:Content Standard E Science and Technology Standards:Abilities of technological design0vfalsefalsefalsefalsefalse3NSES:5-8:Content Standard E Science and Technology Standards:Understandings about science and technology0wfalsefalsefalsefalsetrue3F_-_Science_in_personal_/_social_perspectivesDevelop decision-making skills in relation to personal social issuesfalsefalsefalsetruefalse3NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Natural hazards0xfalsefalsefalsefalsefalse3NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Personal health0yfalsefalsefalsefalsefalse3NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Populations, resources, and environments0zfalsefalsefalsefalsefalse3NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Risks and benefits000falsefalsefalsefalsefalse3NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Science and technology in society001falsefalsefalsefalsetrue3G_-_History_and_nature_of_scienceEmphasizes the clarification of different aspects of scientific inquiry, the human aspects of science, and the role that science has played in the development of various culturesfalsefalsefalsetruetrue3NSES:5-8:Content Standard G History and Nature of Science Standards:History of science002falsefalsefalsefalsefalse3NSES:5-8:Content Standard G History and Nature of Science Standards:Nature of science003falsefalsefalsefalsefalse3NSES:5-8:Content Standard G History and Nature of Science Standards:Science as a human endeavor004falsefalsefalsefalsetrue39-12Pertains to content for 9th through 12th gradefalsefalsefalsetruetrue2Unifying_concepts_and_processesEmpahsizes conceptual and procedural schemes that unify science disciplinesfalsefalsefalsetruefalse3NSES:9-12:Unifying Concepts and Processes Standards:Change, constancy, and measurement013falsefalsefalsefalsefalse3NSES:9-12:Unifying Concepts and Processes Standards:Evidence, models, and explanation014falsefalsefalsefalsefalse3NSES:9-12:Unifying Concepts and Processes Standards:Evolution and equilibrium015falsefalsefalsefalsefalse3NSES:9-12:Unifying Concepts and Processes Standards:Form and function016falsefalsefalsefalsefalse3NSES:9-12:Unifying Concepts and Processes Standards:Systems, order, and organization017falsefalsefalsefalsetrue3A_-_Science_as_inquiryThe combination of the processes of science, scientific knowledge and reasoning to understand sciencefalsefalsefalsetruefalse3NSES:9-12:Content Standard A Science as Inquiry Standards:Abilities necessary to do scientific inquiry00afalsefalsefalsefalsefalse3NSES:9-12:Content Standard A Science as Inquiry Standards:Understandings about scientific inquiry00bfalsefalsefalsefalsetrue3B_-_Physical_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of physical sciencefalsefalsefalsetruefalse3NSES:9-12:Content Standard B Physical Science Standards:Chemical reactions00cfalsefalsefalsefalsefalse3NSES:9-12:Content Standard B Physical Science Standards:Conservation of energy and increase in disorder00dfalsefalsefalsefalsefalse3NSES:9-12:Content Standard B Physical Science Standards:Interactions of energy and matter00efalsefalsefalsefalsefalse3NSES:9-12:Content Standard B Physical Science Standards:Motions and forces00ffalsefalsefalsefalsefalse3NSES:9-12:Content Standard B Physical Science Standards:Structure and properties of matter00gfalsefalsefalsefalsefalse3NSES:9-12:Content Standard B Physical Science Standards:Structure of atoms00hfalsefalsefalsefalsetrue3C_-_Life_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of life sciencefalsefalsefalsetruefalse3NSES:9-12:Content Standard C Life Science Standards:Behavior of organisms00ifalsefalsefalsefalsefalse3NSES:9-12:Content Standard C Life Science Standards:Biological evolution00jfalsefalsefalsefalsefalse3NSES:9-12:Content Standard C Life Science Standards:Interdependence of organisms00kfalsefalsefalsefalsefalse3NSES:9-12:Content Standard C Life Science Standards:Matter, energy, and organization in living systems00lfalsefalsefalsefalsefalse3NSES:9-12:Content Standard C Life Science Standards:Molecular basis of heredity00mfalsefalsefalsefalsefalse3NSES:9-12:Content Standard C Life Science Standards:The cell00nfalsefalsefalsefalsetrue3D_-_Earth_and_space_scienceEncompasses the subject matter, facts, concepts, principls, theories and models of Earth and space sciencefalsefalsefalsetruefalse3NSES:9-12:Content Standard D Earth and Space Science Standards:Energy in the earth system00ofalsefalsefalsefalsefalse3NSES:9-12:Content Standard D Earth and Space Science Standards:Geochemical cycles00pfalsefalsefalsefalsefalse3NSES:9-12:Content Standard D Earth and Space Science Standards:Origin and evolution of the earth system00qfalsefalsefalsefalsefalse3NSES:9-12:Content Standard D Earth and Space Science Standards:Origin and evolution of the universe00rfalsefalsefalsefalsetrue3E_-_Science_and_technologyEstablish connections between the natural and designed worlds and provide opportunities to develop decision-making abilitiesfalsefalsefalsetruefalse3NSES:9-12:Content Standard E Science and Technology Standards:Abilities of technological design00sfalsefalsefalsefalsefalse3NSES:9-12:Content Standard E Science and Technology Standards:Understandings about science and technology00tfalsefalsefalsefalsetrue3F_-_Science_in_personal_/_social_perspectivesDevelop decision-making skills in relation to personal social issuesfalsefalsefalsetruefalse3NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Environmental quality00ufalsefalsefalsefalsefalse3NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Natural and human-induced hazards00vfalsefalsefalsefalsefalse3NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Natural resources00wfalsefalsefalsefalsefalse3NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Personal and community health00xfalsefalsefalsefalsefalse3NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Population growth00yfalsefalsefalsefalsefalse3NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Science and technology in local, national, and global challenges00zfalsefalsefalsefalsetrue3G_-_History_and_nature_of_scienceEmphasizes the clarification of different aspects of scientific inquiry, the human aspects of science, and the role that science has played in the development of various culturesfalsefalsefalsetruetrue3NSES:9-12:Content Standard G History and Nature of Science Standards:Historical perspectives010falsefalsefalsefalsefalse3NSES:9-12:Content Standard G History and Nature of Science Standards:Nature of scientific knowledge011falsefalsefalsefalsefalse3NSES:9-12:Content Standard G History and Nature of Science Standards:Science as a human endeavor012falsefalsefalsefalsetrue3National_Geography_StandardsNational Geography Standards published by the National Council for Geographic Education (NCGE)falsefalsefalsetruefalse1Environment_and_societyfalsefalsefalsetruefalse2NCGE:Environment and Society:How human actions modify the physical environment00falsefalsefalsefalsefalse2NCGE:Environment and Society:How physical systems affect human systems01falsefalsefalsefalsefalse2NCGE:Environment and Society:The changes that occur in the meaning, use, distribution, and importance of resources02falsefalsefalsefalsetrue2Human_systemsfalsefalsefalsetruefalse2NCGE:Human Systems:How forces of cooperation and