New York State Standards for Mathematics: Grade 2

NY.3. Mathematics, Science, and Technology: Students will understand the concepts of and become proficient with the skills of mathematics, communicate and reason mathematically; become problem solvers by using appropriate tools and strategies, through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability.

3.1. Problem Solving Strand: Students will build new mathematical knowledge through problem solving.

2.PS.1. Explore, examine, and make observations about a social problem or mathematical situation.

2.PS.2. Interpret information correctly, identify the problem, and generate possible solutions.

3.2. Problem Solving Strand: Students will solve problems that arise in mathematics and in other contexts.

2.PS.3. Act out or model with manipulatives activities involving mathematical content from literature and/or story telling.

2.PS.4. Formulate problems and solutions from everyday situations (e.g., counting the number of children in the class, using the calendar to teach counting).

3.3. Problem Solving Strand: Students will apply and adapt a variety of appropriate strategies to solve problems.

2.PS.5. Use informal counting strategies to find solutions.

2.PS.6. Experience teacher-directed questioning process to understand problems.

2.PS.7. Compare and discuss ideas for solving a problem with teacher and/or students to justify their thinking.

2.PS.8. Use manipulatives (e.g., tiles, blocks) to model the action in problems.

2.PS.9. Use drawings/pictures to model the action in problems.

3.4. Problem Solving Strand: Students will monitor and reflect on the process of mathematical problem solving.

2.PS.10. Explain to others how a problem was solved, giving strategies and justifications.

3.5. Reasoning and Proof Strand: Students will recognize reasoning and proof as fundamental aspects of mathematics.

2.RP.1. Understand that mathematical statements can be true or false.

2.RP.2. Recognize that mathematical ideas need to be supported by evidence.

3.6. Reasoning and Proof Strand: Students will make and investigate mathematical conjectures.

2.RP.3. Investigate the use of knowledgeable guessing as a mathematical tool.

2.RP.4. Explore guesses, using a variety of objects and manipulatives.

3.7. Reasoning and Proof Strand: Students will develop and evaluate mathematical arguments and proofs.

2.RP.5. Justify general claims, using manipulatives.

2.RP.6. Develop and explain an argument verbally or with objects.

2.RP.7. Listen to and discuss claims other students make.

3.8. Reasoning and Proof Strand: Students will select and use various types of reasoning and methods of proof.

2.RP.8. Use trial and error strategies to verify claims.

3.9. Communication Strand: Students will organize and consolidate their mathematical thinking through communication.

2.CM.1. Understand how to organize their thought processes.

2.CM.2. Verbally support their reasoning and answer.

3.10. Communication Strand: Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

2.CM.3. Share mathematical ideas through the manipulation of objects, drawings, pictures, charts, and symbols in both written and verbal explanations.

3.11. Communication Strand: Students will analyze and evaluate the mathematical thinking and strategies of others.

2.CM.4. Listen to solutions shared by other students.

2.CM.5. Formulate mathematically relevant questions.

3.12. Communication Strand: Students will use the language of mathematics to express mathematical ideas precisely.

2.CM.6. Use appropriate mathematical terms, vocabulary, and language.

3.13. Connections Strand: Students will recognize and use connections among mathematical ideas.

2.CN.1. Recognize the connections of patterns in their everyday experiences to mathematical ideas.

2.CN.2. Understand and use the connections between numbers and the quantities they represent to solve problems.

2.CN.3. Compare the similarities and differences of mathematical ideas.

3.14. Connections Strand: Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

2.CN.4. Understand how models of situations involving objects, pictures, and symbols relate to mathematical ideas.

2.CN.5. Understand meanings of operations and how they relate to one another.

2.CN.6. Understand how mathematical models represent quantitative relationships.

3.15. Connections Strand: Students will recognize and apply mathematics in contexts outside of mathematics.

2.CN.7. Recognize the presence of mathematics in their daily lives.

2.CN.8. Recognize and apply mathematics to solve problems.

2.CN.9. Recognize and apply mathematics to objects, pictures and symbols.

3.16. Representation Strand: Students will create and use representations to organize, record, and communicate mathematical ideas.

2.R.1. Use multiple representations, including verbal and written language, acting out or modeling a situation, drawings, and/or symbols as representations.

2.R.2. Share mental images of mathematical ideas and understandings.

2.R.3. Use standard and nonstandard representations.

3.17. Representation Strand: Students will select, apply, and translate among mathematical representations to solve problems.

2.R.4. Connect mathematical representations with problem solving.

3.18. Representation Strand: Students will use representations to model and interpret physical, social, and mathematical phenomena.

2.R.5. Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree).

2.R.6. Use mathematics to show and understand social phenomena (e.g., count and represent sharing cookies between friends).

2.R.7. Use mathematics to show and understand mathematical phenomena (e.g., draw pictures to show a story problem or show number value using fingers on your hand).

3.19. Number Sense and Operations Strand: Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems.

2.N.1. Number Systems Skip count to 100 by 2's, 5's, 10's.

2.N.2. Number Systems Count back from 100 by 1's, 5's, 10's using a number chart.

