cs National_Science_Education_Standards_(NSES) NSES represents the National Science Education Standards National Science Education Standards (NSES) NSES false false false true false 1 K-4 Pertains to content for kindergarten through 4th grade K-4 false false false true false 2 Unifying_concepts_and_processes Empahsizes conceptual and procedural schemes that unify science disciplines Unifying concepts and processes false false false true false 3 NSES:K-4:Unifying Concepts and Processes Standards:Change, constancy, and measurement 01s Change, constancy, and measurement false false false false false 3 NSES:K-4:Unifying Concepts and Processes Standards:Evidence, models, and explanation 01t Evidence, models, and explanation false false false false false 3 NSES:K-4:Unifying Concepts and Processes Standards:Evolution and equilibrium 01u Evolution and equilibrium false false false false false 3 NSES:K-4:Unifying Concepts and Processes Standards:Form and function 01v Form and function false false false false false 3 NSES:K-4:Unifying Concepts and Processes Standards:Systems, order, and organization 01w Systems, order, and organization false false false false true 3 A_-_Science_as_inquiry The combination of the processes of science, scientific knowledge and reasoning to understand science A - Science as inquiry false false false true false 3 NSES:K-4:Content Standard A Science as Inquiry Standards:Abilities necessary to do scientific inquiry 018 Abilities necessary to do scientific inquiry false false false false false 3 NSES:K-4:Content Standard A Science as Inquiry Standards:Understanding about scientific inquiry 019 Understanding about scientific inquiry false false false false true 3 B_-_Physical_science Encompasses the subject matter, facts, concepts, principls, theories and models of physical science B - Physical science false false false true false 3 NSES:K-4:Content Standard B Physical Science Standards:Light, heat, electricity, and magnetism 01a Light, heat, electricity, and magnetism false false false false false 3 NSES:K-4:Content Standard B Physical Science Standards:Position and motion of objects 01b Position and motion of objects false false false false false 3 NSES:K-4:Content Standard B Physical Science Standards:Properties of objects and materials 01c Properties of objects and materials false false false false true 3 C_-_Life_science Encompasses the subject matter, facts, concepts, principls, theories and models of life science C - Life science false false false true false 3 NSES:K-4:Content Standard C Life Science Standards:Characteristics of organisms 01d Characteristics of organisms false false false false false 3 NSES:K-4:Content Standard C Life Science Standards:Life cycles of organisms 01e Life cycles of organisms false false false false false 3 NSES:K-4:Content Standard C Life Science Standards:Organisms and environments 01f Organisms and environments false false false false true 3 D_-_Earth_and_space_science Encompasses the subject matter, facts, concepts, principls, theories and models of Earth and space science D - Earth and space science false false false true false 3 NSES:K-4:Content Standard D Earth and Space Science Standards:Changes in earth and sky 01g Changes in earth and sky false false false false false 3 NSES:K-4:Content Standard D Earth and Space Science Standards:Objects in the sky 01h Objects in the sky false false false false false 3 NSES:K-4:Content Standard D Earth and Space Science Standards:Properties of earth materials 01i Properties of earth materials false false false false true 3 E_-_Science_and_technology Establish connections between the natural and designed worlds and provide opportunities to develop decision-making abilities E - Science and technology false false false true false 3 NSES:K-4:Content Standard E Science and Technology Standards:Abilities of technological design 01j Abilities of technological design false false false false false 3 NSES:K-4:Content Standard E Science and Technology Standards:Abilities to distinguish between natural objects and objects made by humans 01k Abilities to distinguish between natural objects and objects made by humans false false false false false 3 NSES:K-4:Content Standard E Science and Technology Standards:Understanding about science and technology 01l Understanding about sci. / tech. false false false false true 3 F_-_Science_in_personal_/_social_perspectives Develop decision-making skills in relation to personal social issues F - Science in personal / social perspectives false false false true false 3 NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Changes in environments 01m Changes in environments false false false false false 3 NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Characteristics and changes in populations 01n Characteristics / changes in populations false false false false false 3 NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Personal health 01o Personal health false false false false false 3 NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Science and technology in local challenges 01p Sci. / tech. in local challenges false false false false false 3 NSES:K-4:Content Standard F Science in Personal and Social Perspectives Standards:Types of resources 01q Types of resources false false false false true 3 G_-_History_and_nature_of_science Emphasizes 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 cultures G - History and nature of science false false false true true 3 NSES:K-4:Content Standard G History and Nature of Science Standards:Science as a human endeavor 01r Science as a human endeavor false false false false true 3 5-8 Pertains to content for 5th through 8th grade 5-8 false false false true false 2 Unifying_concepts_and_processes Empahsizes conceptual and procedural schemes that unify science disciplines Unifying concepts and processes false false false true false 3 NSES:5-8:Unifying Concepts and Processes Standards:Change, constancy, and measurement 005 Change, constancy, and measurement false false false false false 3 NSES:5-8:Unifying Concepts and Processes Standards:Evidence, models, and explanation 006 Evidence, models, and explanation false false false false false 3 NSES:5-8:Unifying Concepts and Processes Standards:Evolution and equilibrium 007 Evolution and equilibrium false false false false false 3 NSES:5-8:Unifying Concepts and Processes Standards:Form and function 008 Form and function false false false false false 3 NSES:5-8:Unifying Concepts and Processes Standards:Systems, order, and organization 009 Systems, order, and organization false false false false true 3 A_-_Science_as_inquiry The combination of the processes of science, scientific knowledge and reasoning to understand science A - Science as inquiry false false false true false 3 NSES:5-8:Content Standard A Science as Inquiry Standards:Abilities necessary to do scientific inquiry 0i Abilities necessary to do scientific inquiry false false false false false 3 NSES:5-8:Content Standard A Science as Inquiry Standards:Understanding about scientific inquiry 0j Understanding about scientific inquiry false false false false true 3 B_-_Physical_science Encompasses the subject matter, facts, concepts, principls, theories and models of physical science B - Physical science false false false true false 3 NSES:5-8:Content Standard B Physical Science Standards:Motion and forces 0k Motion and forces false false false false false 3 NSES:5-8:Content Standard B Physical Science Standards:Properties and changes of properties in matter 0l Properties and changes of properties in matter false false false false false 3 NSES:5-8:Content Standard B Physical Science Standards:Transfer of energy 0m Transfer of energy false false false false true 3 C_-_Life_science Encompasses the subject matter, facts, concepts, principls, theories and models of life science C - Life science false false false true false 3 NSES:5-8:Content Standard C Life Science Standards:Diversity and adaptations of organisms 0n Diversity and adaptations of organisms false false false false false 3 NSES:5-8:Content Standard C Life Science Standards:Population and ecosystems 0o Population and ecosystems false false false false false 3 NSES:5-8:Content Standard C Life Science Standards:Regulation and behavior 0p Regulation and behavior false false false false false 3 NSES:5-8:Content Standard C Life Science Standards:Reproduction and heredity 0q Reproduction and heredity false false false false false 3 NSES:5-8:Content Standard C Life Science Standards:Structure and function in living systems 0r Structure and function in living systems false false false false true 3 D_-_Earth_and_space_science Encompasses the subject matter, facts, concepts, principls, theories and models of Earth and space science D - Earth and space science false false false true false 3 NSES:5-8:Content Standard D Earth and Space Science Standards:Earth in the solar system 0s Earth in the solar system false false false false false 3 NSES:5-8:Content Standard D Earth and Space Science Standards:Earth's history 0t Earth's history false false false false false 3 NSES:5-8:Content Standard D Earth and Space Science Standards:Structure of the earth system 0u Structure of the earth system false false false false true 3 E_-_Science_and_technology Establish connections between the natural and designed worlds and provide opportunities to develop decision-making abilities E - Science and technology false false false true false 3 NSES:5-8:Content Standard E Science and Technology Standards:Abilities of technological design 0v Abilities of technological design false false false false false 3 NSES:5-8:Content Standard E Science and Technology Standards:Understandings about science and technology 0w Understandings about sci. / tech. false false false false true 3 F_-_Science_in_personal_/_social_perspectives Develop decision-making skills in relation to personal social issues F - Science in personal / social perspectives false false false true false 3 NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Natural hazards 0x Natural hazards false false false false false 3 NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Personal health 0y Personal health false false false false false 3 NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Populations, resources, and environments 0z Populations, resources, environments false false false false false 3 NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Risks and benefits 000 Risks and benefits false false false false false 3 NSES:5-8:Content Standard F Science in Personal and Social Perspectives Standards:Science and technology in society 001 Sci. / tech. in society false false false false true 3 G_-_History_and_nature_of_science Emphasizes 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 cultures G - History and nature of science false false false true true 3 NSES:5-8:Content Standard G History and Nature of Science Standards:History of science 002 History of science false false false false false 3 NSES:5-8:Content Standard G History and Nature of Science Standards:Nature of science 003 Nature of science false false false false false 3 NSES:5-8:Content Standard G History and Nature of Science Standards:Science as a human endeavor 004 Science as a human endeavor false false false false true 3 9-12 Pertains to content for 9th through 12th grade 9-12 false false false true true 2 Unifying_concepts_and_processes Empahsizes conceptual and procedural schemes that unify science disciplines Unifying concepts and processes false false false true false 3 NSES:9-12:Unifying Concepts and Processes Standards:Change, constancy, and measurement 013 Change, constancy, and measurement false false false false false 3 NSES:9-12:Unifying Concepts and Processes Standards:Evidence, models, and explanation 014 Evidence, models, and explanation false false false false false 3 NSES:9-12:Unifying Concepts and Processes Standards:Evolution and equilibrium 015 Evolution and equilibrium false false false