conflict among people influence the division and control of Earth's surface03falsefalsefalsefalsefalse2NCGE:Human Systems:The characteristics, distribution, and migration of human populations on Earth's surface04falsefalsefalsefalsefalse2NCGE:Human Systems:The characteristics, distributions, and complexity of Earth's cultural mosaics05falsefalsefalsefalsefalse2NCGE:Human Systems:The patterns and networks of economic interdependence on Earth's surface06falsefalsefalsefalsefalse2NCGE:Human Systems:The process, patterns, and functions of human settlement07falsefalsefalsefalsetrue2Physical_systemsfalsefalsefalsetruefalse2NCGE:Physical Systems:The characteristics and spatial distribution of ecosystems on Earth's surface08falsefalsefalsefalsefalse2NCGE:Physical Systems:The physical processes that shape the patterns of Earth's surface09falsefalsefalsefalsetrue2Places_and_regionsfalsefalsefalsetruefalse2NCGE:Places and Regions:How culture and experience influence people's perception of places and regions0afalsefalsefalsefalsefalse2NCGE:Places and Regions:That people create regions to interpret Earth's complexity0bfalsefalsefalsefalsefalse2NCGE:Places and Regions:The physical and human characteristics of places0cfalsefalsefalsefalsetrue2The_uses_of_geographyfalsefalsefalsetruefalse2NCGE:The Uses of Geography:How to apply geography to interpret the past0dfalsefalsefalsefalsefalse2NCGE:The Uses of Geography:How to apply geography to interpret the present and plan for the future0efalsefalsefalsefalsetrue2The_world_in_spatial_termsfalsefalsefalsetruetrue2NCGE:The World in Spatial Terms:How to analyze the spatial organization of people, places, and environments on Earth's surface0ffalsefalsefalsefalsefalse2NCGE:The World in Spatial Terms:How to use maps and other geographic representations, tools, and technologies to acquire, process, and report information0gfalsefalsefalsefalsefalse2NCGE:The World in Spatial Terms:How to use mental maps to organize information about people, places, and environments0hfalsefalsefalsefalsetrue2National_Council_of_Teachers_of_Mathematics_(NCTM)NCTM represents the math content standardsNCTMtruefalsefalsetruetrue1Pre_K-2Pertains to content for pre-kindergarten through 2nd gradefalsefalsefalsetruefalse2Number_and_operationsarithmetic manipulationsfalsefalsefalsetruefalse3Understand_numbersways of representing numbers, relationships among numbers, and number systemsfalsefalsefalsetruefalse4NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Count with understanding and recognize 'how many' in sets of objects01xfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use multiple models to develop initial understandings of place value and the base-ten number system01yfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections01zfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers020falsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Connect number words and numerals to the quantities they represent, using various physical models and representations021falsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2022falsefalsefalsefalsetrue4Understand_meanings_of_operationsfalsefalsefalsetruefalse4NCTM:Pre-K-2:Number and operations:Understand meanings of operations and how they relate to one another:Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations023falsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Understand meanings of operations and how they relate to one another:Understand the effects of adding and subtracting whole numbers024falsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Understand meanings of operations and how they relate to one another:Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally025falsefalsefalsefalsetrue4Compute_fluently_and_make_reasonable_estimatesfalsefalsefalsetruetrue4NCTM:Pre-K-2:Number and operations:Compute fluently and make reasonable estimates:Develop and use strategies for whole-number computations, with a focus on addition and subtraction026falsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Compute fluently and make reasonable estimates:Develop fluency with basic number combinations for addition and subtraction027falsefalsefalsefalsefalse4NCTM:Pre-K-2:Number and operations:Compute fluently and make reasonable estimates:Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators028falsefalsefalsefalsetrue4Algebraproperties and relationships between entities that are represented in symbolic formfalsefalsefalsetruefalse3Understand_patterns,_relations,_and_functionsfalsefalsefalsetruefalse4NCTM:Pre-K-2:Algebra:Understand patterns, relations, and functions:Sort, classify, and order objects by size, number, and other properties029falsefalsefalsefalsefalse4NCTM:Pre-K-2:Algebra:Understand patterns, relations, and functions:Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another02afalsefalsefalsefalsefalse4NCTM:Pre-K-2:Algebra:Understand patterns, relations, and functions:Analyze how both repeating and growing patterns are generated02bfalsefalsefalsefalsetrue4Represent_and_analyze_mathematical_situationsfalsefalsefalsetruefalse4NCTM:Pre-K-2:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Illustrate general principles and properties of operations, such as commutativity, using specific numbers02cfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations02dfalsefalsefalsefalsetrue4Use_mathematical_models_to_represent_and_understand_quantitative_relationshipsfalsefalsefalsetruefalse4NCTM:Pre-K-2:Algebra:Use mathematical models to represent and understand quantitative relationships:Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols02efalsefalsefalsefalsetrue4Analyze_change_in_various_contextsfalsefalsefalsetruetrue4NCTM:Pre-K-2:Algebra:Analyze change in various contexts:Describe qualitative change, such as a student's growing taller02ffalsefalsefalsefalsefalse4NCTM:Pre-K-2:Algebra:Analyze change in various contexts:Describe quantitative change, such as a student's growing two inches in one year02gfalsefalsefalsefalsetrue4Geometryproperties and relationships of points, lines, angles, surfaces and solidsfalsefalsefalsetruefalse3Analyze_characteristics_and_properties_of_two-_and_three-dimensional_geometric_shapesfalsefalsefalsetruefalse4NCTM:Pre-K-2:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes02hfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Describe attributes and parts of two- and three-dimensional shapes02ifalsefalsefalsefalsefalse4NCTM:Pre-K-2:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes02jfalsefalsefalsefalsetrue4Specify_locations_and_describe_spatial_relationshipsfalsefalsefalsetruefalse4NCTM:Pre-K-2:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Describe, name, and interpret relative positions in space and apply ideas about relative position02kfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance02lfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Find and name locations with simple relationships such as 'near to' and in coordinate systems such as maps02mfalsefalsefalsefalsetrue4Apply_transformations_and_use_symmetry_to_analyze_mathematical_situationsfalsefalsefalsetruefalse4NCTM:Pre-K-2:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Recognize and apply slides, flips, and turns02nfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Recognize