New York State Standards for Mathematics: Grade 3

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.

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

3.PS.2. Understand that some ways of representing a problem are more helpful than others.

3.PS.3. 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.

3.PS.4. Act out or model with manipulatives activities involving mathematical content from literature.

3.PS.5. Formulate problems and solutions from everyday situations.

3.PS.6. Translate from a picture/diagram to a numeric expression.

3.PS.7. Represent problem situations in oral, written, concrete, pictorial, and graphical forms.

3.PS.8. Select an appropriate representation of a problem.

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

3.PS.9. Use trial and error to solve problems.

3.PS.10. Use process of elimination to solve problems.

3.PS.11. Make pictures/diagrams of problems.

3.PS.12. Use physical objects to model problems.

3.PS.13. Work in collaboration with others to solve problems.

3.PS.14. Make organized lists to solve numerical problems.

3.PS.15. Make charts to solve numerical problems.

3.PS.16. Analyze problems by identifying relationships.

3.PS.17. Analyze problems by identifying relevant versus irrelevant information.

3.PS.18. Analyze problems by observing patterns.

3.PS.19. The student will state a problem in their own words.

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

3.PS.20. Determine what information is needed to solve a problem.

3.PS.21. Discuss with peers to understand a problem situation.

3.PS.22. Discuss the efficiency of different representations of a problem.

3.PS.23. Verify results of a problem.

3.PS.24. Recognize invalid approaches.

3.PS.25. Determine whether a solution is reasonable in the context of the original problem.

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

3.RP.1. Use representations to support mathematical ideas.

3.RP.2. Determine whether a mathematical statement is true or false and explain why.

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

3.RP.3. Investigate the use of knowledgeable guessing by generalizing mathematical ideas.

3.RP.4. Make conjectures from a variety of representations.

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

3.RP.5. Justify general claims or conjectures, using manipulatives, models, and expressions.

3.RP.6. Develop and explain an argument using oral, written, concrete, pictorial, and/or graphical forms.

3.RP.7. Discuss, listen, and make comments that support or reject claims made by other students.

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

3.RP.8. Support an argument by trying many cases.

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

3.CM.1. Understand and explain how to organize their thought process.

3.CM.2. Verbally explain their rationale for strategy selection.

3.CM.3. Provide reasoning both in written and verbal form.

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

3.CM.4. Organize and accurately label work.

3.CM.5. Share organized mathematical ideas through the manipulation of objects, drawings, pictures, charts, graphs, tables, diagrams, models, symbols, and expressions in written and verbal form.

3.CM.6. Answer clarifying questions from others.

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

3.CM.7. Listen for understanding of mathematical solutions shared by other students.

3.CM.8. Consider strategies used and solutions found in relation to their own work.

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

3.CM.9. Increase their use of mathematical vocabulary and language when communicating with others.

3.CM.10. Describe objects, relationships, solutions and rationale using appropriate vocabulary.

3.CM.11. Decode and comprehend mathematical visuals and symbols to construct meaning.

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

3.CN.1. Recognize, understand, and make connections in their everyday experiences to mathematical ideas.

3.CN.2. Compare and contrast mathematical ideas.

3.CN.3. Connect and apply mathematical information to solve problems.

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

3.CN.4. Understand multiple representations and how they are related.

3.CN.5. Model situations with objects and representations and be able to make observations.

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

3.CN.6. Recognize the presence of mathematics in their daily lives.

3.CN.7. Apply mathematics to solve problems that develop outside of mathematics.

3.CN.8. Recognize and apply mathematics to other disciplines.

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

3.R.1. Use verbal and written language, physical models, drawing charts, graphs, tables, symbols, and equations as representations.

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

3.R.3. Recognize and use external mathematical representations.

3.R.4. Use standard and nonstandard representations with accuracy and detail.

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

3.R.5. Understand similarities and differences in representations.

3.R.6. Connect mathematical representations with problem solving.

3.R.7. Construct effective representations to solve problems.

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

3.R.8. Use mathematics to show and understand physical phenomena (e.g., estimate and represent the number of apples in a tree).

3.R.9. Use mathematics to show and understand social phenomena (e.g., determine the number of buses required for a field trip).

3.R.10. Use mathematics to show and understand mathematical phenomena (e.g., use a multiplication grid to solve odd and even number problems).

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

3.N.1. Number Systems: Skip count by 25's, 50's, 100's to 1,000.

3.N.2. Number Systems: Read and write whole numbers to 1,000.