false false 3 NSES:9-12:Unifying Concepts and Processes Standards:Form and function 016 Form and function false false false false false 3 NSES:9-12:Unifying Concepts and Processes Standards:Systems, order, and organization 017 Systems, order, and organization false false false false true 3 A_-_Science_as_inquiry The combination of the processes of science, scientific knowledge and reasoning to understand science A - Science as inquiry false false false true false 3 NSES:9-12:Content Standard A Science as Inquiry Standards:Abilities necessary to do scientific inquiry 00a Abilities necessary to do scientific inquiry false false false false false 3 NSES:9-12:Content Standard A Science as Inquiry Standards:Understandings about scientific inquiry 00b Understandings about scientific inquiry false false false false true 3 B_-_Physical_science Encompasses the subject matter, facts, concepts, principls, theories and models of physical science B - Physical science false false false true false 3 NSES:9-12:Content Standard B Physical Science Standards:Chemical reactions 00c Chemical reactions false false false false false 3 NSES:9-12:Content Standard B Physical Science Standards:Conservation of energy and increase in disorder 00d Conservation of energy and increase in disorder false false false false false 3 NSES:9-12:Content Standard B Physical Science Standards:Interactions of energy and matter 00e Interactions of energy and matter false false false false false 3 NSES:9-12:Content Standard B Physical Science Standards:Motions and forces 00f Motions and forces false false false false false 3 NSES:9-12:Content Standard B Physical Science Standards:Structure and properties of matter 00g Structure and properties of matter false false false false false 3 NSES:9-12:Content Standard B Physical Science Standards:Structure of atoms 00h Structure of atoms false false false false true 3 C_-_Life_science Encompasses the subject matter, facts, concepts, principls, theories and models of life science C - Life science false false false true false 3 NSES:9-12:Content Standard C Life Science Standards:Behavior of organisms 00i Behavior of organisms false false false false false 3 NSES:9-12:Content Standard C Life Science Standards:Biological evolution 00j Biological evolution false false false false false 3 NSES:9-12:Content Standard C Life Science Standards:Interdependence of organisms 00k Interdependence of organisms false false false false false 3 NSES:9-12:Content Standard C Life Science Standards:Matter, energy, and organization in living systems 00l Matter, energy, and organization in living systems false false false false false 3 NSES:9-12:Content Standard C Life Science Standards:Molecular basis of heredity 00m Molecular basis of heredity false false false false false 3 NSES:9-12:Content Standard C Life Science Standards:The cell 00n The cell false false false false true 3 D_-_Earth_and_space_science Encompasses the subject matter, facts, concepts, principls, theories and models of Earth and space science D - Earth and space science false false false true false 3 NSES:9-12:Content Standard D Earth and Space Science Standards:Energy in the earth system 00o Energy in the earth system false false false false false 3 NSES:9-12:Content Standard D Earth and Space Science Standards:Geochemical cycles 00p Geochemical cycles false false false false false 3 NSES:9-12:Content Standard D Earth and Space Science Standards:Origin and evolution of the earth system 00q Origin and evolution of the earth system false false false false false 3 NSES:9-12:Content Standard D Earth and Space Science Standards:Origin and evolution of the universe 00r Origin and evolution of the universe false false false false true 3 E_-_Science_and_technology Establish connections between the natural and designed worlds and provide opportunities to develop decision-making abilities E - Science and technology false false false true false 3 NSES:9-12:Content Standard E Science and Technology Standards:Abilities of technological design 00s Abilities of technological design false false false false false 3 NSES:9-12:Content Standard E Science and Technology Standards:Understandings about science and technology 00t Understandings about science and technology false false false false true 3 F_-_Science_in_personal_/_social_perspectives Develop decision-making skills in relation to personal social issues F - Science in personal / social perspectives false false false true false 3 NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Environmental quality 00u Environmental quality false false false false false 3 NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Natural and human-induced hazards 00v Natural and human-induced hazards false false false false false 3 NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Natural resources 00w Natural resources false false false false false 3 NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Personal and community health 00x Personal and community health false false false false false 3 NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Population growth 00y Population growth false false false false false 3 NSES:9-12:Content Standard F Science in Personal and Social Perspectives Standards:Science and technology in local, national, and global challenges 00z Sci. / tech. in local, national, and global challenges false false false false true 3 G_-_History_and_nature_of_science Emphasizes 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 cultures G - History and nature of science false false false true true 3 NSES:9-12:Content Standard G History and Nature of Science Standards:Historical perspectives 010 Historical perspectives false false false false false 3 NSES:9-12:Content Standard G History and Nature of Science Standards:Nature of scientific knowledge 011 Nature of scientific knowledge false false false false false 3 NSES:9-12:Content Standard G History and Nature of Science Standards:Science as a human endeavor 012 Science as a human endeavor false false false false true 3 National_Geography_Standards National Geography Standards published by the National Council for Geographic Education (NCGE) National Geography Standards false false false true false 1 Environment_and_society Environment and society false false false true false 2 NCGE:Environment and Society:How human actions modify the physical environment 00 How human actions modify the physical env. false false false false false 2 NCGE:Environment and Society:How physical systems affect human systems 01 How physical systems affect human systems false false false false false 2 NCGE:Environment and Society:The changes that occur in the meaning, use, distribution, and importance of resources 02 The changes that occur in the meaning, use, distribution, and importance of resources false false false false true 2 Human_systems Human systems false false false true false 2 NCGE:Human Systems:How forces of cooperation and conflict among people influence the division and control of Earth's surface 03 How forces of cooperation and conflict among people influence the division and control of Earth's surface false false false false false 2 NCGE:Human Systems:The characteristics, distribution, and migration of human populations on Earth's surface 04 The characteristics, distribution, and migration of human populations on Earth's surface false false false false false 2 NCGE:Human Systems:The characteristics, distributions, and complexity of Earth's cultural mosaics 05 The characteristics, distributions, and complexity of Earth's cultural mosaics false false false false false 2 NCGE:Human Systems:The patterns and networks of economic interdependence on Earth's surface 06 The patterns and networks of economic interdependence on Earth's surface false false false false false 2 NCGE:Human Systems:The process, patterns, and functions of human settlement 07 The process, patterns, and functions of human settlement false false false false true 2 Physical_systems Physical systems false false false true false 2 NCGE:Physical Systems:The characteristics and spatial distribution of ecosystems on Earth's surface 08 The characteristics and spatial distribution of ecosystems on Earth's surface false false false false false 2 NCGE:Physical Systems:The physical processes that shape the patterns of Earth's surface 09 The physical processes that shape the patterns of Earth's surface false false false false true 2 Places_and_regions Places and regions false false false true false 2 NCGE:Places and Regions:How culture and experience influence people's perception of places and regions 0a How culture and experience influence people's perception of places and regions false false false false false 2 NCGE:Places and Regions:That people create regions to interpret Earth's complexity 0b That people create regions to interpret Earth's complexity false false false false false 2 NCGE:Places and Regions:The physical and human characteristics of places 0c The physical and human characteristics of places false false false false true 2 The_uses_of_geography The uses of geography false false false true false 2 NCGE:The Uses of Geography:How to apply geography to interpret the past 0d How to apply geography to interpret the past false false false false false 2 NCGE:The Uses of Geography:How to apply geography to interpret the present and plan for the future 0e How to apply geography to interpret the present and plan for the future false false false false true 2 The_world_in_spatial_terms The world in spatial terms false false false true true 2 NCGE:The World in Spatial Terms:How to analyze the spatial organization of people, places, and environments on Earth's surface 0f How to analyze the spatial organization of people, places, and environments on Earth's surface false false false false false 2 NCGE:The World in Spatial Terms:How to use maps and other geographic representations, tools, and technologies to acquire, process, and report information 0g How to use maps and other geographic representations, tools, and technologies to acquire, process, and report information false false false false false 2 NCGE:The World in Spatial Terms:How to use mental maps to organize information about people, places, and environments 0h How to use mental maps to organize information about people, places, and environments false false false false true 2 National_Council_of_Teachers_of_Mathematics_(NCTM) NCTM represents the math content standards National Council of Teachers of Mathematics (NCTM) NCTM true false false true true 1 Pre_K-2 Pertains to content for pre-kindergarten through 2nd grade Pre K-2 false false false true false 2 Number_and_operations arithmetic manipulations Number and operations false false false true false 3 Understand_numbers ways of representing numbers, relationships among numbers, and number systems Understand numbers false false false true false 4 NCTM: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 objects 01x Count with understanding and recognize 'how many' in sets of objects false false false false false 4 NCTM: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 system 01y Use multiple models to develop initial understandings of place value and the base-ten number system false false false false false 4 NCTM: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 connections 01z Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections false false false false false 4 NCTM: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 numbers 020 Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers false false false false false 4 NCTM: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 representations 021 Connect number words and numerals to the quantities they represent, using various physical models and representations false false false false false 4 NCTM: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 1/2 022 Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2 false false false false true 4 Understand_meanings_of_operations