Ohio's Academic Content Standards in Mathematics

By the end of grade 12

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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 12 1. Determine what properties (closure, identity, inverse, commutative and associative) hold for operations with complex numbers. (ORC Resources) 2. Apply combinations as a method to create coefficients for the Binomial Theorem, and make connections to everyday and workplace problem situations. (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 12 1. Solve problems involving derived measurements; e.g., acceleration and pressure. (ORC Resources) 2. Use radian measures in the solution of problems involving angular velocity and acceleration. (ORC Resources) 3. Apply informal concepts of successive approximation, upper and lower bounds, and limits in measurement situations; e.g., measurement of some quantities, such as volume of a cone, can be determined by sequences of increasingly accurate approximations. (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 12 1. Use matrices to represent translations, reflections, rotations, dilations and their compositions. (ORC Resources) 2. Derive and apply the basic trigonometric identities; i.e., angle addition, angle subtraction, and double angle. (ORC Resources) 3. Relate graphical and algebraic representations of lines, simple curves and conic sections. (ORC Resources) 4. Recognize and compare specific shapes and properties in multiple geometries; e.g., plane, spherical and hyperbolic. (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 12 1. Analyze the behavior of arithmetic and geometric sequences and series as the number of terms increases. (ORC Resources) 2. Translate between the numeric and symbolic form of a sequence or series. (ORC Resources) 3. Describe and compare the characteristics of transcendental and periodic functions; e.g., general shape, number of roots, domain and range, asymptotic behavior, extrema, local and global behavior. (ORC Resources) 4. Represent the inverse of a transcendental function symbolically. (ORC Resources) 5. Set up and solve systems of equations using matrices and graphs, with and without technology. (ORC Resources) 6. Make arguments about mathematical properties using mathematical induction. (ORC Resources) 7. Make mathematical arguments using the concepts of limit. (ORC Resources) 8. Compare estimates of the area under a curve over a bounded interval by partitioning the region with rectangles; e.g., make successive estimates using progressively smaller rectangles. (ORC Resources) 9. Translate freely between polar and Cartesian coordinate systems. (ORC Resources) 10. Use the concept of limit to find instantaneous rate of change for a point on a graph as the slope of a tangent at a point. (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 12 1. Identify and use various sampling methods (voluntary response, convenience sample, random sample, stratified random sample, census) in a study. (ORC Resources) 2. Transform bivariate data so it can be modeled by a function; e.g., use logarithms to allow nonlinear relationship to be modeled by linear function. (ORC Resources) 3. Describe the shape and find all summary statistics for a set of univariate data, and describe how a linear transformation affects shape, center and spread. (ORC Resources) 4. Apply the concept of a random variable to generate and interpret probability distributions, including binomial, normal and uniform. (ORC Resources) 5. Use sampling distributions as the basis for informal inference. (ORC Resources) 6. Use theoretical or experimental probability, including simulations, to determine probabilities in real-world problem situations involving uncertainty, such as mutually exclusive events, complementary events and conditional probability. (ORC Resources)

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