Skip to main content
Hello,
Guest
Sign In
Home
Standards
View Standards
Vertical Viewer
Keyword Search
Browse Standards
Download PDFs
Educational Resources
Search
Content Providers
Featured Content
Vocabulary
Assessment
NYS Assessment Builder
Test Preparation
NYSED Resources
Community
My Navigator
My NYLearns
Teacher Tools
Support
User Manuals
Video Tutorials
FAQs
Assessment Updates
Subscription Information
Features
System Requirements
Blog
Browse Standards
View all PreK-12 NYS Learning Standards in a dropdown list format.
- Drill Down
- Print
- Create PDF
- Send to a Friend
- Add to My ePortfolio
- Educational Resources
- Assessments
- Common Core
Reset Browse Standards
Standard Area - ELA: English Language Arts (NYS P-12 Common Core)
Standard Area - ELA: English Language Arts (NYS P-12 Common Core)
Standard Area - LHSS: Literacy in History/Social Studies (NYS 5-12 Common Core)
Standard Area - LHSS: Literacy in History/Social Studies (NYS 5-12 Common Core)
Standard Area - LSTS: Literacy in Science and Technical Subjects (NYS 6-12 Common Core)
Standard Area - LSTS: Literacy in Science and Technical Subjects (NYS 6-12 Common Core)
Standard Area - Math: Mathematics (NYS P-12 Common Core)
Standard Area - Math: Mathematics (NYS P-12 Common Core)
Grade Band - Math.P-8: Prekindergarten - Eighth Grade
PDF
Print
Send to a Friend
Grade Band - Math.P-8: Prekindergarten - Eighth Grade
Grade Level - PK: Prekindergarten
PDF
Print
Send to a Friend
Grade Level - PK: Prekindergarten
Domain - PK.CC: Counting and Cardinality
PDF
Print
Send to a Friend
Vertical Viewer
Domain - PK.CC: Counting and Cardinality
Vertical Viewer
Domain - PK.OA: Operations and Algebraic Thinking
PDF
Print
Send to a Friend
Vertical Viewer
Domain - PK.OA: Operations and Algebraic Thinking
Vertical Viewer
Domain - PK.MD: Measurement and Data
PDF
Print
Send to a Friend
Vertical Viewer
Domain - PK.MD: Measurement and Data
Vertical Viewer
Domain - PK.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - PK.G: Geometry
Vertical Viewer
Grade Level - K: Kindergarten
PDF
Print
Send to a Friend
Grade Level - K: Kindergarten
Domain - K.CC: Counting and Cardinality
PDF
Print
Send to a Friend
Vertical Viewer
Domain - K.CC: Counting and Cardinality
Vertical Viewer
Domain - K.OA: Operations and Algebraic Thinking
PDF
Print
Send to a Friend
Vertical Viewer
Domain - K.OA: Operations and Algebraic Thinking
Vertical Viewer
Domain - K.NBT: Number and Operations in Base Ten
PDF
Print
Send to a Friend
Vertical Viewer
Domain - K.NBT: Number and Operations in Base Ten
Vertical Viewer
Domain - K.MD: Measurement and Data
PDF
Print
Send to a Friend
Vertical Viewer
Domain - K.MD: Measurement and Data
Vertical Viewer
Domain - K.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - K.G: Geometry
Vertical Viewer
Grade Level - 1: Grade 1
PDF
Print
Send to a Friend
Grade Level - 1: Grade 1
Domain - 1.OA: Operations and Algebraic Thinking
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 1.OA: Operations and Algebraic Thinking
Vertical Viewer
Domain - 1.NBT: Number and Operations in Base Ten
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 1.NBT: Number and Operations in Base Ten
Vertical Viewer
Domain - 1.MD: Measurement and Data
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 1.MD: Measurement and Data
Vertical Viewer
Domain - 1.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 1.G: Geometry
Vertical Viewer
Grade Level - 2: Grade 2
PDF
Print
Send to a Friend
Grade Level - 2: Grade 2
Domain - 2.OA: Operations and Algebraic Thinking
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 2.OA: Operations and Algebraic Thinking
Vertical Viewer
Domain - 2.NBT: Number and Operations in Base Ten
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 2.NBT: Number and Operations in Base Ten
Vertical Viewer
Domain - 2.MD: Measurement and Data
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 2.MD: Measurement and Data
Vertical Viewer
Domain - 2.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 2.G: Geometry
Vertical Viewer
Grade Level - 3: Grade 3
PDF
Print
Send to a Friend
Grade Level - 3: Grade 3
Domain - 3.OA: Operations and Algebraic Thinking
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 3.OA: Operations and Algebraic Thinking
Vertical Viewer
Domain - 3.NBT: Number and Operations in Base Ten
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 3.NBT: Number and Operations in Base Ten
Vertical Viewer