Understand meanings of operations false false false true false 4 NCTM: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 operations 023 Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations false false false false false 4 NCTM: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 numbers 024 Understand the effects of adding and subtracting whole numbers false false false false false 4 NCTM: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 equally 025 Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally false false false false true 4 Compute_fluently_and_make_reasonable_estimates Compute fluently and make reasonable estimates false false false true true 4 NCTM: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 subtraction 026 Develop and use strategies for whole-number computations, with a focus on addition and subtraction false false false false false 4 NCTM:Pre-K-2:Number and operations:Compute fluently and make reasonable estimates:Develop fluency with basic number combinations for addition and subtraction 027 Develop fluency with basic number combinations for addition and subtraction false false false false false 4 NCTM: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 calculators 028 Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators false false false false true 4 Algebra properties and relationships between entities that are represented in symbolic form Algebra false false false true false 3 Understand_patterns,_relations,_and_functions Understand patterns, relations, and functions false false false true false 4 NCTM:Pre-K-2:Algebra:Understand patterns, relations, and functions:Sort, classify, and order objects by size, number, and other properties 029 Sort, classify, and order objects by size, number, and other properties false false false false false 4 NCTM: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 another 02a Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another false false false false false 4 NCTM:Pre-K-2:Algebra:Understand patterns, relations, and functions:Analyze how both repeating and growing patterns are generated 02b Analyze how both repeating and growing patterns are generated false false false false true 4 Represent_and_analyze_mathematical_situations Represent and analyze mathematical situations false false false true false 4 NCTM: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 numbers 02c Illustrate general principles and properties of operations, such as commutativity, using specific numbers false false false false false 4 NCTM: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 notations 02d Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations false false false false true 4 Use_mathematical_models_to_represent_and_understand_quantitative_relationships Use mathematical models to represent and understand quantitative relationships false false false true false 4 NCTM: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 symbols 02e Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols false false false false true 4 Analyze_change_in_various_contexts Analyze change in various contexts false false false true true 4 NCTM:Pre-K-2:Algebra:Analyze change in various contexts:Describe qualitative change, such as a student's growing taller 02f Describe qualitative change, such as a student's growing taller false false false false false 4 NCTM:Pre-K-2:Algebra:Analyze change in various contexts:Describe quantitative change, such as a student's growing two inches in one year 02g Describe quantitative change, such as a student's growing two inches in one year false false false false true 4 Geometry properties and relationships of points, lines, angles, surfaces and solids Geometry false false false true false 3 Analyze_characteristics_and_properties_of_two-_and_three-dimensional_geometric_shapes Analyze characteristics and properties of two- and three-dimensional geometric shapes false false false true false 4 NCTM: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 shapes 02h Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes false false false false false 4 NCTM: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 shapes 02i Describe attributes and parts of two- and three-dimensional shapes false false false false false 4 NCTM: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 shapes 02j Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes false false false false true 4 Specify_locations_and_describe_spatial_relationships Specify locations and describe spatial relationships false false false true false 4 NCTM: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 position 02k Describe, name, and interpret relative positions in space and apply ideas about relative position false false false false false 4 NCTM: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 distance 02l Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance false false false false false 4 NCTM: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 maps 02m Find and name locations with simple relationships such as 'near to' and in coordinate systems such as maps false false false false true 4 Apply_transformations_and_use_symmetry_to_analyze_mathematical_situations Apply transformations and use symmetry to analyze mathematical situations false false false true false 4 NCTM:Pre-K-2:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Recognize and apply slides, flips, and turns 02n Recognize and apply slides, flips, and turns false false false false false 4 NCTM:Pre-K-2:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Recognize and create shapes that have symmetry 02o Recognize and create shapes that have symmetry false false false false true 4 Use_visualization,_spatial_reasoning,_and_geometric_modeling_to_solve_problems Use visualization, spatial reasoning, and geometric modeling to solve problems false false false true true 4 NCTM: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 visualization 02p Create mental images of geometric shapes using spatial memory and spatial visualization false false false false false 4 NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Recognize and represent shapes from different perspectives 02q Recognize and represent shapes from different perspectives false false false false false 4 NCTM:Pre-K-2:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Relate ideas in geometry to ideas in number and measurement 02r Relate ideas in geometry to ideas in number and measurement false false false false false 4 NCTM: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 location 02s Recognize geometric shapes and structures in the environment and specify their location false false false false true 4 Measurement the assignment of a numerical value to an attribute of an object Measurement false false false true false 3 Understand_measurable_attributes_of_objects_and_the_units,_systems,_and_processes_of_measurement Understand measurable attributes of objects and the units, systems, and processes of measurement false false false true false 4 NCTM: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 time 02t Recognize the attributes of length, volume, weight, area, and time false false false false false 4 NCTM:Pre-K-2:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Compare and order objects according to these attributes 02u Compare and order objects according to these attributes false false false false false 4 NCTM: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 units 02v Understand how to measure using nonstandard and standard units false false false false false 4 NCTM: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 measured 02w Select an appropriate unit and tool for the attribute being measured false false false false true 4 Apply_appropriate_techniques,_tools,_and_formulas_to_determine_measurements Apply appropriate techniques, tools, and formulas to determine measurements false false false true true 4 NCTM: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 end 02x Measure with multiple copies of units of the same size, such as paper clips laid end to end false false false false false 4 NCTM: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 meterstick 02y 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 false false false false false 4 NCTM:Pre-K-2:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use tools to measure 02z Use tools to measure false false false false false 4 NCTM:Pre-K-2:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop common referents for measures to make comparisons and estimates 030 Develop common referents for measures to make comparisons and estimates false false false false true 4 Data_analysis_and_probability numerical or statistical information that can be used to make decisions Data analysis and probability false false false true false 3 Formulate_questions Formulate questions false false false true false 4 NCTM: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 surroundings 031 Pose questions and gather data about themselves and their surroundings false false false false false 4 NCTM: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 objects 032 Sort and classify objects according to their attributes and organize data about the objects false false false false false 4 NCTM: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 graphs 033 Represent data using concrete objects, pictures, and graphs false false false false true 4 Select_and_use_appropriate_statistical_methods_to_analyze_data Select and use appropriate statistical methods to analyze data false false false true false 4 NCTM: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 show 034 Describe parts of the data and the set of data as a whole to determine what the data show false false false false true 4 Develop_and_evaluate_inferences_and_predictions_that_are_based_on_data Develop and evaluate inferences and predictions that are based on data false false false true false 4 NCTM: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 unlikely 035 Discuss events related to students' experiences as likely or unlikely false false false false true 4 Understand_and_apply_basic_concepts_of_probability Understand and apply basic concepts of probability false false false true true 4 NCTM:Pre-K-2:Data analysis and probability:Understand and apply basic concepts of probability 036 Understand and apply basic concepts of probability false false false false true 4 Problem_solving methods and abilities to use mathematical reasoning to arrive at unknown solutions Problem solving false false false true false 3 NCTM:Pre-K-2:Problem solving:Build new mathematical knowledge through problem solving 037 Build new mathematical knowledge through problem solving false false false false false 3 NCTM:Pre-K-2:Problem solving:Solve problems that arise in mathematics and in other contexts 038 Solve problems that arise in mathematics and in other contexts false false false false false 3 NCTM:Pre-K-2:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems 039 Apply and adapt a variety of appropriate strategies to solve problems false false false false false 3 NCTM:Pre-K-2:Problem solving:Monitor and reflect on the process of mathematical problem solving 03a Monitor and reflect on the process of mathematical problem solving false false false false true 3 Reasoning_and_proof the ability to make a hypothesis and apply mathematical logic (inductive reasoning) to arrive at conclusions Reasoning and proof false false false true false 3 NCTM:Pre-K-2:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics 03b Recognize reasoning and proof as fundamental aspects of mathematics false false false false false 3 NCTM:Pre-K-2:Reasoning and proof:Make and investigate mathematical conjectures 03c Make and investigate mathematical conjectures false false false false false 3 NCTM:Pre-K-2:Reasoning and proof:Develop and evaluate mathematical arguments and proofs 03d Develop and evaluate mathematical arguments and proofs false false false false false 3 NCTM:Pre-K-2:Reasoning