Ohio's Academic Content Standards in Mathematics

By the end of grade 8

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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 8 1. Use scientific notation to express large numbers and small numbers between 0 and 1. (ORC Resources) 2. Recognize that natural numbers, whole numbers, integers, rational numbers and irrational numbers are subsets of the real number system. (ORC Resources) 3. Apply order of operations to simplify expressions and perform computations involving integer exponents and radicals. (ORC Resources) 4. Explain and use the inverse and identity properties and use inverse relationships (addition/subtraction, multiplication/division, squaring/square roots) in problem solving situations. (ORC Resources) 5. Determine when an estimate is sufficient and when an exact answer is needed in problem situations, and evaluate estimates in relation to actual answers; e.g., very close, less than, greater than. (ORC Resources) 6. Estimate, compute and solve problems involving rational numbers, including ratio, proportion and percent, and judge the reasonableness of solutions. (ORC Resources) 7. Find the square root of perfect squares, and approximate the square root of non-perfect squares as consecutive integers between which the root lies; e.g., is between 11 and 12. (ORC Resources) 8. Add, subtract, multiply, divide and compare numbers written in scientific notation. (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 8 1. Compare and order the relative size of common U.S. customary units and metric units; e.g., mile and kilometer, gallon and liter, pound and kilogram. (ORC Resources) 2. Use proportional relationships and formulas to convert units from one measurement system to another; e.g., degrees Fahrenheit to degrees Celsius. (ORC Resources) 3. Use appropriate levels of precision when calculating with measurements. (ORC Resources) 4. Derive formulas for surface area and volume and justify them using geometric models and common materials. For example, find: a. the surface area of a cylinder as a function of its height and radius; and b. that the volume of a pyramid (or cone) is one-third of the volume of a prism (or cylinder) with the same base area and height. (ORC Resources) 5. Determine surface area for pyramids by analyzing their parts. (ORC Resources) 6. Solve and determine the reasonableness of the results for problems involving rates and derived measurements, such as velocity and density, using formulas, models and graphs. (ORC Resources) 7. Apply proportional reasoning to solve problems involving indirect measurements or rates. (ORC Resources) 8. Find the sum of the interior and exterior angles of regular convex polygons with and without measuring the angles with a protractor. (ORC Resources) 9. Demonstrate understanding of the concepts of perimeter, circumference and area by using established formula for triangles, quadrilaterals, and circles to determine the surface area and volume of prisms, pyramids, cylinders, spheres and cones. (Note: Only volume should be calculated for spheres and cones.) (ORC Resources) 10. Use conventional formulas to find the surface area and volume of prisms, pyramids and cylinders and the volume of spheres and cones to a specified level of precision. (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 8 1. Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of two-dimensional figures and three-dimensional objects. (ORC Resources) 2. Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal. (ORC Resources) 3. Use proportions in several forms to solve problems involving similar figures (part-to-part, part-to-whole, corresponding sides between figures). (ORC Resources) 4. Represent and analyze shapes using coordinate geometry; e.g., given three vertices and the type of quadrilateral, find the coordinates of the fourth vertex. (ORC Resources) 5. Draw the results of translations, reflections, rotations and dilations of objects in the coordinate plane, and determine properties that remain fixed; e.g., lengths of sides remain the same under translations. (ORC Resources) 6. Draw nets for a variety of prisms, pyramids, cylinders and cones. (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 8 1. Relate the various representations of a relationship; i.e., relate a table to graph, description and symbolic form. (ORC Resources) 2. Generalize patterns and sequences by describing how to find the nth term. (ORC Resources) 3. Identify functions as linear or nonlinear based on information given in a table, graph or equation. (ORC Resources) 4. Extend the uses of variables to include covariants where y depends on x. (ORC Resources) 5. Use physical models to add and subtract monomials and polynomials, and to multiply a polynomial by a monomial. (ORC Resources) 6. Describe the relationship between the graph of a line and its equation, including being able to explain the meaning of slope as a constant rate of change and y-intercept in real-world problems. (ORC Resources) 7. Use symbolic algebra (equations and inequalities), graphs and tables to represent situations and solve problems. (ORC Resources) 8. Write, simplify and evaluate algebraic expressions (including formulas) to generalize situations and solve problems. (ORC Resources) 9. Solve linear equations and inequalities graphically, symbolically and using technology. (ORC Resources) 10. Solve 2 by 2 systems of linear equations graphically and by simple substitution. (ORC Resources) 11. Interpret the meaning of the solution of a 2 by 2 system of equations; i.e., point, line, no solution. (ORC Resources) 12. Solve simple quadratic equations graphically; e.g., y = x² - 16. (ORC Resources) 13. Compute and interpret slope, midpoint and distance given a set of ordered pairs. (ORC Resources) 14. Differentiate and explain types of changes in mathematical relationships, such as linear vs. nonlinear, continuous vs. noncontinuous, direct variation vs. inverse variation. (ORC Resources) 15. Describe and compare how changes in an equation affects the related graphs; e.g., for a linear equation changing the coefficient of x affects the slope and changing the constant affects the intercepts. (ORC Resources) 16. Use graphing calculators or computers to analyze change; e.g., interest compounded over time as a nonlinear growth pattern. (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 8 1. Use, create and interpret scatterplots and other types of graphs as appropriate. (ORC Resources) 2. Evaluate different graphical representations of the same data to determine which is the most appropriate representation for an identified purpose; e.g., line graph for change over time, circle graph for part-to-whole comparison, scatterplot for relationship between two variants. (ORC Resources) 3. Differentiate between discrete and continuous data and appropriate ways to represent each. (ORC Resources) 4. Compare two sets of data using measures of center (mean, mode, median) and measures of spread (range, quartiles, interquartile range, percentiles). (ORC Resources) 5. Explain the mean's sensitivity to extremes and its use in comparison with the median and mode. (ORC Resources) 6. Make conjectures about possible relationship in a scatterplot and approximate line of best fit. (ORC Resources) 7. Identify different ways of selecting samples, such as survey response, random sample, representative sample and convenience sample. (ORC Resources) 8. Describe how the relative size of a sample compared to the target population affects the validity of predictions. (ORC Resources) 9. Construct convincing arguments based on analysis of data and interpretation of graphs. (ORC Resources) 10. Calculate the number of possible outcomes for a situation, recognizing and accounting for when items may occur more than once or when order is important. (ORC Resources) 11. Demonstrate an understanding that the probability of either of two disjoint events occurring can be found by adding the probabilities for each and that the probability of one independent event following another can be found by multiplying the probabilities. (ORC Resources)