Ohio State Standards for Mathematics: Grade 3

OH.NNSO. Number, Number Sense and Operations: Students demonstrate number sense, including an understanding of number systems and operations and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods.

NNSO.A. Use place value structure of the base-ten number system to read, write, represent and compare whole numbers and decimals.

NNSO.B. Recognize and generate equivalent representations for whole numbers, fractions and decimals.

NNSO.C. Represent commonly used fractions and mixed numbers using words and physical models.

NNSO.D. Use models, points of reference and equivalent forms of commonly used fractions to judge the size of fractions and to compare, describe and order them.

NNSO.E. Recognize and classify numbers as prime or composite and list factors.

NNSO.F. Count money and make change using both coins and paper bills.

NNSO.G. Model and use commutative and associative properties for addition and multiplication.

NNSO.H. Use relationships between operations, such as subtraction as the inverse of addition and division as the inverse of multiplication.

NNSO.I. Demonstrate fluency in multiplication facts with factors through 10 and corresponding divisions.

NNSO.J. Estimate the results of whole number computations using a variety of strategies, and judge the reasonableness.

NNSO.K. Analyze and solve multi-step problems involving addition, subtraction, multiplication and division of whole numbers.

NNSO.L. Use a variety of methods and appropriate tools (mental math, paper and pencil, calculators) for computing with whole numbers.

NNSO.M. Add and subtract commonly used fractions with like denominators and decimals, using models and paper and pencil.

NNSO.1. Grade Level Indicator: Number and Number Systems: Identify and generate equivalent forms of whole numbers; e.g., 36, 30 + 6, 9 x 4, 46 - 10, number of inches in a yard.

NNSO.2. Grade Level Indicator: Number and Number Systems: Use place value concepts to represent whole numbers and decimals using numerals, words, expanded notation and physical models.

NNSO.3. Grade Level Indicator: Number and Number Systems: Use mathematical language and symbols to compare and order; e.g., less than, greater than, at most, at least.

NNSO.4. Grade Level Indicator: Number and Number Systems: Count money and make change using coins and paper bills to ten dollars.

NNSO.5. Grade Level Indicator: Number and Number Systems: Represent fractions and mixed numbers using words, numerals and physical models.

NNSO.6. Grade Level Indicator: Number and Number Systems: Compare and order commonly used fractions and mixed numbers using number lines, models (such as fraction circles or bars), points of reference (such as more or less than 1/2), and equivalent forms found using physical or visual models.

NNSO.7. Grade Level Indicator: Number and Number Systems: Recognize and use decimal and fraction concepts and notations as related ways of representing parts of a whole or a set; e.g., 3 of 10 marbles are red can also be described as 3/10 and 3 tenths are red.

NNSO.8. Grade Level Indicator: Meaning of Operations: Model, represent and explain multiplication; e.g., repeated addition, skip counting, rectangular arrays and area model.

NNSO.9. Grade Level Indicator: Meaning of Operations: Model, represent and explain division; e.g., sharing equally, repeated subtraction, rectangular arrays and area model.

NNSO.10. Grade Level Indicator: Meaning of Operations: Explain and use relationships between operations, such as: relate addition and subtraction as inverse operations; relate multiplication and division as inverse operations; relate addition to multiplication (repeated addition); relate subtraction to division (repeated subtraction).

NNSO.11. Grade Level Indicator: Meaning of Operations: Model and use the commutative and associative properties for addition and multiplication.

NNSO.12. Grade Level Indicator: Computation and Estimation: Add and subtract whole numbers with and without regrouping.

NNSO.13. Grade Level Indicator: Computation and Estimation: Demonstrate fluency in multiplication facts through 10 and corresponding division facts.

NNSO.14. Grade Level Indicator: Computation and Estimation: Divide 2- and 3-digit numbers by a single-digit number, without remainders for division.

NNSO.15. Grade Level Indicator: Computation and Estimation: Evaluate the reasonableness of computations based upon operations and the numbers involved; e.g., considering relative size, place value and estimates.

OH.M. Measurement: Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies.

M.A. Select appropriate units for perimeter, area, weight, volume (capacity), time and temperature, using: objects of uniform size; U.S. customary units; e.g., mile, square inch, cubic inch, second, degree Fahrenheit, and other units as appropriate; metric units; e.g., millimeter, kilometer, square centimeter, kilogram, cubic centimeter, degree Celsius, and other units as appropriate.

M.B. Know that the number of units is inversely related to the size of the unit for any item being measured.