and proof:Select and use various types of reasoning and methods of proof 03e Select and use various types of reasoning and methods of proof false false false false true 3 Communication the ability to express and share mathematical concepts Communication false false false true false 3 NCTM:Pre-K-2:Communication:Organize and consolidate their mathematical thinking through communication 03f Organize and consolidate their mathematical thinking through communication false false false false false 3 NCTM:Pre-K-2:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others 03g Communicate their mathematical thinking coherently and clearly to peers, teachers, and others false false false false false 3 NCTM:Pre-K-2:Communication:Analyze and evaluate the mathematical thinking and strategies of others 03h Analyze and evaluate the mathematical thinking and strategies of others false false false false true 3 Connections the ability to recognize common themes across different mathematical concepts or other subjects Connections false false false true false 3 NCTM:Pre-K-2:Connections:Recognize and use connections among mathematical ideas 03i Recognize and use connections among mathematical ideas false false false false false 3 NCTM:Pre-K-2:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole 03j Understand how mathematical ideas interconnect and build on one another to produce a coherent whole false false false false false 3 NCTM:Pre-K-2:Connections:Recognize and apply mathematics in contexts outside of mathematics 03k Recognize and apply mathematics in contexts outside of mathematics false false false false true 3 Representation the ability to illustrate mathematical concepts Representation false false false true true 3 NCTM:Pre-K-2:Representation:Create and use representations to organize, record, and communicate mathematical ideas 03l Create and use representations to organize, record, and communicate mathematical ideas false false false false false 3 NCTM:Pre-K-2:Representation:Select, apply, and translate among mathematical representations to solve problems 03m Select, apply, and translate among mathematical representations to solve problems false false false false false 3 NCTM:Pre-K-2:Representation:Use representations to model and interpret physical, social, and mathematical phenomena 03n Use representations to model and interpret physical, social, and mathematical phenomena false false false false true 3 3-5 Pertains to content for 3rd through 5th grades 3-5 false false false true false 2 Number_and_operations arithmetic manipulations Number and operations false false false true false 3 Understand_numbers Understand numbers false false false true false 4 NCTM: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 decimals 03o Understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals false false false false false 4 NCTM: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 numbers 03p Recognize equivalent representations for the same number and generate them by decomposing and composing numbers false false false false false 4 NCTM: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 numbers 03q 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 false false false false false 4 NCTM: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 fractions 03r Use models, benchmarks, and equivalent forms to judge the size of fractions false false false false false 4 NCTM: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 percents 03s Recognize and generate equivalent forms of commonly used fractions, decimals, and percents false false false false false 4 NCTM: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 applications 03t Explore numbers less than 0 by extending the number line and through familiar applications false false false false false 4 NCTM: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 factors 03u Describe classes of numbers according to characteristics such as the nature of their factors false false false false true 4 Understand_meanings_of_operations Understand meanings of operations false false false true false 4 NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Understand various meanings of multiplication and division 03v Understand various meanings of multiplication and division false false false false false 4 NCTM:3-5:Number and operations:Understand meanings of operations and how they relate to one another:Understand the effects of multiplying and dividing whole numbers 03w Understand the effects of multiplying and dividing whole numbers false false false false false 4 NCTM: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 problems 03x Identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems false false false false false 4 NCTM: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 addition 03y Understand and use properties of operations, such as the distributivity of multiplication over addition false false false false true 4 Compute_fluently_and_make_reasonable_estimates Compute fluently and make reasonable estimates false false false true true 4 NCTM: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 50 03z Develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 x 50 false false false false false 4 NCTM:3-5:Number and operations:Compute fluently and make reasonable estimates:Develop fluency in adding, subtracting, multiplying, and dividing whole numbers 040 Develop fluency in adding, subtracting, multiplying, and dividing whole numbers false false false false false 4 NCTM: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 results 041 Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results false false false false false 4 NCTM: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' experience 042 Develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience false false false false false 4 NCTM: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 decimals 043 Use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals false false false false false 4 NCTM: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 tools 044 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 false false false false true 4 Algebra properties and relationships between entities that are represented in symbolic form Algebra false false false true false 3 Understand_patterns,_relations,_and_functions Understand patterns, relations, and functions false false false true false 4 NCTM:3-5:Algebra:Understand patterns, relations, and functions:Describe, extend, and make generalizations about geometric and numeric patterns 045 Describe, extend, and make generalizations about geometric and numeric patterns false false false false false 4 NCTM:3-5:Algebra:Understand patterns, relations, and functions:Represent and analyze patterns and functions, using words, tables, and graphs 046 Represent and analyze patterns and functions, using words, tables, and graphs false false false false true 4 Represent_and_analyze_mathematical_situations Represent and analyze mathematical situations false false false true false 4 NCTM: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 numbers 047 Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers false false false false false 4 NCTM: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 symbol 048 Represent the idea of a variable as an unknown quantity using a letter or a symbol false false false false false 4 NCTM:3-5:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Express mathematical relationships using equations 049 Express mathematical relationships using equations false false false false true 4 Use_mathematical_models_to_represent_and_understand_quantitative_relationships Use mathematical models to represent and understand quantitative relationships false false false true false 4 NCTM: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 conclusions 04a Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions false false false false true 4 Analyze_change_in_various_contexts Analyze change in various contexts false false false true true 4 NCTM:3-5:Algebra:Analyze change in various contexts:Investigate how a change in one variable relates to a change in a second variable 04b Investigate how a change in one variable relates to a change in a second variable false false false false false 4 NCTM:3-5:Algebra:Analyze change in various contexts:Identify and describe situations with constant or varying rates of change and compare them 04c Identify and describe situations with constant or varying rates of change and compare them false false false false true 4 Geometry properties and relationships of points, lines, angles, surfaces and solids Geometry false false false true false 3 Analyze_characteristics_and_properties_of_two-_and_three-dimensional_geometric_shapes Analyze characteristics and properties of two- and three-dimensional geometric shapes false false false true false 4 NCTM: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 attributes 04d Identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes false false false false false 4 NCTM: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 pyramids 04e Classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids false false false false false 4 NCTM: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 shapes 04f Investigate, describe, and reason about the results of subdividing, combining, and transforming shapes false false false false false 4 NCTM:3-5:Geometry:Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about:Explore congruence and similarity 04g Explore congruence and similarity false false false false false 4 NCTM: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 conclusions 04h Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions false false false false true 4 Specify_locations_and_describe_spatial_relationships Specify locations and describe spatial relationships false false false true false 4 NCTM: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 vocabulary 04i Describe location and movement using common language and geometric vocabulary false false false false false 4 NCTM: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 paths 04j Make and use coordinate systems to specify locations and to describe paths false false false false false 4 NCTM: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 system 04k Find the distance between points along horizontal and vertical lines of a coordinate system false false false false true 4 Apply_transformations_and_use_symmetry_to_analyze_mathematical_situations Apply transformations and use symmetry to analyze mathematical situations false false false true false 4 NCTM:3-5:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Predict and describe the results of sliding, flipping, and turning two-dimensional shapes 04l Predict and describe the results of sliding, flipping, and turning two-dimensional shapes false false false false false 4 NCTM: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 congruent 04m Describe a motion or a series of motions that will show that two shapes are congruent false false false false false 4 NCTM: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 designs 04n Identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs false false false false true 4 Use_visualization,_spatial_reasoning,_and_geometric_modeling_to_solve_problems Use visualization, spatial reasoning, and geometric modeling to solve problems false false false true true 4 NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Build and draw geometric objects 04o Build and draw geometric objects false false false false false 4 NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Create and describe mental images of objects, patterns, and paths 04p Create and describe mental images of objects, patterns, and paths false false false false false 4 NCTM: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 object 04q Identify and build a three-dimensional object from two-dimensional representations of that object false false false false false 4 