Ohio's Academic Content Standards in Mathematics

By the end of grade 5

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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 5 1. Use models and visual representation to develop the concept of ratio as part-to-part and part-to-whole, and the concept of percent as part-to-whole. (ORC Resources) 2. Use various forms of "one" to demonstrate the equivalence of fractions; e.g., 18/24 = 9/12 x 2/2 = 3/4 x 6/6. (ORC Resources) 3. Identify and generate equivalent forms of fractions, decimals and percents. (ORC Resources) 4. Round decimals to a given place value and round fractions (including mixed numbers) to the nearest half. (ORC Resources) 5. Recognize and identify perfect squares and their roots. (ORC Resources) 6. Represent and compare numbers less than 0 by extending the number line and using familiar applications; e.g., temperature, owing money. (ORC Resources) 7. Use commutative, associative, distributive, identity and inverse properties to simplify and perform computations. (ORC Resources) 8. Identify and use relationships between operations to solve problems. (ORC Resources) 9. Use order of operations, including use of parentheses, to simplify numerical expressions. (ORC Resources) 10. Justify why fractions need common denominators to be added or subtracted. (ORC Resources) 11. Explain how place value is related to addition and subtraction of decimals; e.g., 0.2 + 0.14; the two tenths is added to the one tenth because they are both tenths. (ORC Resources) 12. Use physical models, points of reference, and equivalent forms to add and subtract commonly used fractions with like and unlike denominators and decimals. (ORC Resources) 13. Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies. (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 5 1. Identify and select appropriate units to measure angles; i.e., degrees. (ORC Resources) 2. Identify paths between points on a grid or coordinate plane and compare the lengths of the paths; e.g., shortest path, paths of equal length. (ORC Resources) 3. Demonstrate and describe the differences between covering the faces (surface area) and filling the interior (volume) of three-dimensional objects. (ORC Resources) 4. Demonstrate understanding of the differences among linear units, square units and cubic units. (ORC Resources) 5. Make conversions within the same measurement system while performing computations. (ORC Resources) 6. Use strategies to develop formulas for determining perimeter and area of triangles, rectangles and parallelograms, and volume of rectangular prisms. (ORC Resources) 7. Use benchmark angles (e.g.; 45°, 90°, 120°) to estimate the measure of angles, and use a tool to measure and draw angles. (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 5 1. Draw circles, and identify and determine relationships among the radius, diameter, center and circumference; e.g., radius is half the diameter, the ratio of the circumference of a circle to its diameter is an approximation of . (ORC Resources) 2. Use standard language to describe line, segment, ray, angle, skew, parallel and perpendicular. (ORC Resources) 3. Label vertex, rays, interior and exterior for an angle. (ORC Resources) 4. Describe and use properties of congruent figures to solve problems. (ORC Resources) 5. Use physical models to determine the sum of the interior angles of triangles and quadrilaterals. (ORC Resources) 6. Extend understanding of coordinate system to include points whose x or y values may be negative numbers. (ORC Resources) 7. Understand that the measure of an angle is determined by the degree of rotation of an angle side rather than the length of either side. (ORC Resources) 8. Predict what three-dimensional object will result from folding a two-dimensional net, then confirm the prediction by folding the net. (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 5 1. Justify a general rule for a pattern or a function by using physical materials, visual representations, words, tables or graphs. (ORC Resources) 2. Use calculators or computers to develop patterns, and generalize them using tables and graphs. (ORC Resources) 3. Use variables as unknown quantities in general rules when describing patterns and other relationships. (ORC Resources) 4. Create and interpret the meaning of equations and inequalities representing problem situations. (ORC Resources) 5. Model problems with physical materials and visual representations, and use models, graphs and tables to draw conclusions and make predictions. (ORC Resources) 6. Describe how the quantitative change in a variable affects the value of a related variable; e.g., describe how the rate of growth varies over time, based upon data in a table or graph. (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 5 1. Read, construct and interpret frequency tables, circle graphs and line graphs. (ORC Resources) 2. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data. (ORC Resources) 3. Read and interpret increasingly complex displays of data, such as double bar graphs. (ORC Resources) 4. Determine appropriate data to be collected to answer questions posed by students or teacher, collect and display data, and clearly communicate findings. (ORC Resources) 5. Modify initial conclusions, propose and justify new interpretations and predictions as additional data are collected. (ORC Resources) 6. Determine and use the range, mean, median and mode, and explain what each does and does not indicate about the set of data. (ORC Resources) 7. List and explain all possible outcomes in a given situation. (ORC Resources) 8. Identify the probability of events within a simple experiment, such as three chances out of eight. (ORC Resources) 9. Use 0,1 and ratios between 0 and 1 to represent the probability of outcomes for an event, and associate the ratio with the likelihood of the outcome. (ORC Resources) 10. Compare what should happen (theoretical/expected results) with what did happen (experimental/actual results) in a simple experiment. (ORC Resources) 11. Make predictions based on experimental and theoretical probabilities. (ORC Resources)