2.N.3. Number Systems Skip count by 3's to 36 for multiplication readiness.

2.N.4. Number Systems Skip count by 4's to 48 for multiplication readiness.

2.N.5. Number Systems Compare and order numbers to 100.

2.N.6. Number Systems Develop an understanding of the base ten system: 10 ones = 1 ten; 10 tens = 1 hundred; 10 hundreds = 1 thousand.

2.N.7. Number Systems Use a variety of strategies to compose and decompose two-digit numbers.

2.N.8. Number Systems Understand and use the commutative property of addition.

2.N.9. Number Systems Name the number before and the number after a given number, and name the number(s) between two given numbers up to 100 (with and without the use of a number line or a hundreds chart).

2.N.10. Number Systems Use and understand verbal ordinal terms.

2.N.11. Number Systems Read written ordinal terms (first through ninth) and use them to represent ordinal relations.

2.N.12. Number Systems Use zero as the identity element for addition.

2.N.13. Number Systems Recognize the meaning of zero in the place value system (0-100).

2.N.14. Number Theory: Use concrete materials to justify a number as odd or even.

3.20. Number Sense and Operations Strand: Students will understand meanings of operations and procedures, and how they relate to one another.

2.N.15. Operations: Determine sums and differences of number sentences by various means (e.g., families, related facts, inverse operations, addition doubles, and doubles plus one).

2.N.16. Operations: Use a variety of strategies to solve addition and subtraction problems using one- and two-digit numbers with and without regrouping.

2.N.17. Operations: Demonstrate fluency and apply addition and subtraction facts up to and including 18.

2.N.18. Operations: Use doubling to add 2-digit numbers.

2.N.19. Operations: Use compensation to add 2-digit numbers.

2.N.20. Operations: Develop readiness for multiplication by using repeated addition.

2.N.21. Operations: Develop readiness for division by using repeated subtraction, dividing objects into groups (fair share).

3.21. Number Sense and Operations Strand: Students will compute accurately and make reasonable estimates.

2.N.22. Estimation: Estimate the number in a collection to 100 and then compare by counting the actual items in the collection.

3.22. Algebra Strand: Students will perform algebraic procedures accurately.

2.A.1. Equations and Inequalities: Use the symbols <, >, = (with and without the use of a number line) to compare whole numbers up to 100.

3.23. Algebra Strand: Students will recognize, use, and represent algebraically patterns, relations, and functions.

2.A.2. Patterns, Relations, and Functions: Describe and extend increasing or decreasing (+,-) sequences and patterns (numbers or objects up to 100).

3.24. Geometry Strand: Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.

2.G.1. Shapes: Experiment with slides, flips, and turns to compare two dimensional shapes.

2.G.2. Shapes: Identify and appropriately name two-dimensional shapes: circle, square, rectangle, and triangle (both regular and irregular).

2.G.3. Shapes: Compose (put together) and decompose (break apart) two-dimensional shapes.

3.25. Geometry Strand: Students will identify and justify geometric relationships, formally and informally.

2.G.4. Geometric Relationships: Group objects by like properties.

3.26. Geometry Strand: Students will apply transformations and symmetry to analyze problem solving situations.

2.G.5. Transformational Geometry: Explore and predict the outcome of slides, flips, and turns of two-dimensional shapes.

2.G.6. Transformational Geometry: Explore line symmetry.

3.27. Measurement Strand: Students will determine what can be measured and how, using appropriate methods and formulas.

2.M.1. Units of Measurement: Use non-standard and standard units to measure both vertical and horizontal lengths.

2.M.2. Units of Measurement: Use a ruler to measure standard units (including whole inches and whole feet).

2.M.3. Units of Measurement: Compare and order objects according to the attribute of length.

2.M.4. Units of Measurement: Recognize mass as a qualitative measure (e.g., Which is heavier? Which is lighter?).

2.M.5. Units of Measurement: Compare and order objects, using lighter than and heavier than.

3.28. Measurement Strand: Students will use units to give meaning to measurements.

2.M.6. Units: Know and recognize coins (penny, nickel, dime, quarter) and bills ($1, $5, $10, and $20).

2.M.7. Units: Recognize the whole dollar notation as $1, etc.

2.M.8. Units: Identify equivalent combinations to make one dollar.

2.M.9. Units: Tell time to the half hour and five minutes using both digital and analog clocks.

3.29. Measurement Strand: Students will develop strategies for estimating measurements.

2.M.10. Estimation: Select and use standard (customary) and non-standard units to estimate measurements.

3.30. Statistics and Probability Strand: Students will collect, organize, display, and analyze data.

2.S.1. Collection of Data: Formulate questions about themselves and their surroundings.

2.S.2. Collection of Data: Collect and record data (using tallies) related to the question.

2.S.3. Organization and Display of Data: Display data in pictographs and bar graphs using concrete objects or a representation of the object.

2.S.4. Analysis of Data Compare and interpret data in terms of describing quantity (similarity or differences).

3.31. Statistics and Probability Strand: Students will make predictions that are based upon data analysis.

2.S.5. Predictions from Data: Discuss conclusions and make predictions from graphs.