NCTM:3-5:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Identify and draw a two-dimensional representation of a three-dimensional object 04r Identify and draw a two-dimensional representation of a three-dimensional object false false false false false 4 NCTM: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 measurement 04s Use geometric models to solve problems in other areas of mathematics, such as number and measurement false false false false false 4 NCTM: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 life 04t Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life false false false false true 4 Measurement the assignment of a numerical value to an attribute of an object Measurement false false false true false 3 Understand_measurable_attributes_of_objects_and_the_units,_systems,_and_processes_of_measurement Understand measurable attributes of objects and the units, systems, and processes of measurement false false false true false 4 NCTM: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 attribute 04u Understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute false false false false false 4 NCTM: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 systems 04v Understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems false false false false false 4 NCTM: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 measurement 04w Carry out simple unit conversions, such as from centimeters to meters, within a system of measurement false false false false false 4 NCTM: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 precision 04x Understand that measurements are approximations and how differences in units affect precision false false false false false 4 NCTM: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 way 04y Explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way false false false false true 4 Apply_appropriate_techniques,_tools,_and_formulas_to_determine_measurements Apply appropriate techniques, tools, and formulas to determine measurements false false false true true 4 NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes 04z Develop strategies for estimating the perimeters, areas, and volumes of irregular shapes false false false false false 4 NCTM: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 angles 050 Select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles false false false false false 4 NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Select and use benchmarks to estimate measurements 051 Select and use benchmarks to estimate measurements false false false false false 4 NCTM: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 parallelograms 052 Develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms false false false false false 4 NCTM:3-5:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Develop strategies to determine the surface areas and volumes of rectangular solids 053 Develop strategies to determine the surface areas and volumes of rectangular solids false false false false true 4 Data_analysis_and_probability numerical or statistical information that can be used to make decisions Data analysis and probability false false false true false 3 Formulate_questions Formulate questions false false false true false 4 NCTM: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 set 054 Design investigations to address a question and consider how data-collection methods affect the nature of the data set false false false false false 4 NCTM: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 experiments 055 Collect data using observations, surveys, and experiments false false false false false 4 NCTM: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 graphs 056 Represent data using tables and graphs such as line plots, bar graphs, and line graphs false false false false false 4 NCTM: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 data 057 Recognize the differences in representing categorical and numerical data false false false false true 4 Select_and_use_appropriate_statistical_methods_to_analyze_data Select and use appropriate statistical methods to analyze data false false false true false 4 NCTM: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 distributed 058 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 false false false false false 4 NCTM: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 set 059 Use measures of center, focusing on the median, and understand what each does and does not indicate about the data set false false false false false 4 NCTM: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 data 05a Compare different representations of the same data and evaluate how well each representation shows important aspects of the data false false false false true 4 Develop_and_evaluate_inferences_and_predictions_that_are_based_on_data Develop and evaluate inferences and predictions that are based on data false false false true false 4 NCTM: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 predictions 05b Propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions false false false false true 4 Understand_and_apply_basic_concepts_of_probability Understand and apply basic concepts of probability false false false true true 4 NCTM: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 impossible 05c Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible false false false false false 4 NCTM:3-5:Data analysis and probability:Understand and apply basic concepts of probability:Predict the probability of outcomes of simple experiments and test the predictions 05d Predict the probability of outcomes of simple experiments and test the predictions false false false false false 4 NCTM: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 1 05e Understand that the measure of the likelihood of an event can be represented by a number from 0 to 1 false false false false true 4 Problem_solving methods and abilities to use mathematical reasoning to arrive at unknown solutions Problem solving false false false true false 3 NCTM:3-5:Problem solving:Build new mathematical knowledge through problem solving 05f Build new mathematical knowledge through problem solving false false false false false 3 NCTM:3-5:Problem solving:Solve problems that arise in mathematics and in other contexts 05g Solve problems that arise in mathematics and in other contexts false false false false false 3 NCTM:3-5:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems 05h Apply and adapt a variety of appropriate strategies to solve problems false false false false false 3 NCTM:3-5:Problem solving:Monitor and reflect on the process of mathematical problem solving 05i Monitor and reflect on the process of mathematical problem solving false false false false true 3 Reasoning_and_proof the ability to make a hypothesis and apply mathematical logic (inductive reasoning) to arrive at conclusions Reasoning and proof false false false true false 3 NCTM:3-5:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics 05j Recognize reasoning and proof as fundamental aspects of mathematics false false false false false 3 NCTM:3-5:Reasoning and proof:Make and investigate mathematical conjectures 05k Make and investigate mathematical conjectures false false false false false 3 NCTM:3-5:Reasoning and proof:Develop and evaluate mathematical arguments and proofs 05l Develop and evaluate mathematical arguments and proofs false false false false false 3 NCTM:3-5:Reasoning and proof:Select and use various types of reasoning and methods of proof 05m Select and use various types of reasoning and methods of proof false false false false true 3 Communication the ability to express and share mathematical concepts Communication false false false true false 3 NCTM:3-5:Communication:Organize and consolidate their mathematical thinking through communication 05n Organize and consolidate their mathematical thinking through communication false false false false false 3 NCTM:3-5:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others 05o Communicate their mathematical thinking coherently and clearly to peers, teachers, and others false false false false false 3 NCTM:3-5:Communication:Analyze and evaluate the mathematical thinking and strategies of others 05p Analyze and evaluate the mathematical thinking and strategies of others false false false false false 3 NCTM:3-5:Communication:Use the language of mathematics to express mathematical ideas precisely 05q Use the language of mathematics to express mathematical ideas precisely false false false false true 3 Connections the ability to recognize common themes across different mathematical concepts or other subjects Connections false false false true false 3 NCTM:3-5:Connections:Recognize and use connections among mathematical ideas 05r Recognize and use connections among mathematical ideas false false false false false 3 NCTM:3-5:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole 05s Understand how mathematical ideas interconnect and build on one another to produce a coherent whole false false false false false 3 NCTM:3-5:Connections:Recognize and apply mathematics in contexts outside of mathematics 05t Recognize and apply mathematics in contexts outside of mathematics false false false false true 3 Representation the ability to illustrate mathematical concepts Representation false false false true true 3 NCTM:3-5:Representation:Create and use representations to organize, record, and communicate mathematical ideas 05u Create and use representations to organize, record, and communicate mathematical ideas false false false false false 3 NCTM:3-5:Representation:Select, apply, and translate among mathematical representations to solve problems 05v Select, apply, and translate among mathematical representations to solve problems false false false false false 3 NCTM:3-5:Representation:Use representations to model and interpret physical, social, and mathematical phenomena 05w Use representations to model and interpret physical, social, and mathematical phenomena false false false false true 3 6-8 Pertains to content for 6th through 8th grades 6-8 false false false true false 2 Number_and_operations arithmetic manipulations Number and operations false false false true false 3 Understand_numbers Understand numbers false false false true false 4 NCTM: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 problems 05x Work flexibly with fractions, decimals, and percents to solve problems false false false false false 4 NCTM: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 line 05y Compare and order fractions, decimals, and percents efficiently and find their approximate locations on a number line false false false false false 4 NCTM: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 1 05z Develop meaning for percents greater than 100 and less than 1 false false false false false 4 NCTM: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 relationships 060 Understand and use ratios and proportions to represent quantitative relationships false false false false false 4 NCTM: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 notation 061 Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation false false false false false 4 NCTM: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 problems 062 Use factors, multiples, prime factorization, and relatively prime numbers to solve problems false false false false false 4 NCTM: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 them 063 Develop meaning for integers and represent and compare quantities with them false false false false true 4 Understand_meanings_of_operations Understand meanings of operations false false false true false 4 NCTM: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 integers 064 Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers false false false false false 4 NCTM: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 decimals 065 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 false false false false false 4 NCTM: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 problems 066 