Ohio State Standards for Mathematics: Grade 4

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 fractions and decimals.

NNSO.2. Grade Level Indicator: Number and Number Systems: Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.

NNSO.3. Grade Level Indicator: Number and Number Systems: Round whole numbers to a given place value.

NNSO.4. Grade Level Indicator: Number and Number Systems: Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite.

NNSO.5. Grade Level Indicator: Number and Number Systems: Use models and points of reference to compare commonly used fractions.

NNSO.6. Grade Level Indicator: Meaning of Operations: Use associative and distributive properties to simplify and perform computations; e.g., use left to right multiplication and the distributive property to find an exact answer without paper and pencil.

NNSO.7. Grade Level Indicator: Meaning of Operations: Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money.

NNSO.8. Grade Level Indicator: Computation and Estimation: Solve problems involving counting money and making change, using both coins and paper bills.

NNSO.9. Grade Level Indicator: Computation and Estimation: Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.

NNSO.10. Grade Level Indicator: Computation and Estimation: Use physical models, visual representations, and paper and pencil to add and subtract decimals and commonly used fractions with like denominators.

NNSO.11. Grade Level Indicator: Computation and Estimation: Develop and explain strategies for performing computations mentally.

NNSO.12. Grade Level Indicator: Computation and Estimation: Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.

NNSO.13. Grade Level Indicator: Computation and Estimation: Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator.

NNSO.14. Grade Level Indicator: Computation and Estimation: Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.

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: Relate the number of units to the size of the units used to measure an object; e.g., compare the number of cups to fill a pitcher to the number of quarts to fill the same pitcher.

M.2. Grade Level Indicator: Measurement Units: Demonstrate and describe perimeter as surrounding and area as covering a two-dimensional shape, and volume as filling a three-dimensional object.

M.3. Grade Level Indicator: Measurement Units: Identify and select appropriate units to measure: perimeter-string or links (inches or centimeters); area-tiles (square inches or square centimeters); volume-cubes (cubic inches or cubic centimeters).

M.4. Grade Level Indicator: Use Measurement Techniques and Tools: Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume.

M.5. Grade Level Indicator: Use Measurement Techniques and Tools: Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons.

M.6. Grade Level Indicator: Use Measurement Techniques and Tools: Write, solve and verify solutions to multi-step problems involving measurement.

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: Identify, describe and model intersecting, parallel and perpendicular lines and line segments; e.g., use straws or other material to model lines.

GSS.2. Grade Level Indicator: Characteristics and Properties: Describe, classify, compare and model two- and three-dimensional objects using their attributes.

GSS.3. Grade Level Indicator: Characteristics and Properties: Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids.

GSS.4. Grade Level Indicator: Characteristics and Properties: Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles).

GSS.5. Grade Level Indicator: Spatial Relationships: Describe points, lines and planes, and identify models in the environment.

GSS.6. Grade Level Indicator: Spatial Relationships: Specify locations and plot ordered pairs on a coordinate plane, using first quadrant points.

GSS.7. Grade Level Indicator: Transformations and Symmetry: Identify, describe and use reflections (flips), rotations (turns), and translations (slides) in solving geometric problems; e.g., use transformations to determine if 2 shapes are congruent.

GSS.8. Grade Level Indicator: Visualization and Geometric Models: Use geometric models to solve problems in other areas of mathematics, such as number (multiplication/division) and measurement (area, perimeter, border).

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: Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications.

PFA.2. Grade Level Indicator: Use Patterns, Relations and Functions: Represent and analyze patterns and functions using words, tables and graphs.

PFA.3. Grade Level Indicator: Use Algebraic Representation: Construct a table of values to solve problems associated with a mathematical relationship.

PFA.4. Grade Level Indicator: Use Algebraic Representation: Use rules and variables to describe patterns and other relationships.

PFA.5. Grade Level Indicator: Use Algebraic Representation: Represent mathematical relationships with equations or inequalities.

PFA.6. Grade Level Indicator: Analyze Change: Describe how a change in one variable affects the value of a related variable; e.g., as one increases the other increases or as one increases the other decreases.

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: Create a plan for collecting data for a specific purpose.

DAP.2. Grade Level Indicator: Data Collection: Represent and interpret data using tables, bar graphs, line plots and line graphs.

DAP.3. Grade Level Indicator: Data Collection: Interpret and construct Venn diagrams to sort and describe data.

DAP.4. Grade Level Indicator: Data Collection: Compare different representations of the same data to evaluate how well each representation shows important aspects of the data, and identify appropriate ways to display the data.

DAP.5. Grade Level Indicator: Data Collection: Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs.

DAP.6. Grade Level Indicator: Statistical Methods: Describe the characteristics of a set of data based on a graphical representation, such as range of the data, clumps of data, and holes in the data.

DAP.7. Grade Level Indicator: Statistical Methods: Identify the median of a set of data and describe what it indicates about the data.

DAP.8. Grade Level Indicator: Statistical Methods: Use range, median and mode to make comparisons among related sets of data.

DAP.9. Grade Level Indicator: Probability: Conduct simple probability experiments and draw conclusions from the results; e.g., rolling number cubes or drawing marbles from a bag.

DAP.10. Grade Level Indicator: Probability: Represent the likelihood of possible outcomes for chance situations; e.g., probability of selecting a red marble from a bag containing 3 red and 5 white marbles.

DAP.11. Grade Level Indicator: Probability: Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain).

DAP.12. Grade Level Indicator: Probability: Place events in order of likelihood and use a diagram or appropriate language to compare the chance of each event occurring; e.g. impossible, unlikely, equal, likely, certain.

DAP.13. Grade Level Indicator: List and count all possible combinations using one member from each of several sets, each containing 2 or 3 members; e.g., the number of possible outfits from 3 shirts, 2 shorts and 2 pairs of shoes.

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.