Domain - 3.NF: Number and Operations-Fractions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 3.NF: Number and Operations-Fractions
Vertical Viewer
Domain - 3.MD: Measurement and Data
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 3.MD: Measurement and Data
Vertical Viewer
Domain - 3.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 3.G: Geometry
Vertical Viewer
Grade Level - 4: Grade 4
PDF
Print
Send to a Friend
Grade Level - 4: Grade 4
Domain - 4.OA: Operations and Algebraic Thinking
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 4.OA: Operations and Algebraic Thinking
Vertical Viewer
Domain - 4.NBT: Number and Operations in Base Ten
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 4.NBT: Number and Operations in Base Ten
Vertical Viewer
Domain - 4.NF: Number and Operations-Fractions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 4.NF: Number and Operations-Fractions
Vertical Viewer
Domain - 4.MD: Measurement and Data
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 4.MD: Measurement and Data
Vertical Viewer
Domain - 4.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 4.G: Geometry
Vertical Viewer
Grade Level - 5: Grade 5
PDF
Print
Send to a Friend
Grade Level - 5: Grade 5
Domain - 5.OA: Operations and Algebraic Thinking
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 5.OA: Operations and Algebraic Thinking
Vertical Viewer
Domain - 5.NBT: Number and Operations in Base Ten
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 5.NBT: Number and Operations in Base Ten
Vertical Viewer
Domain - 5.NF: Number and Operations-Fractions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 5.NF: Number and Operations-Fractions
Vertical Viewer
Domain - 5.MD: Measurement and Data
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 5.MD: Measurement and Data
Vertical Viewer
Domain - 5.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 5.G: Geometry
Vertical Viewer
Grade Level - 6: Grade 6
PDF
Print
Send to a Friend
Grade Level - 6: Grade 6
Domain - 6.RP: Ratios and Proportional Relationships
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 6.RP: Ratios and Proportional Relationships
Vertical Viewer
Domain - 6.NS: The Number System
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 6.NS: The Number System
Vertical Viewer
Domain - 6.EE: Expressions and Equations
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 6.EE: Expressions and Equations
Vertical Viewer
Domain - 6.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 6.G: Geometry
Vertical Viewer
Domain - 6.SP: Statistics and Probability
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 6.SP: Statistics and Probability
Vertical Viewer
Grade Level - 7: Grade 7
PDF
Print
Send to a Friend
Grade Level - 7: Grade 7
Domain - 7.RP: Ratios and Proportional Relationships
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 7.RP: Ratios and Proportional Relationships
Vertical Viewer
Domain - 7.NS: The Number System
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 7.NS: The Number System
Vertical Viewer
Domain - 7.EE: Expressions and Equations
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 7.EE: Expressions and Equations
Vertical Viewer
Domain - 7.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 7.G: Geometry
Vertical Viewer
Domain - 7.SP: Statistics and Probability
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 7.SP: Statistics and Probability
Vertical Viewer
Grade Level - 8: Grade 8
PDF
Print
Send to a Friend
Grade Level - 8: Grade 8
Domain - 8.NS: The Number System
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 8.NS: The Number System
Vertical Viewer
Domain - 8.EE: Expressions and Equations
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 8.EE: Expressions and Equations
Vertical Viewer
Domain - 8.F: Functions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 8.F: Functions
Vertical Viewer
Domain - 8.G: Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 8.G: Geometry
Vertical Viewer
Domain - 8.SP: Statistics and Probability
PDF
Print
Send to a Friend
Vertical Viewer
Domain - 8.SP: Statistics and Probability
Vertical Viewer
Grade Band - Math.HS: High School
PDF
Print
Send to a Friend
Grade Band - Math.HS: High School
Conceptual Category - N: Number and Quantity
PDF
Print
Send to a Friend
Conceptual Category - N: Number and Quantity
Domain - N-RN: The Real Number System
PDF
Print
Send to a Friend
Vertical Viewer
Domain - N-RN: The Real Number System
Vertical Viewer
Domain - N-Q: Quantities
PDF
Print