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 false false false false true 4 Compute_fluently_and_make_reasonable_estimates Compute fluently and make reasonable estimates false false false true true 4 NCTM: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 methods 067 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 false false false false false 4 NCTM: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 use 068 Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use false false false false false 4 NCTM: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 results 069 Develop and use strategies to estimate the results of rational-number computations and judge the reasonableness of the results false false false false false 4 NCTM: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 ratios 06a Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios false false false false true 4 Algebra properties and relationships between entities that are represented in symbolic form Algebra false false false true false 3 Understand_patterns,_relations,_and_functions Understand patterns, relations, and functions false false false true false 4 NCTM:6-8:Algebra:Understand patterns, relations, and functions:Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules 06b Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules false false false false false 4 NCTM:6-8:Algebra:Understand patterns, relations, and functions:Relate and compare different forms of representation for a relationship 06c Relate and compare different forms of representation for a relationship false false false false false 4 NCTM:6-8:Algebra:Understand patterns, relations, and functions:Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations 06d Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations false false false false true 4 Represent_and_analyze_mathematical_situations Represent and analyze mathematical situations false false false true false 4 NCTM:6-8:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Develop an initial conceptual understanding of different uses of variables 06e Develop an initial conceptual understanding of different uses of variables false false false false false 4 NCTM: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 slope 06f Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope false false false false false 4 NCTM: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 relationships 06g Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships false false false false false 4 NCTM: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 equations 06h Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations false false false false true 4 Use_mathematical_models_to_represent_and_understand_quantitative_relationships Use mathematical models to represent and understand quantitative relationships false false false true false 4 NCTM: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 equations 06i Model and solve contextualized problems using various representations, such as graphs, tables, and equations false false false false true 4 Analyze_change_in_various_contexts Analyze change in various contexts false false false true true 4 NCTM:6-8:Algebra:Analyze change in various contexts:Use graphs to analyze the nature of changes in quantities in linear relationships 06j Use graphs to analyze the nature of changes in quantities in linear relationships false false false false true 4 Geometry properties and relationships of points, lines, angles, surfaces and solids Geometry false false false true false 3 Analyze_characteristics_and_properties_of_two-_and_three-dimensional_geometric_shapes Analyze characteristics and properties of two- and three-dimensional geometric shapes false false false true false 4 NCTM: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 properties 06k Precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties false false false false false 4 NCTM: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 objects 06l Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects false false false false false 4 NCTM: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 relationship 06m Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship false false false false true 4 Specify_locations_and_describe_spatial_relationships Specify locations and describe spatial relationships false false false true false 4 NCTM: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 shapes 06n Use coordinate geometry to represent and examine the properties of geometric shapes false false false false false 4 NCTM: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 sides 06o Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides false false false false true 4 Apply_transformations_and_use_symmetry_to_analyze_mathematical_situations Apply transformations and use symmetry to analyze mathematical situations false false false true false 4 NCTM: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 scaling 06p Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling false false false false false 4 NCTM:6-8:Geometry:Apply transformations and use symmetry to analyze mathematical situations:Examine the congruence, similarity, and line or rotational symmetry of objects using transformations 06q Examine the congruence, similarity, and line or rotational symmetry of objects using transformations false false false false true 4 Use_visualization,_spatial_reasoning,_and_geometric_modeling_to_solve_problems Use visualization, spatial reasoning, and geometric modeling to solve problems false false false true true 4 NCTM: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 measures 06r Draw geometric objects with specified properties, such as side lengths or angle measures false false false false false 4 NCTM: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 volume 06s Use two-dimensional representations of three-dimensional objects to visualize and solve problems such as those involving surface area and volume false false false false false 4 NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use visual tools such as networks to represent and solve problems 06t Use visual tools such as networks to represent and solve problems false false false false false 4 NCTM:6-8:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use geometric models to represent and explain numerical and algebraic relationships 06u Use geometric models to represent and explain numerical and algebraic relationships false false false false false 4 NCTM: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 life 06v Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life false false false false true 4 Measurement the assignment of a numerical value to an attribute of an object Measurement false false false true false 3 Understand_measurable_attributes_of_objects_and_the_units,_systems,_and_processes_of_measurement Understand measurable attributes of objects and the units, systems, and processes of measurement false false false true false 4 NCTM:6-8:Measurement:Understand measurable attributes of objects and the units, systems, and processes of measurement:Understand both metric and customary systems of measurement 06w Understand both metric and customary systems of measurement false false false false false 4 NCTM: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 system 06x Understand relationships among units and convert from one unit to another within the same system false false false false false 4 NCTM: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 volume 06y Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume false false false false true 4 Apply_appropriate_techniques,_tools,_and_formulas_to_determine_measurements Apply appropriate techniques, tools, and formulas to determine measurements false false false true true 4 NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use common benchmarks to select appropriate methods for estimating measurements 06z Use common benchmarks to select appropriate methods for estimating measurements false false false false false 4 NCTM: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 precision 070 Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision false false false false false 4 NCTM: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 shapes 071 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 false false false false false 4 NCTM: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 cylinders 072 Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders false false false false false 4 NCTM:6-8:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Solve problems involving scale factors, using ratio and proportion 073 Solve problems involving scale factors, using ratio and proportion false false false false false 4 NCTM: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 density 074 Solve simple problems involving rates and derived measurements for such attributes as velocity and density false false false false true 4 Data_analysis_and_probability numerical or statistical information that can be used to make decisions Data analysis and probability false false false true false 3 Formulate_questions Formulate questions false false false true false 4 NCTM: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 population 075 Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population false false false false false 4 NCTM: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 scatterplots 076 Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots false false false false true 4 Select_and_use_appropriate_statistical_methods_to_analyze_data Select and use appropriate statistical methods to analyze data false false false true false 4 NCTM: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 range 077 Find, use, and interpret measures of center and spread, including mean and interquartile range false false false false false 4 NCTM: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 scatterplots 078 Discuss and understand the correspondence between data sets and their graphical representations, especially histograms, stem-and-leaf plots, box plots, and scatterplots false false false false true 4 Develop_and_evaluate_inferences_and_predictions_that_are_based_on_data Develop and evaluate inferences and predictions that are based on data false false false true false 4 NCTM: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 taken 079 Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken false false false false false 4 NCTM: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 fit 07a Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit false false false false false 4 NCTM: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 them 07b Use conjectures to formulate new questions and plan new studies to answer them false false false false true 4 Understand_and_apply_basic_concepts_of_probability Understand and apply basic concepts of probability false false false true true 4 NCTM:6-8:Data analysis and probability:Understand and apply basic concepts of probability:Understand and use appropriate terminology to describe complementary and mutually exclusive events 07c Understand and use appropriate terminology to describe complementary and mutually exclusive events false false false false false 4 NCTM: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 simulations 07d Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations false false false false false 4 NCTM: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 models 07e Compute probabilities for simple compound events, using such methods as organized lists, tree diagrams, and area models false false false false true 4 Problem_solving methods and abilities to use mathematical reasoning to arrive at unknown solutions Problem solving false false false true false 3 NCTM:6-8:Problem solving:Build new mathematical knowledge through problem solving 07f Build new mathematical knowledge through problem solving false false false false false 3 NCTM:6-8:Problem solving:Solve