and create shapes that have symmetry02ofalsefalsefalsefalsetrue4Use_visualization,_spatial_reasoning,_and_geometric_modeling_to_solve_problemsfalsefalsefalsetruetrue4NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Create mental images of geometric shapes using spatial memory and spatial visualization02pfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize and represent shapes from different perspectives02qfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Relate ideas in geometry to ideas in number and measurement02rfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize geometric shapes and structures in the environment and specify their location02sfalsefalsefalsefalsetrue4Measurementthe assignment of a numerical value to an attribute of an objectfalsefalsefalsetruefalse3Understand_measurable_attributes_of_objects_and_the_units,_systems,_and_processes_of_measurementfalsefalsefalsetruefalse4NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Recognize the attributes of length, volume, weight, area, and time02tfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Compare and order objects according to these attributes02ufalsefalsefalsefalsefalse4NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand how to measure using nonstandard and standard units02vfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Select an appropriate unit and tool for the attribute being measured02wfalsefalsefalsefalsetrue4Apply_appropriate_techniques,_tools,_and_formulas_to_determine_measurementsfalsefalsefalsetruetrue4NCTM:Pre-K-2:Measurement: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 end02xfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick02yfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use tools to measure02zfalsefalsefalsefalsefalse4NCTM:Pre-K-2:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop common referents for measures to make comparisons and estimates030falsefalsefalsefalsetrue4Data_analysis_and_probabilitynumerical or statistical information that can be used to make decisionsfalsefalsefalsetruefalse3Formulate_questionsfalsefalsefalsetruefalse4NCTM:Pre-K-2:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Pose questions and gather data about themselves and their surroundings031falsefalsefalsefalsefalse4NCTM:Pre-K-2:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Sort and classify objects according to their attributes and organize data about the objects032falsefalsefalsefalsefalse4NCTM:Pre-K-2:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Represent data using concrete objects, pictures, and graphs033falsefalsefalsefalsetrue4Select_and_use_appropriate_statistical_methods_to_analyze_datafalsefalsefalsetruefalse4NCTM:Pre-K-2:Data analysis and probability: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 show034falsefalsefalsefalsetrue4Develop_and_evaluate_inferences_and_predictions_that_are_based_on_datafalsefalsefalsetruefalse4NCTM:Pre-K-2:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Discuss events related to students' experiences as likely or unlikely035falsefalsefalsefalsetrue4Understand_and_apply_basic_concepts_of_probabilityfalsefalsefalsetruetrue4NCTM:Pre-K-2:Data analysis and probability:Understand and apply basic concepts of probability036falsefalsefalsefalsetrue4Problem_solvingmethods and abilities to use mathematical reasoning to arrive at unknown solutionsfalsefalsefalsetruefalse3NCTM:Pre-K-2:Problem solving:Build new mathematical knowledge through problem solving037falsefalsefalsefalsefalse3NCTM:Pre-K-2:Problem solving:Solve problems that arise in mathematics and in other contexts038falsefalsefalsefalsefalse3NCTM:Pre-K-2:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems039falsefalsefalsefalsefalse3NCTM:Pre-K-2:Problem solving:Monitor and reflect on the process of mathematical problem solving03afalsefalsefalsefalsetrue3Reasoning_and_proofthe ability to make a hypothesis and apply mathematical logic (inductive reasoning) to arrive at conclusionsfalsefalsefalsetruefalse3NCTM:Pre-K-2:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics03bfalsefalsefalsefalsefalse3NCTM:Pre-K-2:Reasoning and proof:Make and investigate mathematical conjectures03cfalsefalsefalsefalsefalse3NCTM:Pre-K-2:Reasoning and proof:Develop and evaluate mathematical arguments and proofs03dfalsefalsefalsefalsefalse3NCTM:Pre-K-2:Reasoning and proof:Select and use various types of reasoning and methods of proof03efalsefalsefalsefalsetrue3Communicationthe ability to express and share mathematical conceptsfalsefalsefalsetruefalse3NCTM:Pre-K-2:Communication:Organize and consolidate their mathematical thinking through communication03ffalsefalsefalsefalsefalse3NCTM:Pre-K-2:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others03gfalsefalsefalsefalsefalse3NCTM:Pre-K-2:Communication:Analyze and evaluate the mathematical thinking and strategies of others03hfalsefalsefalsefalsetrue3Connectionsthe ability to recognize common themes across different mathematical concepts or other subjectsfalsefalsefalsetruefalse3NCTM:Pre-K-2:Connections:Recognize and use connections among mathematical ideas03ifalsefalsefalsefalsefalse3NCTM:Pre-K-2:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole03jfalsefalsefalsefalsefalse3NCTM:Pre-K-2:Connections:Recognize and apply mathematics in contexts outside of mathematics03kfalsefalsefalsefalsetrue3Representationthe ability to illustrate mathematical conceptsfalsefalsefalsetruetrue3NCTM:Pre-K-2:Representation:Create and use representations to organize, record, and communicate mathematical ideas03lfalsefalsefalsefalsefalse3NCTM:Pre-K-2:Representation:Select, apply, and translate among mathematical representations to solve problems03mfalsefalsefalsefalsefalse3NCTM:Pre-K-2:Representation:Use representations to model and interpret physical, social, and mathematical phenomena03nfalsefalsefalsefalsetrue33-5Pertains to content for 3rd through 5th gradesfalsefalsefalsetruefalse2Number_and_operationsarithmetic manipulationsfalsefalsefalsetruefalse3Understand_numbersfalsefalsefalsetruefalse4NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals03ofalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Recognize equivalent representations for the same number and generate them by decomposing and composing numbers03pfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers03qfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use models, benchmarks, and equivalent forms to judge the size of fractions03rfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Recognize and generate equivalent forms of commonly used fractions, decimals, and percents03sfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Explore numbers less than 0 by extending the number line and through familiar applications03tfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Describe classes of numbers according to characteristics such as the nature of their factors03ufalsefalsefalsefalsetrue4Understand_meanings_of_operationsfalsefalsefalsetruefalse4NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Understand various meanings of multiplication and division03vfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Understand the effects of multiplying and dividing whole