Send to a Friend
Vertical Viewer
Domain - N-Q: Quantities
Vertical Viewer
Domain - N-CN: The Complex Number System
PDF
Print
Send to a Friend
Vertical Viewer
Domain - N-CN: The Complex Number System
Vertical Viewer
Domain - N-VM: Vector and Matrix Quantities
PDF
Print
Send to a Friend
Vertical Viewer
Domain - N-VM: Vector and Matrix Quantities
Vertical Viewer
Conceptual Category - A: Algebra
PDF
Print
Send to a Friend
Conceptual Category - A: Algebra
Domain - A-SSE: Seeing Structure in Expressions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - A-SSE: Seeing Structure in Expressions
Vertical Viewer
Domain - A-APR: Arithmetic with Polynomials and Rational Expressions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - A-APR: Arithmetic with Polynomials and Rational Expressions
Vertical Viewer
Domain - A-CED: Creating Equations
PDF
Print
Send to a Friend
Vertical Viewer
Domain - A-CED: Creating Equations
Vertical Viewer
Domain - A-REI: Reasoning with Equations and Inequalities
PDF
Print
Send to a Friend
Vertical Viewer
Domain - A-REI: Reasoning with Equations and Inequalities
Vertical Viewer
Conceptual Category - F: Functions
PDF
Print
Send to a Friend
Conceptual Category - F: Functions
Domain - F-IF: Interpreting Functions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - F-IF: Interpreting Functions
Vertical Viewer
Domain - F-BF: Building Functions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - F-BF: Building Functions
Vertical Viewer
Domain - F-LE: Linear, Quadratic, and Exponential Models
PDF
Print
Send to a Friend
Vertical Viewer
Domain - F-LE: Linear, Quadratic, and Exponential Models
Vertical Viewer
Domain - F-TF: Trigonometric Functions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - F-TF: Trigonometric Functions
Assessments
Vertical Viewer
Conceptual Category - M: Modeling
PDF
Print
Send to a Friend
Conceptual Category - M: Modeling
Standard - M.1:
Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards.
PDF
Print
Send to a Friend
Educational Resources
Standard - M.1:
Modeling Standards: Modeling is best interpreted not as a collection of isolated topics but rather in relation to other standards.
Educational Resources
Conceptual Category - G: Geometry
PDF
Print
Send to a Friend
Conceptual Category - G: Geometry
Domain - G-CO: Congruence
PDF
Print
Send to a Friend
Vertical Viewer
Domain - G-CO: Congruence
Assessments
Vertical Viewer
Domain - G-SRT: Similarity, Right Triangles, and Trigonometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - G-SRT: Similarity, Right Triangles, and Trigonometry
Assessments
Vertical Viewer
Domain - G-C: Circles
PDF
Print
Send to a Friend
Vertical Viewer
Domain - G-C: Circles
Assessments
Vertical Viewer
Domain - G-GPE: Expressing Geometric Properties with Equations
PDF
Print
Send to a Friend
Vertical Viewer
Domain - G-GPE: Expressing Geometric Properties with Equations
Assessments
Vertical Viewer
Domain - G-GMD: Geometric Measurement and Dimension
PDF
Print
Send to a Friend
Vertical Viewer
Domain - G-GMD: Geometric Measurement and Dimension
Assessments
Vertical Viewer
Domain - G-MG: Modeling with Geometry
PDF
Print
Send to a Friend
Vertical Viewer
Domain - G-MG: Modeling with Geometry
Assessments
Vertical Viewer
Conceptual Category - S: Statistics and Probability
PDF
Print
Send to a Friend
Conceptual Category - S: Statistics and Probability
Domain - S-ID: Interpreting Categorical and Quantitative Data
PDF
Print
Send to a Friend
Vertical Viewer
Domain - S-ID: Interpreting Categorical and Quantitative Data
Vertical Viewer
Domain - S-IC: Making Inferences and Justifying Conclusions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - S-IC: Making Inferences and Justifying Conclusions
Vertical Viewer
Domain - S-CP: Conditional Probability and the Rules of Probability
PDF
Print
Send to a Friend
Vertical Viewer
Domain - S-CP: Conditional Probability and the Rules of Probability
Vertical Viewer
Domain - S-MD: Using Probability to Make Decisions
PDF
Print
Send to a Friend
Vertical Viewer
Domain - S-MD: Using Probability to Make Decisions
Vertical Viewer
Mathematical Practice Standards - Math.MP:
Standards for Mathematical Practice
PDF
Print
Send to a Friend
Mathematical Practice Standards - Math.MP:
Standards for Mathematical Practice
Mathematical Practice - Math.MP.1:
Make sense of problems and persevere in solving them.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice - Math.MP.1:
Make sense of problems and persevere in solving them.