M.C. Develop common referents for units of measure for length, weight, volume (capacity) and time to make comparisons and estimates.

M.D. Identify appropriate tools and apply counting techniques for measuring side lengths, perimeter and area of squares, rectangles, and simple irregular two-dimensional shapes, volume of rectangular prisms, and time and temperature.

M.E. Tell time to the nearest minute.

M.1. Grade Level Indicator: Measurement Units: Identify and select appropriate units for measuring: length- miles, kilometers and other units of measure as appropriate; volume (capacity)-gallons; weight-ounces, pounds, grams, or kilograms; temperature-degrees (Fahrenheit or Celsius).

M.2. Grade Level Indicator: Measurement Units: Establish personal or common referents to include additional units; e.g., a gallon container of milk; a postage stamp is about a square inch.

M.3. Grade Level Indicator: Measurement Units: Tell time to the nearest minute and find elapsed time using a calendar or a clock.

M.4. Grade Level Indicator: Measurement Units: Read thermometers in both Fahrenheit and Celsius scales.

M.5. Grade Level Indicator: Use Measurement Techniques and Tools: Estimate and measure length, weight and volume (capacity), using metric and U.S. customary units, accurate to the nearest 1/2 or 1/4 unit as appropriate.

M.6. Grade Level Indicator: Use Measurement Techniques and Tools: Use appropriate measurement tools and techniques to construct a figure or approximate an amount of specified length, weight or volume (capacity); e.g., construct a rectangle with length 2 1/2 inches and width 3 inches, fill a measuring cup to the 3/4 cup mark.

M.7. Grade Level Indicator: Use Measurement Techniques and Tools: Make estimates for perimeter, area and volume using links, tiles, cubes and other models.

OH.GSS. Geometry and Spatial Sense: Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects, and transformations to analyze mathematical situations and solve problems.

GSS.A. Provide rationale for groupings and comparisons of two-dimensional figures and three-dimensional objects.

GSS.B. Describe and identify points, lines and planes in the environment.

GSS.C. Describe and identify intersecting, parallel and perpendicular lines or segments in the environment.

GSS.D. Identify and draw right, obtuse, acute and straight angles.

GSS.E. Use attributes to describe, classify and sketch plane figures and build solid objects.

GSS.F. Develop definitions of classes of shapes.

GSS.G. Find and name locations in coordinate systems.

GSS.H. Identify and describe line and rotational symmetry in two-dimensional shapes and designs.

GSS.I. Describe, identify and model reflections, rotations and translations, using physical materials.

GSS.J. Describe a motion or series of transformations that show two shapes are congruent.

GSS.1. Grade Level Indicator: Characteristics and Properties: Analyze and describe properties of two-dimensional shapes and three-dimensional objects using terms such as vertex, edge, angle, side and face.

GSS.2. Grade Level Indicator: Characteristics and Properties: Identify and describe the relative size of angles with respect to right angles as follows: Use physical models, like straws, to make different sized angles by opening and closing the sides, not by changing the side lengths; Identify, classify and draw right, acute, obtuse and straight angles.

GSS.3. Grade Level Indicator: Spatial Relationships: Find and name locations on a labeled grid or coordinate system; e.g., a map or graph.

GSS.4. Grade Level Indicator: Transformations and Symmetry: Draw lines of symmetry to verify symmetrical two-dimensional shapes.

GSS.5. Grade Level Indicator: Visualization and Geometric Models: Build a three-dimensional model of an object composed of cubes; e.g., construct a model based on an illustration or actual object.

OH.PFA. Patterns, Functions and Algebra: Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs and equations.

PFA.A. Analyze and extend patterns, and describe the rule in words.

PFA.B. Use patterns to make predictions, identify relationships, and solve problems.

PFA.C. Write and solve open sentences and explain strategies.

PFA.D. Represent an unknown quantity as a variable using a symbol, including letters.

PFA.E. Use variables to create and solve equations representing problem situations.

PFA.F. Construct and use a table of values to solve problems associated with mathematical relationships.

PFA.G. Describe how a change in one variable affects the value of a related variable.

PFA.1. Grade Level Indicator: Use Patterns, Relations and Functions: Extend multiplicative and growing patterns, and describe the pattern or rule in words.

PFA.2. Grade Level Indicator: Use Patterns, Relations and Functions: Analyze and replicate arithmetic sequences with and without a calculator.

PFA.3. Grade Level Indicator: Use Patterns, Relations and Functions: Use patterns to make predictions, identify relationships, and solve problems.