numbers03wfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems03xfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Understand and use properties of operations, such as the distributivity of multiplication over addition03yfalsefalsefalsefalsetrue4Compute_fluently_and_make_reasonable_estimatesfalsefalsefalsetruetrue4NCTM:3-5:Number and operations: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 5003zfalsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Develop fluency in adding, subtracting, multiplying, and dividing whole numbers040falsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results041falsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience042falsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals043falsefalsefalsefalsefalse4NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates: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 tools044falsefalsefalsefalsetrue4Algebraproperties and relationships between entities that are represented in symbolic formfalsefalsefalsetruefalse3Understand_patterns,_relations,_and_functionsfalsefalsefalsetruefalse4NCTM:3-5:Algebra:Understand patterns, relations, and functions:Describe, extend, and make generalizations about geometric and numeric patterns045falsefalsefalsefalsefalse4NCTM:3-5:Algebra:Understand patterns, relations, and functions:Represent and analyze patterns and functions, using words, tables, and graphs046falsefalsefalsefalsetrue4Represent_and_analyze_mathematical_situationsfalsefalsefalsetruefalse4NCTM:3-5:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers047falsefalsefalsefalsefalse4NCTM:3-5:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Represent the idea of a variable as an unknown quantity using a letter or a symbol048falsefalsefalsefalsefalse4NCTM:3-5:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Express mathematical relationships using equations049falsefalsefalsefalsetrue4Use_mathematical_models_to_represent_and_understand_quantitative_relationshipsfalsefalsefalsetruefalse4NCTM:3-5:Algebra: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 conclusions04afalsefalsefalsefalsetrue4Analyze_change_in_various_contextsfalsefalsefalsetruetrue4NCTM:3-5:Algebra:Analyze change in various contexts:Investigate how a change in one variable relates to a change in a second variable04bfalsefalsefalsefalsefalse4NCTM:3-5:Algebra:Analyze change in various contexts:Identify and describe situations with constant or varying rates of change and compare them04cfalsefalsefalsefalsetrue4Geometryproperties and relationships of points, lines, angles, surfaces and solidsfalsefalsefalsetruefalse3Analyze_characteristics_and_properties_of_two-_and_three-dimensional_geometric_shapesfalsefalsefalsetruefalse4NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes04dfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids04efalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes04ffalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Explore congruence and similarity04gfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions04hfalsefalsefalsefalsetrue4Specify_locations_and_describe_spatial_relationshipsfalsefalsefalsetruefalse4NCTM:3-5:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Describe location and movement using common language and geometric vocabulary04ifalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Make and use coordinate systems to specify locations and to describe paths04jfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Find the distance between points along horizontal and vertical lines of a coordinate system04kfalsefalsefalsefalsetrue4Apply_transformations_and_use_symmetry_to_analyze_mathematical_situationsfalsefalsefalsetruefalse4NCTM:3-5:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Predict and describe the results of sliding, flipping, and turning two-dimensional shapes04lfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Describe a motion or a series of motions that will show that two shapes are congruent04mfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs04nfalsefalsefalsefalsetrue4Use_visualization,_spatial_reasoning,_and_geometric_modeling_to_solve_problemsfalsefalsefalsetruetrue4NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Build and draw geometric objects04ofalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Create and describe mental images of objects, patterns, and paths04pfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Identify and build a three-dimensional object from two-dimensional representations of that object04qfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Identify and draw a two-dimensional representation of a three-dimensional object04rfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric models to solve problems in other areas of mathematics, such as number and measurement04sfalsefalsefalsefalsefalse4NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life04tfalsefalsefalsefalsetrue4Measurementthe assignment of a numerical value to an attribute of an objectfalsefalsefalsetruefalse3Understand_measurable_attributes_of_objects_and_the_units,_systems,_and_processes_of_measurementfalsefalsefalsetruefalse4NCTM:3-5: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 attribute04ufalsefalsefalsefalsefalse4NCTM:3-5:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems04vfalsefalsefalsefalsefalse4NCTM:3-5:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement04wfalsefalsefalsefalsefalse4NCTM:3-5:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand that measurements are approximations and how differences in units affect precision04xfalsefalsefalsefalsefalse4NCTM:3-5:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way04yfalsefalsefalsefalsetrue4Apply_appropriate_techniques,_tools,_and_formulas_to_determine_measurementsfalsefalsefalsetruetrue4NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes04zfalsefalsefalsefalsefalse4NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles050falsefalsefalsefalsefalse4NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Select and use benchmarks to estimate measurements051falsefalsefalsefalsefalse4NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms052falsefalsefalsefalsefalse4NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop strategies to determine the surface areas and volumes of rectangular solids053falsefalsefalsefalsetrue4Data_analysis_and_probabilitynumerical or statistical information that can be used to make decisionsfalsefalsefalsetruefalse3Formulate_questionsfalsefalsefalsetruefalse4NCTM:3-5:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Design investigations to address a question and consider how data-collection methods affect the nature of the data set054falsefalsefalsefalsefalse4NCTM:3-5:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Collect data using observations, surveys, and experiments055falsefalsefalsefalsefalse4NCTM:3-5:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Represent data using tables and graphs such as line plots, bar graphs, and line graphs056falsefalsefalsefalsefalse4NCTM:3-5:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Recognize the differences in representing categorical and numerical data057falsefalsefalsefalsetrue4Select_and_use_appropriate_statistical_methods_to_analyze_datafalsefalsefalsetruefalse4NCTM:3-5:Data analysis