3.N.3. Number Systems: Compare and order numbers to 1,000.

3.N.4. Number Systems: Understand the place value structure of the base ten number system: 10 ones = 1 ten; 10 tens = 1 hundred; 10 hundreds = 1 thousand.

3.N.5. Number Systems: Use a variety of strategies to compose and decompose three-digit numbers.

3.N.6. Number Systems: Use and explain the commutative property of addition and multiplication.

3.N.7. Number Systems: Use 1 as the identity element for multiplication.

3.N.8. Number Systems: Use the zero property of multiplication.

3.N.9. Number Systems: Understand and use the associative property of addition.

3.N.10. Number Systems: Develop an understanding of fractions as part of a whole unit and as parts of a collection.

3.N.11. Number Systems: Use manipulatives, visual models, and illustrations to name and represent unit fractions or a set of objects.

3.N.12. Number Systems: Understand and recognize the meaning of numerator and denominator in the symbolic form of a fraction.

3.N.13. Number Systems: Recognize fractional numbers as equal parts of a whole.

3.N.14. Number Systems: Explore equivalent fractions (1/2, 1/3, 1/4).

3.N.15. Number Systems: Compare and order unit fractions (1/2, 1/3, 1/4) and find their approximate locations on a number line.

3.N.16. Number Theory: Identify odd and even numbers.

3.N.17. Number Theory: Develop an understanding of the properties of odd/even numbers as a result of addition or subtraction.

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

3.N.18. Operations: Use a variety of strategies to add and subtract 3-digit numbers (with and without regrouping).

3.N.19. Operations: Develop fluency with single-digit multiplication facts.

3.N.20. Operations: Use a variety of strategies to solve multiplication problems with factors up to 12 x 12.

3.N.21. Operations: Use the area model, tables, patterns, arrays, and doubling to provide meaning for multiplication.

3.N.22. Operations: Demonstrate fluency and apply single-digit division facts.

3.N.23. Operations: Use tables, patterns, halving, and manipulatives to provide meaning for division.

3.N.24. Operations: Develop strategies for selecting the appropriate computational and operational method in problem solving situations.

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

3.N.25. Estimation: Estimate numbers up to 500.

3.N.26. Estimation: Recognize real world situations in which an estimate (rounding) is more appropriate.

3.N.27. Estimation: Check reasonableness of an answer by using estimation.

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

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

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

3.A.2. Patterns, Relations, and Functions: Describe and extend numeric (+, -) and geometric patterns.

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

3.G.1. Shapes Define and use correct terminology when referring to shapes (circle, triangle, square, rectangle, rhombus, trapezoid, and hexagon).

3.G.2. Shapes Identify congruent and similar figures.

3.G.3. Shapes Name, describe, compare, and sort three-dimensional shapes: cube, cylinder, sphere, prism, and cone.

3.G.4. Shapes Identify the faces on a three-dimensional shape as two-dimensional shapes.

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

3.G.5. Transformational Geometry: Identify and construct lines of symmetry.

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

3.M.1. Units of Measurement: Select tools and units (customary) appropriate for the length measured.

3.M.2. Units of Measurement: Use a ruler/yardstick to measure to the nearest standard unit (whole and 1/2 inches, whole feet, and whole yards).

3.M.3. Units of Measurement: Measure objects, using ounces and pounds.

3.M.4. Units of Measurement: Recognize capacity as an attribute that can be measured.

3.M.5. Units of Measurement: Compare capacities (e.g., Which contains more? Which contains less?).

3.M.6. Units of Measurement: Measure capacity, using cups, pints, quarts, and gallons.

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

3.M.7. Units: Count and represent combined coins and dollars, using currency symbols ($0.00).

3.M.8. Units: Relate unit fractions to the face of the clock: Whole = 60 minutes; 1/2 = 30 minutes; 1/4 = 15 minutes.

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

3.M.9. Estimation: Tell time to the minute, using digital and analog clocks.

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

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

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

3.S.2. Collection of Data: Collect data using observation and surveys, and record appropriately.

3.S.3. Organization and Display of Data: Construct a frequency table to represent a collection of data.

3.S.4. Organization and Display of Data: Identify the parts of pictographs and bar graphs.

3.S.5. Organization and Display of Data: Display data in pictographs and bar graphs.

3.S.6. Organization and Display of Data: State the relationships between pictographs and bar graphs.

3.S.7. Analysis of Data: Read and interpret data in bar graphs and pictographs.

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

3.S.8. Predictions from Data: Formulate conclusions and make predictions from graphs.