problems that arise in mathematics and in other contexts 07g Solve problems that arise in mathematics and in other contexts false false false false false 3 NCTM:6-8:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems 07h Apply and adapt a variety of appropriate strategies to solve problems false false false false false 3 NCTM:6-8:Problem solving:Monitor and reflect on the process of mathematical problem solving 07i Monitor and reflect on the process of mathematical problem solving false false false false false 3 NCTM:6-8:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics 07j Recognize reasoning and proof as fundamental aspects of mathematics false false false false true 3 Reasoning_and_proof the ability to make a hypothesis and apply mathematical logic (inductive reasoning) to arrive at conclusions Reasoning and proof false false false true false 3 NCTM:6-8:Reasoning and proof:Make and investigate mathematical conjectures 07k Make and investigate mathematical conjectures false false false false false 3 NCTM:6-8:Reasoning and proof:Develop and evaluate mathematical arguments and proofs 07l Develop and evaluate mathematical arguments and proofs false false false false false 3 NCTM:6-8:Reasoning and proof:Select and use various types of reasoning and methods of proof 07m Select and use various types of reasoning and methods of proof false false false false true 3 Communication the ability to express and share mathematical concepts Communication false false false true false 3 NCTM:6-8:Communication:Organize and consolidate their mathematical thinking through communication 07n Organize and consolidate their mathematical thinking through communication false false false false false 3 NCTM:6-8:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others 07o Communicate their mathematical thinking coherently and clearly to peers, teachers, and others false false false false false 3 NCTM:6-8:Communication:Analyze and evaluate the mathematical thinking and strategies of others 07p Analyze and evaluate the mathematical thinking and strategies of others false false false false false 3 NCTM:6-8:Communication:Use the language of mathematics to express mathematical ideas precisely 07q Use the language of mathematics to express mathematical ideas precisely false false false false true 3 Connections the ability to recognize common themes across different mathematical concepts or other subjects Connections false false false true false 3 NCTM:6-8:Connections:Recognize and use connections among mathematical ideas 07r Recognize and use connections among mathematical ideas false false false false false 3 NCTM:6-8:Connections:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole 07s Understand how mathematical ideas interconnect and build on one another to produce a coherent whole false false false false false 3 NCTM:6-8:Connections:Recognize and apply mathematics in contexts outside of mathematics 07t Recognize and apply mathematics in contexts outside of mathematics false false false false true 3 Representation the ability to illustrate mathematical concepts Representation false false false true true 3 NCTM:6-8:Representation:Create and use representations to organize, record, and communicate mathematical ideas 07u Create and use representations to organize, record, and communicate mathematical ideas false false false false false 3 NCTM:6-8:Representation:Select, apply, and translate among mathematical representations to solve problems 07v Select, apply, and translate among mathematical representations to solve problems false false false false false 3 NCTM:6-8:Representation:Use representations to model and interpret physical, social, and mathematical phenomena 07w Use representations to model and interpret physical, social, and mathematical phenomena false false false false true 3 9-12 Pertains to content for 9th through 12th grades 9-12 false false false true true 2 Number_and_operations arithmetic manipulations Number and operations false false false true false 3 Understand_numbers Understand numbers false false false true false 4 NCTM: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 them 07x Develop a deeper understanding of very large and very small numbers and of various representations of them false false false false false 4 NCTM: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 solutions 07y 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 false false false false false 4 NCTM: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 system 07z Understand vectors and matrices as systems that have some of the properties of the real-number system false false false false false 4 NCTM: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 numbers 080 Use number-theory arguments to justify relationships involving whole numbers false false false false true 4 Understand_meanings_of_operations Understand meanings of operations false false false true false 4 NCTM: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 quantities 081 Judge the effects of such operations as multiplication, division, and computing powers and roots on the magnitudes of quantities false false false false false 4 NCTM: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 matrices 082 Develop an understanding of properties of, and representations for, the addition and multiplication of vectors and matrices false false false false false 4 NCTM: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 techniques 083 Develop an understanding of permutations and combinations as counting techniques false false false false true 4 Compute_fluently_and_make_reasonable_estimates Compute fluently and make reasonable estimates false false false true true 4 NCTM: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 cases 084 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 false false false false false 4 NCTM:9-12:Number and operations:Compute fluently and make reasonable estimates:Judge the reasonableness of numerical computations and their results 085 Judge the reasonableness of numerical computations and their results false false false false true 4 Algebra properties and relationships between entities that are represented in symbolic form Algebra false false false true false 3 Understand_patterns,_relations,_and_functions Understand patterns, relations, and functions false false false true false 4 NCTM:9-12:Algebra:Understand patterns, relations, and functions:Generalize patterns using explicitly defined and recursively defined functions 086 Generalize patterns using explicitly defined and recursively defined functions false false false false false 4 NCTM:9-12:Algebra:Understand patterns, relations, and functions:Understand relations and functions and select, convert flexibly among, and use various representations for them 087 Understand relations and functions and select, convert flexibly among, and use various representations for them false false false false false 4 NCTM: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 behavior 088 Analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior false false false false false 4 NCTM: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 expressions 089 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 false false false false false 4 NCTM:9-12:Algebra:Understand patterns, relations, and functions:Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions 08a Understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions false false false false false 4 NCTM:9-12:Algebra:Understand patterns, relations, and functions:Interpret representations of functions of two variables 08b Interpret representations of functions of two variables false false false false true 4 Represent_and_analyze_mathematical_situations Represent and analyze mathematical situations false false false true false 4 NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations 08c Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations false false false false false 4 NCTM: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 cases 08d 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 false false false false false 4 NCTM:9-12:Algebra:Represent and analyze mathematical situations and structures using algebraic symbols:Use symbolic algebra to represent and explain mathematical relationships 08e Use symbolic algebra to represent and explain mathematical relationships false false false false false 4 NCTM: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 relations 08f Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations false false false false false 4 NCTM: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 technology 08g Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology false false false false true 4 Use_mathematical_models_to_represent_and_understand_quantitative_relationships Use mathematical models to represent and understand quantitative relationships false false false true false 4 NCTM: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 relationships 08h Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships false false false false false 4 NCTM: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 contexts 08i Use symbolic expressions, including iterative and recursive forms, to represent relationships arising from various contexts false false false false false 4 NCTM:9-12:Algebra:Use mathematical models to represent and understand quantitative relationships:Draw reasonable conclusions about a situation being modeled 08j Draw reasonable conclusions about a situation being modeled false false false false true 4 Analyze_change_in_various_contexts Analyze change in various contexts false false false true true 4 NCTM:9-12:Algebra:Analyze change in various contexts:Approximate and interpret rates of change from graphical and numerical data 08k Approximate and interpret rates of change from graphical and numerical data false false false false true 4 Geometry properties and relationships of points, lines, angles, surfaces and solids Geometry false false false true false 3 Analyze_characteristics_and_properties_of_two-_and_three-dimensional_geometric_shapes Analyze characteristics and properties of two- and three-dimensional geometric shapes false false false true false 4 NCTM: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 objects 08l Analyze properties and determine attributes of two- and three-dimensional objects false false false false false 4 NCTM: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 them 08m 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 false false false false false 4 NCTM: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 others 08n Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others false false false false false 4 NCTM:9-12:Geometry:Analyze characteristics:Use trigonometric relationships to determine lengths and angle measures 08o Use trigonometric relationships to determine lengths and angle measures false false false false true 4 Specify_locations_and_describe_spatial_relationships Specify locations and describe spatial relationships false false false true false 4 NCTM: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 situations 08p Use Cartesian coordinates and other coordinate systems, such as navigational, polar, or spherical systems, to analyze geometric situations false false false false false 4 NCTM: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 coordinates 08q Investigate conjectures and solve problems involving two- and three-dimensional objects represented with Cartesian coordinates false false false false true 4 Apply_transformations_and_use_symmetry_to_analyze_mathematical_situations Apply transformations and use symmetry to analyze mathematical situations false false false true false 4 NCTM: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 matrices 08r Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices false false false false false 4 NCTM: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 compositions 08s Use various representations to help understand