and probability: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 distributed058falsefalsefalsefalsefalse4NCTM:3-5:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set059falsefalsefalsefalsefalse4NCTM:3-5:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Compare different representations of the same data and evaluate how well each representation shows important aspects of the data05afalsefalsefalsefalsetrue4Develop_and_evaluate_inferences_and_predictions_that_are_based_on_datafalsefalsefalsetruefalse4NCTM:3-5:Data analysis and probability: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 predictions05bfalsefalsefalsefalsetrue4Understand_and_apply_basic_concepts_of_probabilityfalsefalsefalsetruetrue4NCTM:3-5:Data analysis and probability: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 impossible05cfalsefalsefalsefalsefalse4NCTM:3-5:Data analysis and probability:Understand and apply basic concepts of probability:Predict the probability of outcomes of simple experiments and test the predictions05dfalsefalsefalsefalsefalse4NCTM:3-5:Data analysis and probability:Understand and apply basic concepts of probability:Understand that the measure of the likelihood of an event can be represented by a number from 0 to 105efalsefalsefalsefalsetrue4Problem_solvingmethods and abilities to use mathematical reasoning to arrive at unknown solutionsfalsefalsefalsetruefalse3NCTM:3-5:Problem solving:Build new mathematical knowledge through problem solving05ffalsefalsefalsefalsefalse3NCTM:3-5:Problem solving:Solve problems that arise in mathematics and in other contexts05gfalsefalsefalsefalsefalse3NCTM:3-5:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems05hfalsefalsefalsefalsefalse3NCTM:3-5:Problem solving:Monitor and reflect on the process of mathematical problem solving05ifalsefalsefalsefalsetrue3Reasoning_and_proofthe ability to make a hypothesis and apply mathematical logic (inductive reasoning) to arrive at conclusionsfalsefalsefalsetruefalse3NCTM:3-5:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics05jfalsefalsefalsefalsefalse3NCTM:3-5:Reasoning and proof:Make and investigate mathematical conjectures05kfalsefalsefalsefalsefalse3NCTM:3-5:Reasoning and proof:Develop and evaluate mathematical arguments and proofs05lfalsefalsefalsefalsefalse3NCTM:3-5:Reasoning and proof:Select and use various types of reasoning and methods of proof05mfalsefalsefalsefalsetrue3Communicationthe ability to express and share mathematical conceptsfalsefalsefalsetruefalse3NCTM:3-5:Communication:Organize and consolidate their mathematical thinking through communication05nfalsefalsefalsefalsefalse3NCTM:3-5:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others05ofalsefalsefalsefalsefalse3NCTM:3-5:Communication:Analyze and evaluate the mathematical thinking and strategies of others05pfalsefalsefalsefalsefalse3NCTM:3-5:Communication:Use the language of mathematics to express mathematical ideas precisely05qfalsefalsefalsefalsetrue3Connectionsthe ability to recognize common themes across different mathematical concepts or other subjectsfalsefalsefalsetruefalse3NCTM:3-5:Connections:Recognize and use connections among mathematical ideas05rfalsefalsefalsefalsefalse3NCTM:3-5:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole05sfalsefalsefalsefalsefalse3NCTM:3-5:Connections:Recognize and apply mathematics in contexts outside of mathematics05tfalsefalsefalsefalsetrue3Representationthe ability to illustrate mathematical conceptsfalsefalsefalsetruetrue3NCTM:3-5:Representation:Create and use representations to organize, record, and communicate mathematical ideas05ufalsefalsefalsefalsefalse3NCTM:3-5:Representation:Select, apply, and translate among mathematical representations to solve problems05vfalsefalsefalsefalsefalse3NCTM:3-5:Representation:Use representations to model and interpret physical, social, and mathematical phenomena05wfalsefalsefalsefalsetrue36-8Pertains to content for 6th through 8th gradesfalsefalsefalsetruefalse2Number_and_operationsarithmetic manipulationsfalsefalsefalsetruefalse3Understand_numbersfalsefalsefalsetruefalse4NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Work flexibly with fractions, decimals, and percents to solve problems05xfalsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line05yfalsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop meaning for percents greater than 100 and less than 105zfalsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand and use ratios and proportions to represent quantitative relationships060falsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation061falsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use factors, multiples, prime factorization, and relatively prime numbers to solve problems062falsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Develop meaning for integers and represent and compare quantities with them063falsefalsefalsefalsetrue4Understand_meanings_of_operationsfalsefalsefalsetruefalse4NCTM:6-8:Number and operations:Understand meanings of operations and how they relate to one another:Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers064falsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Understand meanings of operations and how they relate to one another: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 decimals065falsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Understand meanings of operations and how they relate to one another:Understand and use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems066falsefalsefalsefalsetrue4Compute_fluently_and_make_reasonable_estimatesfalsefalsefalsetruetrue4NCTM:6-8:Number and operations: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 methods067falsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Compute fluently and make reasonable estimates:Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use068falsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Compute fluently and make reasonable estimates:Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results069falsefalsefalsefalsefalse4NCTM:6-8:Number and operations:Compute fluently and make reasonable estimates:Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios06afalsefalsefalsefalsetrue4Algebraproperties and relationships between entities that are represented in symbolic formfalsefalsefalsetruefalse3Understand_patterns,_relations,_and_functionsfalsefalsefalsetruefalse4NCTM:6-8:Algebra:Understand patterns, relations, and functions:Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules06bfalsefalsefalsefalsefalse4NCTM:6-8:Algebra:Understand patterns, relations, and functions:Relate and compare different forms of representation for a relationship06cfalsefalsefalsefalsefalse4NCTM:6-8:Algebra:Understand patterns, relations, and functions:Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations06dfalsefalsefalsefalsetrue4Represent_and_analyze_mathematical_situationsfalsefalsefalsetruefalse4NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Develop an initial conceptual understanding of different uses of variables06efalsefalsefalsefalsefalse4NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope06ffalsefalsefalsefalsefalse4NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships06gfalsefalsefalsefalsefalse4NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations06hfalsefalsefalsefalsetrue4Use_mathematical_models_to_represent_and_understand_quantitative_relationshipsfalsefalsefalsetruefalse4NCTM:6-8:Algebra:Use