Educational Resources
Mathematical Practice Detail - Math.MP.1.1:
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice Detail - Math.MP.1.1:
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
Educational Resources
Mathematical Practice - Math.MP.2:
Reason abstractly and quantitatively.
PDF
Print
Send to a Friend
Mathematical Practice - Math.MP.2:
Reason abstractly and quantitatively.
Mathematical Practice Detail - Math.MP.2.1:
Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice Detail - Math.MP.2.1:
Mathematically proficient students make sense of the quantities and their relationships in problem situations. Students bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Educational Resources
Mathematical Practice - Math.MP.3:
Construct viable arguments and critique the reasoning of others.
PDF
Print
Send to a Friend
Mathematical Practice - Math.MP.3:
Construct viable arguments and critique the reasoning of others.
Mathematical Practice Detail - Math.MP.3.1:
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice Detail - Math.MP.3.1:
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
Educational Resources
Mathematical Practice - Math.MP.4:
Model with mathematics.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice - Math.MP.4:
Model with mathematics.
Educational Resources
Mathematical Practice Detail - Math.MP.4.1:
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice Detail - Math.MP.4.1:
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
Educational Resources
Mathematical Practice - Math.MP.5:
Use appropriate tools strategically.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice - Math.MP.5:
Use appropriate tools strategically.
Educational Resources
Mathematical Practice Detail - Math.MP.5.1:
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice Detail - Math.MP.5.1:
Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
Educational Resources
Mathematical Practice - Math.MP.6:
Attend to precision.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice - Math.MP.6:
Attend to precision.
Educational Resources
Mathematical Practice Detail - Math.MP.6.1:
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice Detail - Math.MP.6.1:
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
Educational Resources
Mathematical Practice - Math.MP.7:
Look for and make use of structure.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice - Math.MP.7:
Look for and make use of structure.
Educational Resources
Mathematical Practice Detail - Math.MP.7.1:
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
PDF
Print
Send to a Friend
Educational Resources
Mathematical Practice Detail - Math.MP.7.1:
Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
Educational Resources
Mathematical Practice - Math.MP.8:
Look for and express regularity in repeated reasoning.
PDF
Print
Send to a Friend
Mathematical Practice - Math.MP.8:
Look for and express regularity in repeated reasoning.
Mathematical Practice Detail - Math.MP.8.1:
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
PDF
Print
Send to a Friend
Mathematical Practice Detail - Math.MP.8.1:
Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Standard Area - S: Science (NYS P-12)
Standard Area - S: Science (NYS P-12)
Standard Area - SS: Social Studies (NYS K-12 Framework Common Core)
Standard Area - SS: Social Studies (NYS K-12 Framework Common Core)
Standard Area - ARTS: NYS Learning Standards for the Arts (2017)
Standard Area - ARTS: NYS Learning Standards for the Arts (2017)
Standard Area - ARTS: The Arts (1996)
Standard Area - ARTS: The Arts (1996)
Standard Area - CDOS: Career Development and Occupational Studies
Standard Area - CDOS: Career Development and Occupational Studies
Educational Resources
Standard Area - ELA: English Language Arts (2005)
Standard Area - ELA: English Language Arts (2005)
Standard Area - ESL: English as a Second Language
Standard Area - ESL: English as a Second Language
Standard Area - NLA: Native Language Arts
Standard Area - NLA: Native Language Arts
Standard Area - HPF: Health, Physical Education, and Family and Consumer Sciences
Standard Area - HPF: Health, Physical Education, and Family and Consumer Sciences
Standard Area - LOTE: Languages Other Than English
Standard Area - LOTE: Languages Other Than English
Standard Area - MST: Math, Science & Technology
Standard Area - MST: Math, Science & Technology
Standard Area - SS: Social Studies
Standard Area - SS: Social Studies
Educational Resources
Data is Loading...