Ohio's Academic Content Standards in Mathematics

By the end of grade 4

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Number, Number Sense and Operations Standard
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. Indicators for grade 4 1. Identify and generate equivalent forms of fractions and decimals. For example: a. Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., 1/2, 5/10, "five tenths," 0.5, shaded rectangles with half, and five tenths. b. Understand and explain that ten tenths is the same as one whole in both fraction and decimal form. (ORC Resources) 2. Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths. (ORC Resources) 3. Round whole numbers to a given place value. (ORC Resources) 4. Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite. (ORC Resources) 5. Use models and points of reference to compare commonly used fractions. (ORC Resources) 6. 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, such as 5 x 47 = 5 x 40 + 5 x 7 = 200 + 35 = 235. (ORC Resources) 7. 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. (ORC Resources) 8. Solve problems involving counting money and making change, using both coins and paper bills. (ORC Resources) 9. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. (ORC Resources) 10. Use physical models, visual representations, and paper and pencil to add and subtract decimals and commonly used fractions with like denominators. (ORC Resources) 11. Develop and explain strategies for performing computations mentally. (ORC Resources) 12. 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. (ORC Resources) 13. Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator. (ORC Resources) 14. 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. (ORC Resources)

Measurement Standard
Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools, and technologies. Indicators for grade 4 1. 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. (ORC Resources) 2. Demonstrate and describe perimeter as surrounding and area as covering a two-dimensional shape, and volume as filling a three-dimensional object. (ORC Resources) 3. Identify and select appropriate units to measure: a. Perimeter - string or links (inches or centimeters). b. Area - tiles (square inches or square centimeters). c. Volume - cubes (cubic inches or cubic centimeters). (ORC Resources) 4. 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. (ORC Resources) 5. Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons. (ORC Resources) 6. Write, solve and verify solutions to multi-step problems involving measurement. (ORC Resources)

Geometry and Spatial Sense Standard
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. Indicators for grade 4 1. Identify, describe and model intersecting, parallel and perpendicular lines and line segments; e.g., use straws or other material to model lines. (ORC Resources) 2. Describe, classify, compare and model two- and three-dimensional objects using their attributes. (ORC Resources) 3. Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids. (ORC Resources) 4. Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles). (ORC Resources) 5. Describe points, lines and planes, and identify models in the environment. (ORC Resources) 6. Specify locations and plot ordered pairs on a coordinate plane, using first quadrant points. (ORC Resources) 7. Identify, describe and use reflections (flips), rotations (turns), and translations (slides) in solving geometric problems; e.g., use transformations to determine if two shapes are congruent. (ORC Resources) 8. Use geometric models to solve problems in other areas of mathematics, such as number (multiplication/division) and measurement (area, perimeter, border). (ORC Resources)

Patterns, Functions and Algebra Standard
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. Indicators for grade 4 1. Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications. (ORC Resources) 2. Represent and analyze patterns and functions using words, tables and graphs. (ORC Resources) 3. Construct a table of values to solve problems associated with a mathematical relationship. (ORC Resources) 4. Use rules and variables to describe patterns and other relationships. (ORC Resources) 5. Represent mathematical relationships with equations or inequalities. (ORC Resources) 6. 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. (ORC Resources)

Data Analysis and Probability Standard
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. Indicators for grade 4 1. Create a plan for collecting data for a specific purpose. (ORC Resources) 2. Represent and interpret data using tables, bar graphs, line plots and line graphs. (ORC Resources) 3. Interpret and construct Venn diagrams to sort and describe data. (ORC Resources) 4. 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. (ORC Resources) 5. Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs. (ORC Resources) 6. 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. (ORC Resources) 7. Identify the median of a set of data and describe what it indicates about the data. (ORC Resources) 8. Use range, median and mode to make comparisons among related sets of data. (ORC Resources) 9. Conduct simple probability experiments and draw conclusions from the results; e.g., rolling number cubes or drawing marbles from a bag. (ORC Resources) 10. 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. (ORC Resources) 11. Relate the concepts of impossible and certain-to-happen events to the numerical values of 0 (impossible) and 1 (certain). (ORC Resources) 12. 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. (ORC Resources) 13. 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 pair of shoes. (ORC Resources)