mathematical models to represent and understand quantitative relationships:Model and solve contextualized problems using various representations, such as graphs, tables, and equations06ifalsefalsefalsefalsetrue4Analyze_change_in_various_contextsfalsefalsefalsetruetrue4NCTM:6-8:Algebra:Analyze change in various contexts:Use graphs to analyze the nature of changes in quantities in linear relationships06jfalsefalsefalsefalsetrue4Geometryproperties and relationships of points, lines, angles, surfaces and solidsfalsefalsefalsetruefalse3Analyze_characteristics_and_properties_of_two-_and_three-dimensional_geometric_shapesfalsefalsefalsetruefalse4NCTM:6-8:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties06kfalsefalsefalsefalsefalse4NCTM:6-8:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects06lfalsefalsefalsefalsefalse4NCTM:6-8:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship06mfalsefalsefalsefalsetrue4Specify_locations_and_describe_spatial_relationshipsfalsefalsefalsetruefalse4NCTM:6-8:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Use coordinate geometry to represent and examine the properties of geometric shapes06nfalsefalsefalsefalsefalse4NCTM:6-8:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides06ofalsefalsefalsefalsetrue4Apply_transformations_and_use_symmetry_to_analyze_mathematical_situationsfalsefalsefalsetruefalse4NCTM:6-8:Geometry: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 scaling06pfalsefalsefalsefalsefalse4NCTM:6-8:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Examine the congruence, similarity, and line or rotational symmetry of objects using transformations06qfalsefalsefalsefalsetrue4Use_visualization,_spatial_reasoning,_and_geometric_modeling_to_solve_problemsfalsefalsefalsetruetrue4NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Draw geometric objects with specified properties, such as side lengths or angle measures06rfalsefalsefalsefalsefalse4NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume06sfalsefalsefalsefalsefalse4NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use visual tools such as networks to represent and solve problems06tfalsefalsefalsefalsefalse4NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric models to represent and explain numerical and algebraic relationships06ufalsefalsefalsefalsefalse4NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life06vfalsefalsefalsefalsetrue4Measurementthe assignment of a numerical value to an attribute of an objectfalsefalsefalsetruefalse3Understand_measurable_attributes_of_objects_and_the_units,_systems,_and_processes_of_measurementfalsefalsefalsetruefalse4NCTM:6-8:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand both metric and customary systems of measurement06wfalsefalsefalsefalsefalse4NCTM:6-8:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand relationships among units and convert from one unit to another within the same system06xfalsefalsefalsefalsefalse4NCTM:6-8:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume06yfalsefalsefalsefalsetrue4Apply_appropriate_techniques,_tools,_and_formulas_to_determine_measurementsfalsefalsefalsetruetrue4NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use common benchmarks to select appropriate methods for estimating measurements06zfalsefalsefalsefalsefalse4NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision070falsefalsefalsefalsefalse4NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements: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 shapes071falsefalsefalsefalsefalse4NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders072falsefalsefalsefalsefalse4NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Solve problems involving scale factors, using ratio and proportion073falsefalsefalsefalsefalse4NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Solve simple problems involving rates and derived measurements for such attributes as velocity and density074falsefalsefalsefalsetrue4Data_analysis_and_probabilitynumerical or statistical information that can be used to make decisionsfalsefalsefalsetruefalse3Formulate_questionsfalsefalsefalsetruefalse4NCTM:6-8:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population075falsefalsefalsefalsefalse4NCTM:6-8:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots076falsefalsefalsefalsetrue4Select_and_use_appropriate_statistical_methods_to_analyze_datafalsefalsefalsetruefalse4NCTM:6-8:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Find, use, and interpret measures of center and spread, including mean and interquartile range077falsefalsefalsefalsefalse4NCTM:6-8:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots078falsefalsefalsefalsetrue4Develop_and_evaluate_inferences_and_predictions_that_are_based_on_datafalsefalsefalsetruefalse4NCTM:6-8:Data analysis and probability: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 taken079falsefalsefalsefalsefalse4NCTM:6-8:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit07afalsefalsefalsefalsefalse4NCTM:6-8:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Use conjectures to formulate new questions and plan new studies to answer them07bfalsefalsefalsefalsetrue4Understand_and_apply_basic_concepts_of_probabilityfalsefalsefalsetruetrue4NCTM:6-8:Data analysis and probability:Understand and apply basic concepts of probability:Understand and use appropriate terminology to describe complementary and mutually exclusive events07cfalsefalsefalsefalsefalse4NCTM:6-8:Data analysis and probability:Understand and apply basic concepts of probability:Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations07dfalsefalsefalsefalsefalse4NCTM:6-8:Data analysis and probability:Understand and apply basic concepts of probability:Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models07efalsefalsefalsefalsetrue4Problem_solvingmethods and abilities to use mathematical reasoning to arrive at unknown solutionsfalsefalsefalsetruefalse3NCTM:6-8:Problem solving:Build new mathematical knowledge through problem solving07ffalsefalsefalsefalsefalse3NCTM:6-8:Problem solving:Solve problems that arise in mathematics and in other contexts07gfalsefalsefalsefalsefalse3NCTM:6-8:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems07hfalsefalsefalsefalsefalse3NCTM:6-8:Problem solving:Monitor and reflect on the process of mathematical problem solving07ifalsefalsefalsefalsefalse3NCTM:6-8:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics07jfalsefalsefalsefalsetrue3Reasoning_and_proofthe ability to make a hypothesis and apply mathematical logic (inductive reasoning) to arrive at conclusionsfalsefalsefalsetruefalse3NCTM:6-8:Reasoning and proof:Make and investigate mathematical conjectures07kfalsefalsefalsefalsefalse3NCTM:6-8:Reasoning and proof:Develop and evaluate mathematical arguments and proofs07lfalsefalsefalsefalsefalse3NCTM:6-8:Reasoning and proof:Select and use various types of reasoning and methods of proof07mfalsefalsefalsefalsetrue3Communicationthe ability to express and share mathematical conceptsfalsefalsefalsetruefalse3NCTM:6-8:Communication:Organize and consolidate