New York State Standards for Mathematics: Grade 1

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.

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

1.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.

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

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

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

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

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

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

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

1.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.

1.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.

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

1.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.

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

1.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.

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

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

1.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.

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

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

1.CM.1. Understand how to organize their thought processes with teacher guidance.

1.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.

1.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.

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

1.CM.5. Formulate mathematically relevant questions.

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

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

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

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

1.CN.2. Understand the connections between numbers and the quantities they represent.

1.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.

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

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

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

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

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

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

1.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.

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

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

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

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

1.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.

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

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

1.R.7. Use mathematics to show and understand mathematical phenomena (e.g., draw pictures to show a story problem, 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.

1.N.1. Number Systems: Count the items in a collection and know the last counting word tells how many items are in the collection (1 to 100).

1.N.2. Number Systems: Count out (produce) a collection of a specified size (10 to 100 items), using groups of ten.

1.N.3. Number Systems: Quickly see and label with a number, collections of 1 to 10.

1.N.4. Number Systems: Count by 1's to 100.

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

1.N.6. Number Systems: Skip count by 5's to 50.

1.N.7. Number Systems: Skip count by 2's to 20.

1.N.8. Number Systems: Verbally count from a number other than one by 1's.

1.N.9. Number Systems: Count backwards from 20 by 1's.

1.N.10. Number Systems: Draw pictures or other informal symbols to represent a spoken number up to 20.

1.N.11. Number Systems: Identify that spacing of the same number of objects does not affect the quantity (conservation).

1.N.12. Number Systems: Arrange objects in size order (increasing and decreasing).

1.N.13. Number Systems: Write numbers to 100.

1.N.14. Number Systems: Read the number words one, two, three...ten.

1.N.15. Number Systems: Explore and use place value.

1.N.16. Number Systems: Compare and order whole numbers up to 100.

1.N.17. Number Systems: Develop an initial understanding of the base ten system: 10 ones = 1 ten; 10 tens = 1 hundred.

1.N.18. Number Systems: Use a variety of strategies to compose and decompose one-digit numbers.

1.N.19. Number Systems: Understand the commutative property of addition.

1.N.20. 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).

1.N.21. Number Systems: Use before, after, or between to order numbers to 100 (with or without the use of a number line).

1.N.22. Number Systems: Use the words higher, lower, greater, and less to compare two numbers.

1.N.23. Number Systems: Use and understand verbal ordinal terms, first to twentieth.

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

1.N.24. Operations: Develop and use strategies to solve addition and subtraction word problems.

1.N.25. Operations: Represent addition and subtraction word problems and their solutions as number sentences.

1.N.26. Operations: Create problem situations that represent a given number sentence.

1.N.27. Operations: Use a variety of strategies to solve addition and subtraction problems with one- and two-digit numbers without regrouping.

1.N.28. Operations: Demonstrate fluency and apply addition and subtraction facts to and including 10.

1.N.29. Operations: Understand that different parts can be added to get the same whole.

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

1.N.30. Estimation: Estimate the number in a collection to 50 and then compare by counting the actual items in the collection.

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

1.A.1. Patterns, Relations, and Functions: Determine and discuss patterns in arithmetic (what comes next in a repeating pattern, using numbers or objects).

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

1.G.1. Shapes: Match shapes and parts of shapes to justify congruency.

1.G.2. Shapes: Recognize, name, describe, create, sort, and compare two-dimensional and three-dimensional shapes.

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

1.G.3. Transformational Geometry: Experiment with slides, flips, and turns of two-dimensional shapes.

1.G.4. Transformational Geometry: Identify symmetry in two-dimensional shapes.

3.25. Geometry Strand: Students will apply coordinate geometry to analyze problem solving situations.

1.G.5. Coordinate Geometry: Recognize geometric shapes and structures in the environment.

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

1.M.1. Units of Measurement: Recognize length as an attribute that can be measured.

1.M.2. Units of Measurement: Use non-standard units (including finger lengths, paper clips, students' feet and paces) to measure both vertical and horizontal lengths.

1.M.3. Units of Measurement: Informally explore the standard unit of measure, inch.

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

1.M.4. Units: Know vocabulary and recognize coins (penny, nickel, dime, quarter).

1.M.5. Units: Recognize the cent notation as cents.

1.M.6. Units: Use different combinations of coins to make money amounts up to 25 cents.

1.M.7. Units: Recognize specific times (morning, noon, afternoon, evening).

1.M.8. Units: Tell time to the hour, using both digital and analog clocks.

1.M.9. Units: Know the days of the week and months of the year in sequence.

1.M.10. Units: Classify months and connect to seasons and other events.

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

1.M.11. Estimation: Select and use non-standard units to estimate measurements.

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

1.S.1. Collection of Data: Pose questions about themselves and their surrounding.

1.S.2. Collection of Data: Collect and record data related to a question.

1.S.3. Organization and Display of Data: Display data in simple pictographs for quantities up to 20 with units of one.

1.S.4. Organization and Display of Data: Display data in bar graphs using concrete objects with intervals of one.

1.S.5. Organization and Display of Data: Use Venn diagrams to sort and describe data.

1.S.6. Analysis of Data: Interpret data in terms of the words: most, least, greater than, less than, or equal to.

1.S.7. Analysis of Data: Interpret Answer simple questions related to data displayed in pictographs (e.g., category with most, how many more in a category compared to another, how many all together in two categories).

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

1.S.8. Predictions from Data: Discuss conclusions and make predictions in terms of the words likely and unlikely.

1.S.9. Predictions from Data: Construct a question that can be answered by using information from a graph.