Number
Measurement
Geometry
Algebra
Data Analysis
Grade Eleven
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. |
Benchmark A. Demonstrate that vectors and
matrices
are systems having some of the same properties of the real number
system. 1. Determine what properties hold for matrix addition and matrix multiplication; e.g., use examples to show addition is commutative and when multiplication is not commutative. 2. Determine what properties hold for vector addition and multiplication, and for scalar multiplication. Benchmark B. Develop an understanding of properties of and representations for addition and multiplication of vectors and matrices. 1. Determine what properties hold for matrix addition and matrix multiplication; e.g., use examples to show addition is commutative and when multiplication is not commutative. 2. Determine what properties hold for vector addition and multiplication, and for scalar multiplication. 5. Model, using the coordinate plane, vector addition and scalar multiplication. Benchmark C. Apply factorials and exponents, including fractional exponents, to solve practical problems. 3. Use factorial notation and computations to represent and solve problem situations involving arrangements. (Grade 10) 8. Use fractional and negative exponents as optional ways of representing and finding solutions for problem situations; e.g., 272/3 = (271/3)2 = 9. Benchmark 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. 4. Use matrices to represent given information in a problem situation. 6. Compute sums, differences and products of matrices using paper and pencil calculations for simple cases, and technology for more complicated cases. 9. Use vector addition and scalar multiplication to solve problems. Benchmark E. Represent and compute with complex numbers. 3. Represent complex numbers on the complex plane. 7. Compute sums, differences, products and quotients of complex numbers. |
Students estimate and measure to a required
degree of accuracy and precision by selecting and using appropriate
units, tools and technologies. |
Benchmark A. Explain differences among
accuracy, precision and error, and describe how each of those can
affect solutions in measurement situations. 1. Explain how a small error in measurement may lead to a large error in calculated results. (Grade 10) 2. Calculate relative error. (Grade 10) 3. Explain the difference between absolute error and relative error in measurement. (Grade 10) 4. Give examples of how the same absolute error can be problematic in one situation but not in another; e.g., compare “accurate to the nearest foot” when measuring the height of a person versus when measuring the height of a mountain. (Grade 10) 1. Determine the number of significant digits in a measurement. Benchmark B. Apply various measurement scales to describe phenomena and solve problems. 2. Use radian and degree angle measures to solve problems and perform conversions as needed. Benchmark C. Estimate and compute areas and volume in increasingly complex problem situations. 3. Derive a formula for the surface area of a cone as a function of its slant height and the circumference of its base. 4. Calculate distances, areas, surface areas and volumes of composite three-dimensional objects to a specified number of significant digits. Benchmark D. Solve problem situations involving derived measurements; e.g., density, acceleration. 5. Solve real-world problems involving area, surface area, volume and density to a specified degree of precision. |
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, andtransformations to
analyze mathematical situations and solve problems. |
Benchmark A. Use trigonometric
relationships to verify and determine solutions in problem situations. 4. Use trigonometric relationships to determine lengths and angle measures; i.e., Law of Sines and Law of Cosines. 5. Identify, sketch and classify the cross sections of three-dimensional objects. Benchmark B. Represent transformations within a coordinate system using vectors and matrices. 1. Use polar coordinates to specify locations on a plane. 2. Represent translations using vectors. 3. Describe multiplication of a vector and a scalar graphically and algebraically, and apply to problem situations. |
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. |
Benchmark A. Analyze functions by
investigating rates of change, intercepts, zeros, asymptotes, and local
and global behavior. 3. Describe and compare the characteristics of the following families of functions: quadratics with complex roots, polynomials of any degree, logarithms, and rational functions; e.g., general shape, number of roots, domain and range, asymptotic behavior. 4. Identify the maximum and minimum points of polynomial, rational and trigonometric functions graphically and with technology. 5. Identify families of functions with graphs that have rotation symmetry or reflection symmetry about the y-axis, x-axis or y = x. 6. Represent the inverse of a function symbolically and graphically as a reflection about y = x. 10. Describe the characteristics of the graphs of conic sections. 11. Describe how a change in the value of a constant in an exponential, logarithmic or radical equation affects the graph of the equation. Benchmark B. Use the quadratic formula to solve quadratic equations that have complex roots. 8. Solve equations involving radical expressions and complex roots. Benchmark C. Use recursive functions to model and solve problems; e.g., home mortgages, annuities. 1. Identify and describe problem situations involving an iterative process that can be represented as a recursive function; e.g., compound interest. 2. Translate a recursive function into a closed form expression or formula for the nth term to solve a problem situation involving an iterative process; e.g., find the value of an annuity after 7 years. Benchmark D. Apply algebraic methods to represent and generalize problem situations involving vectors and matrices. 7. Model and solve problems with matrices and vectors. 9. Solve 3 by 3 systems of linear equations by elimination and using technology, and interpret graphically what the solution means (a point, line, plane, or no solution). |
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. |
Benchmark A. Create and analyze tabular
and graphical displays of data using appropriate tools, including
spreadsheets and graphing calculators. 4. Create a scatterplot of bivariate data, identify trends, and find a function to model the data. 5. Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation. 7. Describe the standard normal curve and its general properties, and answer questions dealing with data assumed to be normal. 8. Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions. 10. Understand and use the concept of random variable, and compute and interpret the expected value for a random variable in simple cases. Benchmark B. Use descriptive statistics to analyze and summarize data, including measures of center, dispersion, correlation and variability. 3. Describe how a linear transformation of univariate data affects range, mean, mode and median. 5. Use technology to find the Least Squares Regression Line, the regression coefficient, and the correlation coefficient for bivariate data with a linear trend, and interpret each of these statistics in the context of the problem situation. 6. Use technology to compute the standard deviation for a set of data, and interpret standard deviation in relation to the context or problem situation. 8. Analyze and interpret univariate and bivariate data to identify patterns, note trends, draw conclusions, and make predictions. Benchmark 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. 1. Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation. 2. Describe the role of randomization in a well-designed study, especially as compared to a convenience sample, and the generalization of results from each. 9. Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques. Benchmark D. Connect statistical techniques to applications in workplace and consumer situations. 1. Design a statistical experiment, survey or study for a problem; collect data for the problem; and interpret the data with appropriate graphical displays, descriptive statistics, concepts of variability, causation, correlation and standard deviation. 2. Describe the role of randomization in a well-designed study, especially as compared to a convenience sample, and the generalization of results from each. 9. Evaluate validity of results of a study based on characteristics of the study design, including sampling method, summary statistics and data analysis techniques. 11. Examine statements and decisions involving risk; e.g., insurance rates and medical decisions. |
All of the information on
this site is available in pdf and/or Word format at the
Ohio Department of Education Web Site at http://www.ode.state.oh.us/
|
BACK TO MRS. GRAY'S CLASSROOM PAGE
Send comments and suggestions to: comments@mrsgraysclassroom.org
Please
do not copy the graphics from this Web Site. Many of the graphics
are from copyrighted graphic collections on the Internet.
Please go to our
Graphics Page included in our
Educational Links to visit these great sites to download graphics.
Updated 06/20/10
Copyright @ 2010 Mrs. Gray's Classroom
All Rights Reserved