their mathematical thinking through communication07nfalsefalsefalsefalsefalse3NCTM:6-8:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others07ofalsefalsefalsefalsefalse3NCTM:6-8:Communication:Analyze and evaluate the mathematical thinking and strategies of others07pfalsefalsefalsefalsefalse3NCTM:6-8:Communication:Use the language of mathematics to express mathematical ideas precisely07qfalsefalsefalsefalsetrue3Connectionsthe ability to recognize common themes across different mathematical concepts or other subjectsfalsefalsefalsetruefalse3NCTM:6-8:Connections:Recognize and use connections among mathematical ideas07rfalsefalsefalsefalsefalse3NCTM:6-8:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole07sfalsefalsefalsefalsefalse3NCTM:6-8:Connections:Recognize and apply mathematics in contexts outside of mathematics07tfalsefalsefalsefalsetrue3Representationthe ability to illustrate mathematical conceptsfalsefalsefalsetruetrue3NCTM:6-8:Representation:Create and use representations to organize, record, and communicate mathematical ideas07ufalsefalsefalsefalsefalse3NCTM:6-8:Representation:Select, apply, and translate among mathematical representations to solve problems07vfalsefalsefalsefalsefalse3NCTM:6-8:Representation:Use representations to model and interpret physical, social, and mathematical phenomena07wfalsefalsefalsefalsetrue39-12Pertains to content for 9th through 12th gradesfalsefalsefalsetruetrue2Number_and_operationsarithmetic manipulationsfalsefalsefalsetruefalse3Understand_numbersfalsefalsefalsetruefalse4NCTM:9-12:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand numbers:Develop a deeper understanding of very large and very small numbers and of various representations of them07xfalsefalsefalsefalsefalse4NCTM:9-12:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems: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 solutions07yfalsefalsefalsefalsefalse4NCTM:9-12:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Understand vectors and matrices as systems that have some of the properties of the real-number system07zfalsefalsefalsefalsefalse4NCTM:9-12:Number and operations:Understand numbers, ways of representing numbers, relationships among numbers, and number systems:Use number-theory arguments to justify relationships involving whole numbers080falsefalsefalsefalsetrue4Understand_meanings_of_operationsfalsefalsefalsetruefalse4NCTM:9-12:Number and operations:Understand meanings of operations and how they relate to one another:Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities081falsefalsefalsefalsefalse4NCTM:9-12:Number and operations:Understand meanings of operations and how they relate to one another:Develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices082falsefalsefalsefalsefalse4NCTM:9-12:Number and operations:Understand meanings of operations and how they relate to one another:Develop an understanding of permutations and combinations as counting techniques083falsefalsefalsefalsetrue4Compute_fluently_and_make_reasonable_estimatesfalsefalsefalsetruetrue4NCTM:9-12:Number and operations: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 cases084falsefalsefalsefalsefalse4NCTM:9-12:Number and operations:Compute fluently and make reasonable estimates:Judge the reasonableness of numerical computations and their results085falsefalsefalsefalsetrue4Algebraproperties and relationships between entities that are represented in symbolic formfalsefalsefalsetruefalse3Understand_patterns,_relations,_and_functionsfalsefalsefalsetruefalse4NCTM:9-12:Algebra:Understand patterns, relations, and functions:Generalize patterns using explicitly defined and recursively defined functions086falsefalsefalsefalsefalse4NCTM:9-12:Algebra:Understand patterns, relations, and functions:Understand relations and functions and select, convert flexibly among, and use various representations for them087falsefalsefalsefalsefalse4NCTM:9-12:Algebra:Understand patterns, relations, and functions:Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior088falsefalsefalsefalsefalse4NCTM:9-12:Algebra:Understand patterns, relations, and functions:Understand and perform transformations such as arithmetically combining, composing, and inverting commonly used functions, using technology to perform such operations on more-complicated symbolic expressions089falsefalsefalsefalsefalse4NCTM:9-12:Algebra:Understand patterns, relations, and functions:Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions08afalsefalsefalsefalsefalse4NCTM:9-12:Algebra:Understand patterns, relations, and functions:Interpret representations of functions of two variables08bfalsefalsefalsefalsetrue4Represent_and_analyze_mathematical_situationsfalsefalsefalsetruefalse4NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations08cfalsefalsefalsefalsefalse4NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols: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 cases08dfalsefalsefalsefalsefalse4NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use symbolic algebra to represent and explain mathematical relationships08efalsefalsefalsefalsefalse4NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations08ffalsefalsefalsefalsefalse4NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology08gfalsefalsefalsefalsetrue4Use_mathematical_models_to_represent_and_understand_quantitative_relationshipsfalsefalsefalsetruefalse4NCTM:9-12:Algebra: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 relationships08hfalsefalsefalsefalsefalse4NCTM:9-12:Algebra:Use mathematical models to represent and understand quantitative relationships:Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts08ifalsefalsefalsefalsefalse4NCTM:9-12:Algebra:Use mathematical models to represent and understand quantitative relationships:Draw reasonable conclusions about a situation being modeled08jfalsefalsefalsefalsetrue4Analyze_change_in_various_contextsfalsefalsefalsetruetrue4NCTM:9-12:Algebra:Analyze change in various contexts:Approximate and interpret rates of change from graphical and numerical data08kfalsefalsefalsefalsetrue4Geometryproperties and relationships of points, lines, angles, surfaces and solidsfalsefalsefalsetruefalse3Analyze_characteristics_and_properties_of_two-_and_three-dimensional_geometric_shapesfalsefalsefalsetruefalse4NCTM:9-12:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Analyze properties and determine attributes of two- and three-dimensional objects08lfalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships: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 them08mfalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships:Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others08nfalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Analyze characteristics:Use trigonometric relationships to determine lengths and angle measures08ofalsefalsefalsefalsetrue4Specify_locations_and_describe_spatial_relationshipsfalsefalsefalsetruefalse4NCTM:9-12:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations08pfalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Specify locations and describe spatial relationships using coordinate geometry and other representational