East Central Ohio Area Media Center

Resources for Mathematics 11-12 Benchmarks

Number, Number Sense and Operations

A. Demonstrate that vectors and matrices are systems having some of the same properties of the real number system.

B. Develop an understanding of properties of and representations for addition and multiplication of vectors and matrices.

C. Apply factorials and exponents, including fractional exponents, to solve practical problems.

D. Demonstrate fluency in operations with real numbers, vectors and matrices, using mental computation or paper and pencil calculations for simple cases and technology for more complicated cases.

E. Represent and compute with complex numbers.

Measurement

A. Explain differences among accuracy, precision and error, and describe how each of those can affect solutions in measurement situations.

B. Apply various measurement scales to describe phenomena and solve problems.

C. Estimate and compute areas and volume in increasingly complex problem situations.

D. Solve problem situations involving derived measurements; e.g., density, acceleration.

Geometry and Spatial Sense

A. Use trigonometric relationships to verify and determine solutions in problem situations.

B. Represent transformations within a coordinate system using vectors and matrices.

Patterns, Functions and Algebra

A. Analyze functions by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior.

B. Use the quadratic formula to solve quadratic equations that have complex roots.

C. Use recursive functions to model and solve problems; e.g., home mortgages, annuities.

D. Apply algebraic methods to represent and generalize problem situations involving vectors and matrices.

Data Analysis and Probability

A. Create and analyze tabular and graphical displays of data using appropriate tools, including spreadsheets and graphing calculators.

B. Use descriptive statistics to analyze and summarize data, including measures of center, dispersion, correlation and variability.

C. Design and perform a statistical experiment, simulation or study; collect and interpret data; and use descriptive statistics to communicate and support predictions and conclusions.

D. Connect statistical techniques to applications in workplace and consumer situations.

Mathematical Processes

A. Construct algorithms for multi-step and non-routine problems.

B. Construct logical verifications or counter-examples to test conjectures and to justify or refute algorithms and solutions to problems.

C. Assess the adequacy and reliability of information available to solve a problem.

D. Select and use various types of reasoning and methods of proof.

E. Evaluate a mathematical argument and use reasoning and logic to judge its validity.

F. Present complete and convincing arguments and justifications, using inductive and deductive reasoning, adapted to be effective for various audiences.

G. Understand the difference between a statement that is verified by mathematical proof, such as a theorem, and one that is verified empirically using examples or data.

H. Use formal mathematical language and notation to represent ideas, to demonstrate relationships within and among representation systems, and to formulate generalizations.

I. Communicate mathematical ideas orally and in writing with a clear purpose and appropriate for a specific audience.

J. Apply mathematical modeling to workplace and consumer situations, including problem formulation, identification of a mathematical model, interpretation of solution within the model, and validation to original problem situation.

Other Mathematics Grade Level Benchmarks

Grades K-2 Mathematics Benchmarks

Grades 3-4 Mathematics Benchmarks

Grades 5-7 Mathematics Benchmarks

Grades 8-10 Mathematics Benchmarks

Other Academic Content Standards

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