the effects of simple transformations and their compositions false false false false true 4 Use_visualization,_spatial_reasoning,_and_geometric_modeling_to_solve_problems Use visualization, spatial reasoning, and geometric modeling to solve problems false false false true true 4 NCTM: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 tools 08t Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools false false false false false 4 NCTM: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 sections 08u Visualize three-dimensional objects and spaces from different perspectives and analyze their cross sections false false false false false 4 NCTM:9-12:Geometry:Use visualization, spatial reasoning, and geometric modeling to solve problems:Use vertex-edge graphs to model and solve problems 08v Use vertex-edge graphs to model and solve problems false false false false false 4 NCTM: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 mathematics 08w Use geometric models to gain insights into, and answer questions in, other areas of mathematics false false false false false 4 NCTM: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 architecture 08x Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture false false false false true 4 Measurement the assignment of a numerical value to an attribute of an object Measurement false false false true false 3 Understand_measurable_attributes_of_objects_and_the_units,_systems,_and_processes_of_measurement Understand measurable attributes of objects and the units, systems, and processes of measurement false false false true false 4 NCTM: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 measurement 08y Make decisions about units and scales that are appropriate for problem situations involving measurement false false false false true 4 Apply_appropriate_techniques,_tools,_and_formulas_to_determine_measurements Apply appropriate techniques, tools, and formulas to determine measurements false false false true true 4 NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Analyze precision, accuracy, and approximate error in measurement situations 08z Analyze precision, accuracy, and approximate error in measurement situations false false false false false 4 NCTM: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 cylinders 090 Understand and use formulas for the area, surface area, and volume of geometric figures, including cones, spheres, and cylinders false false false false false 4 NCTM: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 situations 091 Apply informal concepts of successive approximation, upper and lower bounds, and limit in measurement situations false false false false false 4 NCTM:9-12:Measurement:Apply appropriate techniques, tools, and formulas to determine measurements:Use unit analysis to check measurement computations 092 Use unit analysis to check measurement computations false false false false true 4 Data_analysis_and_probability numerical or statistical information that can be used to make decisions Data analysis and probability false false false true false 3 Formulate_questions Formulate questions false false false true false 4 NCTM: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 each 093 Understand the differences among various kinds of studies and which types of inferences can legitimately be drawn from each false false false false false 4 NCTM: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 experiments 094 Know the characteristics of well-designed studies, including the role of randomization in surveys and experiments false false false false false 4 NCTM: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 variable 095 Understand the meaning of measurement data and categorical data, of univariate and bivariate data, and of the term variable false false false false false 4 NCTM: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 data 096 Understand histograms, parallel box plots, and scatterplots and use them to display data false false false false false 4 NCTM: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 parameter 097 Compute basic statistics and understand the distinction between a statistic and a parameter false false false false true 4 Select_and_use_appropriate_statistical_methods_to_analyze_data Select and use appropriate statistical methods to analyze data false false false true false 4 NCTM: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 statistics 098 For univariate measurement data, be able to display the distribution, describe its shape, and select and calculate summary statistics false false false false false 4 NCTM: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 tools 099 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 false false false false false 4 NCTM: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 categorical 09a Display and discuss bivariate data where at least one variable is categorical false false false false false 4 NCTM: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 spread 09b Recognize how linear transformations of univariate data affect shape, center, and spread false false false false false 4 NCTM: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 modeled 09c Identify trends in bivariate data and find functions that model the data or transform the data so that they can be modeled false false false false true 4 Develop_and_evaluate_inferences_and_predictions_that_are_based_on_data Develop and evaluate inferences and predictions that are based on data false false false true false 4 NCTM: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 distributions 09d Use simulations to explore the variability of sample statistics from a known population and to construct sampling distributions false false false false false 4 NCTM: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 inference 09e Understand how sample statistics reflect the values of population parameters and use sampling distributions as the basis for informal inference false false false false false 4 NCTM: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 conclusions 09f 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 false false false false false 4 NCTM: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 workplace 09g Understand how basic statistical techniques are used to monitor process characteristics in the workplace false false false false true 4 Understand_and_apply_basic_concepts_of_probability Understand and apply basic concepts of probability false false false true true 4 NCTM: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 cases 09h Understand the concepts of sample space and probability distribution and construct sample spaces and distributions in simple cases false false false false false 4 NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Use simulations to construct empirical probability distributions 09i Use simulations to construct empirical probability distributions false false false false false 4 NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Compute and interpret the expected value of random variables in simple cases 09j Compute and interpret the expected value of random variables in simple cases false false false false false 4 NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Understand the concepts of conditional probability and independent events 09k Understand the concepts of conditional probability and independent events false false false false false 4 NCTM:9-12:Data analysis and probability:Understand and apply basic concepts of probability:Understand how to compute the probability of a compound event 09l Understand how to compute the probability of a compound event false false false false true 4 Problem_solving methods and abilities to use mathematical reasoning to arrive at unknown solutions Problem solving false false false true false 3 NCTM:9-12:Problem solving:Build new mathematical knowledge through problem solving 09m Build new mathematical knowledge through problem solving false false false false false 3 NCTM:9-12:Problem solving:Solve problems that arise in mathematics and in other contexts 09n Solve problems that arise in mathematics and in other contexts false false false false false 3 NCTM:9-12:Problem solving:Apply and adapt a variety of appropriate strategies to solve problems 09o Apply and adapt a variety of appropriate strategies to solve problems false false false false false 3 NCTM:9-12:Problem solving:Monitor and reflect on the process of mathematical problem solving 09p Monitor and reflect on the process of mathematical problem solving false false false false true 3 Reasoning_and_proof the ability to make a hypothesis and apply mathematical logic (inductive reasoning) to arrive at conclusions Reasoning and proof false false false true false 3 NCTM:9-12:Reasoning and proof:Recognize reasoning and proof as fundamental aspects of mathematics 09q Recognize reasoning and proof as fundamental aspects of mathematics false false false false false 3 NCTM:9-12:Reasoning and proof:Make and investigate mathematical conjectures 09r Make and investigate mathematical conjectures false false false false false 3 NCTM:9-12:Reasoning and proof:Develop and evaluate mathematical arguments and proofs 09s Develop and evaluate mathematical arguments and proofs false false false false false 3 NCTM:9-12:Reasoning and proof:Select and use various types of reasoning and methods of proof 09t Select and use various types of reasoning and methods of proof false false false false true 3 Communication the ability to express and share mathematical concepts Communication false false false true false 3 NCTM:9-12:Communication:Organize and consolidate their mathematical thinking through communication 09u Organize and consolidate their mathematical thinking through communication false false false false false 3 NCTM:9-12:Communication:Communicate their mathematical thinking coherently and clearly to peers, teachers, and others 09v Communicate their mathematical thinking coherently and clearly to peers, teachers, and others false false false false false 3 NCTM:9-12:Communication:Analyze and evaluate the mathematical thinking and strategies of others 09w Analyze and evaluate the mathematical thinking and strategies of others false false false false false 3 NCTM:9-12:Communication:Use the language of mathematics to express mathematical ideas precisely 09x Use the language of mathematics to express mathematical ideas precisely false false false false true 3 Connections the ability to recognize common themes across different mathematical concepts or other subjects Connections false false false true false 3 NCTM:9-12:Connection:Recognize and use connections among mathematical ideas 09y Recognize and use connections among mathematical ideas false false false false false 3 NCTM:9-12:Connection:Understand how mathematical ideas interconnect and build on one another to produce a coherent whole 09z Understand how mathematical ideas interconnect and build on one another to produce a coherent whole false false false false false 3 NCTM:9-12:Connection:Recognize and apply mathematics in contexts outside of mathematics 0a0 Recognize and apply mathematics in contexts outside of mathematics false false false false true 3 Representation the ability to illustrate mathematical concepts Representation false false false true true 3 NCTM:9-12:Representation:Create and use representations to organize, record, and communicate mathematical ideas 0a1 Create and use representations to organize, record, and communicate mathematical ideas false false false false false 3 NCTM:9-12:Representation:Select, apply, and translate among mathematical representations to solve problems 0a2 Select, apply, and translate among mathematical representations to solve problems false false false false false 3 NCTM:9-12:Representation:Use representations to model and interpret physical, social, and mathematical phenomena 0a3 Use representations to model and interpret physical, social, and mathematical phenomena false false false false true 3