PFA.4. Grade Level Indicator: Use Algebraic Representations: Model problem situations using objects, pictures, tables, numbers, letters and other symbols.

PFA.5. Grade Level Indicator: Use Algebraic Representations: Write, solve and explain simple mathematical statements.

PFA.6. Grade Level Indicator: Use Algebraic Representations: Express mathematical relationships as equations and inequalities.

PFA.7. Grade Level Indicator: Analyze Change: Create tables to record, organize and analyze data to discover patterns and rules.

PFA.8. Grade Level Indicator: Analyze Change: Identify and describe quantitative changes, especially those involving addition and subtraction; e.g., the height of water in a glass becoming 1 centimeter lower each week due to evaporation.

OH.DAP. Data Analysis and Probability: Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data.

DAP.A. Gather and organize data from surveys and classroom experiments, including data collected over a period of time.

DAP.B. Read and interpret tables, charts, graphs (bar, picture, line, line plot), and timelines as sources of information, identify main idea, draw conclusions, and make predictions.

DAP.C. Construct charts, tables and graphs to represent data, including picture graphs, bar graphs, line graphs, line plots and Venn diagrams.

DAP.D. Read, interpret and construct graphs in which icons represent more than a single unit or intervals greater than one.

DAP.E. Describe data using mode, median and range.

DAP.F. Conduct a simple probability experiment and draw conclusions about the likelihood of possible outcomes.

DAP.G. Identify and represent possible outcomes, such as arrangements of a set of up to four members and possible combinations from several sets, each containing 2 or 3 members.

DAP.H. Use the set of possible outcomes to describe and predict events.

DAP.1. Grade Level Indicator: Data Collection: Collect and organize data from an experiment, such as recording and classifying observations or measurements, in response to a question posed.

DAP.2. Grade Level Indicator: Data Collection: Draw and interpret picture graphs in which a symbol or picture represents more than one object.

DAP.3. Grade Level Indicator: Data Collection: Read, interpret and construct bar graphs with intervals greater than one.

DAP.4. Grade Level Indicator: Data Collection: Support a conclusion or prediction orally and in writing, using information in a table or graph.

DAP.5. Grade Level Indicator: Data Collection: Match a set of data with a graphical representation of the data.

DAP.6. Grade Level Indicator: Data Collection: Translate information freely among charts, tables, line plots, picture graphs and bar graphs; e.g., create a bar graph from the information in a chart.

DAP.7. Grade Level Indicator: Data Collection: Analyze and interpret information represented on a timeline.

DAP.8. Grade Level Indicator: Statistical Methods: Identify the mode of a data set and describe the information it gives about a data set.

DAP.9. Grade Level Indicator: Probability: Conduct a simple experiment or simulation of a simple event, record the results in a chart, table or graph, and use the results to draw conclusions about the likelihood of possible outcomes.

DAP.10. Grade Level Indicator: Probability: Use physical models, pictures, diagrams and lists to solve problems involving possible arrangements or combinations of two to four objects.

OH.MP. Mathematical Processes: Students use mathematical processes and knowledge to solve problems. Students apply problem-solving and decision-making techniques, and communicate mathematical ideas.

MP.A. Apply and justify the use of a variety of problem-solving strategies; e.g., make an organized list, guess and check.

MP.B. Use an organized approach and appropriate strategies to solve multi-step problems.

MP.C. Interpret results in the context of the problem being solved; e.g., the solution must be a whole number of buses when determining the number of buses necessary to transport students.

MP.D. Use mathematical strategies to solve problems that relate to other curriculum areas and the real world; e.g., use a timeline to sequence events; use symmetry in artwork.

MP.E. Link concepts to procedures and to symbolic notation; e.g., model 3 x 4 with a geometric array, represent one-third by dividing an object into three equal parts.

MP.F. Recognize relationships among different topics within mathematics; e.g., the length of an object can be represented by a number.

MP.G. Use reasoning skills to determine and explain the reasonableness of a solution with respect to the problem situation.

MP.H. Recognize basic valid and invalid arguments, and use examples and counter examples, models, number relationships, and logic to support or refute.

MP.I. Represent problem situations in a variety of forms (physical model, diagram, in words or symbols), and recognize when some ways of representing a problem may be more helpful than others.

MP.J. Read, interpret, discuss and write about mathematical ideas and concepts using both everyday and mathematical language.

MP.K. Use mathematical language to explain and justify mathematical ideas, strategies and solutions.