systems:Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates08qfalsefalsefalsefalsetrue4Apply_transformations_and_use_symmetry_to_analyze_mathematical_situationsfalsefalsefalsetruefalse4NCTM:9-12:Geometry: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 matrices08rfalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Use various representations to help understand the effects of simple transformations and their compositions08sfalsefalsefalsefalsetrue4Use_visualization,_spatial_reasoning,_and_geometric_modeling_to_solve_problemsfalsefalsefalsetruetrue4NCTM:9-12:Geometry: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 tools08tfalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections08ufalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use vertex-edge graphs to model and solve problems08vfalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric models to gain insights into, and answer questions in, other areas of mathematics08wfalsefalsefalsefalsefalse4NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture08xfalsefalsefalsefalsetrue4Measurementthe assignment of a numerical value to an attribute of an objectfalsefalsefalsetruefalse3Understand_measurable_attributes_of_objects_and_the_units,_systems,_and_processes_of_measurementfalsefalsefalsetruefalse4NCTM:9-12: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 measurement08yfalsefalsefalsefalsetrue4Apply_appropriate_techniques,_tools,_and_formulas_to_determine_measurementsfalsefalsefalsetruetrue4NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Analyze precision, accuracy, and approximate error in measurement situations08zfalsefalsefalsefalsefalse4NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders090falsefalsefalsefalsefalse4NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations091falsefalsefalsefalsefalse4NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use unit analysis to check measurement computations092falsefalsefalsefalsetrue4Data_analysis_and_probabilitynumerical or statistical information that can be used to make decisionsfalsefalsefalsetruefalse3Formulate_questionsfalsefalsefalsetruefalse4NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each093falsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments094falsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable095falsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Understand histograms, parallel box plots, and scatterplots and use them to display data096falsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them:Compute basic statistics and understand the distinction between a statistic and a parameter097falsefalsefalsefalsetrue4Select_and_use_appropriate_statistical_methods_to_analyze_datafalsefalsefalsetruefalse4NCTM:9-12:Data analysis and probability: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 statistics098falsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools099falsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Display and discuss bivariate data where at least one variable is categorical09afalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Recognize how linear transformations of univariate data affect shape, center, and spread09bfalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Select and use appropriate statistical methods to analyze data:Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled09cfalsefalsefalsefalsetrue4Develop_and_evaluate_inferences_and_predictions_that_are_based_on_datafalsefalsefalsetruefalse4NCTM:9-12:Data analysis and probability: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 distributions09dfalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference09efalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data: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 conclusions09ffalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Develop and evaluate inferences and predictions that are based on data:Understand how basic statistical techniques are used to monitor process characteristics in the workplace09gfalsefalsefalsefalsetrue4Understand_and_apply_basic_concepts_of_probabilityfalsefalsefalsetruetrue4NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases09hfalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Use simulations to construct empirical probability distributions09ifalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Compute and interpret the expected value of random variables in simple cases09jfalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Understand the concepts of conditional probability and independent events09kfalsefalsefalsefalsefalse4NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Understand how to compute the probability of a compound event09lfalsefalsefalsefalsetrue4Problem_solvingmethods and abilities to use mathematical reasoning to arrive at unknown solutionsfalsefalsefalsetruefalse3NCTM:9-12:Problem solving:Build new mathematical knowledge through problem solving09mfalsefalsefalsefalsefalse3NCTM:9-12:Problem solving:Solve problems that arise in mathematics and in other contexts09nfalsefalsefalsefalsefalse3NCTM:9-12:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems09ofalsefalsefalsefalsefalse3NCTM:9-12:Problem solving:Monitor and reflect on the process of mathematical problem solving09pfalsefalsefalsefalsetrue3Reasoning_and_proofthe ability to make a hypothesis and apply mathematical logic (inductive reasoning) to arrive at conclusionsfalsefalsefalsetruefalse3NCTM:9-12:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics09qfalsefalsefalsefalsefalse3NCTM:9-12:Reasoning and proof:Make and investigate mathematical conjectures09rfalsefalsefalsefalsefalse3NCTM:9-12:Reasoning and proof:Develop and evaluate mathematical arguments and proofs09sfalsefalsefalsefalsefalse3NCTM:9-12:Reasoning and proof:Select and use various types of reasoning and methods of proof09tfalsefalsefalsefalsetrue3Communicationthe ability to express and share mathematical conceptsfalsefalsefalsetruefalse3NCTM:9-12:Communication:Organize and consolidate their mathematical thinking through communication09ufalsefalsefalsefalsefalse3NCTM:9-12:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others09vfalsefalsefalsefalsefalse3NCTM:9-12:Communication:Analyze and evaluate the mathematical thinking and strategies of others09wfalsefalsefalsefalsefalse3NCTM:9-12:Communication:Use the language of mathematics to express mathematical ideas precisely09xfalsefalsefalsefalsetrue3Connectionsthe ability to recognize common themes across different mathematical concepts or other subjectsfalsefalsefalsetruefalse3NCTM:9-12:Connection:Recognize and use connections among mathematical ideas09yfalsefalsefalsefalsefalse3NCTM:9-12:Connection:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole09zfalsefalsefalsefalsefalse3NCTM:9-12:Connection:Recognize and apply mathematics in contexts outside of mathematics0a0falsefalsefalsefalsetrue3Representationthe ability to illustrate mathematical conceptsfalsefalsefalsetruetrue3NCTM:9-12:Representation:Create and use representations to organize, record, and communicate mathematical ideas0a1falsefalsefalsefalsefalse3NCTM:9-12:Representation:Select, apply, and translate among mathematical representations to solve problems0a2falsefalsefalsefalsefalse3NCTM:9-12:Representation:Use representations to model and interpret physical, social, and mathematical phenomena0a3falsefalsefalsefalsetrue3