South Dakota State Standards for Mathematics: Grade 11

SD.11.A. Algebra: Students will use the language of algebra to explore, describe, represent, and analyze number expressions and relations that represent variable quantities.

11.A.1. Use procedures to transform algebraic expressions.

11.A.1.1. Comprehension: Students are able to write equivalent forms of algebraic expressions using properties of the set of real numbers.

11.A.1.1.a. Evaluate algebraic expressions.

11.A.1.1.b. Use laws of exponents.

11.A.1.1.c. Use conventional order of operations, including grouping and exponents.

11.A.2. Use a variety of algebraic concepts and methods to solve equations and inequalities.

11.A.2.1. Comprehension: Students are able to use algebraic properties to transform multi-step, single-variable, first-degree equations.

11.A.2.2. Application: Students are able to use algebraic properties to transform multi-step, single-variable, first-degree inequalities and represent solutions using a number line.

11.A.3. Interpret and develop mathematical models.

11.A.3.1. Application: Students are able to create linear models to represent problem situations.

11.A.3.1.a. Calculate and interpret slope.

11.A.3.2. Comprehension: Students are able to distinguish between linear and nonlinear models.

11.A.4. Describe and use properties and behaviors of relations, functions, and inverses.

11.A.4.1. Application: Students are able to use graphs, tables, and equations to represent linear functions.

SD.11.G. Geometry: Students will use the language of geometry to discover, analyze, and communicate geometric concepts, properties, and relationships.

11.G.1. Use deductive and inductive reasoning to recognize and apply properties of geometric figures.

11.G.1.1. Application: Students are able to apply the properties of triangles and quadrilaterals to find unknown parts.

11.G.1.2. Application: Students are able to identify and apply relationships among triangles.

11.G.1.2.a. Definitions and postulates.

11.G.1.2.b. Similarity theorems.

11.G.1.2.c. Congruence theorems.

11.G.2. Use properties of geometric figures to solve problems from a variety of perspectives.

11.G.2.1. Analysis: Students are able to recognize the relationship between a three-dimensional figure and its two-dimensional representation.

11.G.2.1.a. Interpret floor plans

11.G.2.1.b. Follow instructions for assembly of a product, e.g. ''some assembly required''.

11.G.2.2. Application: Students are able to reflect across vertical or horizontal lines, and translate two-dimensional figures.

11.G.2.2.a. Identify lines of symmetry.

11.G.2.2.b. Use the coordinate plane.

11.G.2.3. Application: Students are able to use proportions to solve problems.

SD.11.M. Measurement: Students will apply systems of measurement and use appropriate measurement tools to describe and analyze the world around them.

11.M.1. Apply measurement concepts in practical applications.

11.M.1.1. Comprehension: Students are able to choose appropriate unit label, scale, and precision.

11.M.1.1.a. Determine appropriate scales for histograms, scatterplots, and other graphs.

11.M.1.2. Comprehension: Students are able to use suitable units when describing rate of change.

11.M.1.3. Application: Students are able to use formulas to find perimeter, circumference, and area to solve problems involving common geometric figures.

11.M.1.3.a. Use algebraic expressions with geometric formulas.

SD.11.N. Number Sense: Students will develop and use number sense to investigate the characteristics of numbers in a variety of forms and modes of operation.

11.N.1. Analyze the structural characteristics of the real number system and its various subsystems. Analyze the concept of value, magnitude, and relative magnitude of real numbers.

11.N.1.1. Comprehension: Students are able to identify multiple representations of a real number.

11.N.1.1.a. Given a real number identify the subset(s) of real numbers to which it belongs.

11.N.1.1.b. Represent rational and irrational numbers in different forms.

11.N.1.2. Comprehension: Students are able to apply the concept of place value, magnitude, and relative magnitude of real numbers.

11.N.1.2.a. Scientific notation

11.N.1.2.b. Infinitely many solutions

11.N.1.2.c. Completeness of the real numbers (density, i.e. between any two real numbers is another real number)

11.N.2. Apply number operations with real numbers and other number systems.

11.N.2.1. Comprehension: Students are able to add, subtract, multiply, and divide real numbers including integral exponents.

11.N.3. Develop conjectures, predictions, or estimations to solve problems and verify or justify the results.

11.N.3.1. Analysis: Students are able to use estimation strategies in problem situations to predict results and to check the reasonableness of results.

11.N.3.1.a. Use rounding as an estimation strategy.

11.N.3.1.b. Use non-routine estimation strategies.

11.N.3.2. Comprehension: Students are able to select alternative computational strategies and explain the chosen strategy.

11.N.3.2.a. Use properties of numbers that allow operational shortcuts for computational procedures.

SD.11.S. Statistics & Probability: Students will apply statistical methods to analyze data and explore probability for making decisions and predictions.

11.S.1. Use statistical models to gather, analyze, and display data to draw conclusions.

11.S.1.1. Analysis: Students are able to draw conclusions from a set of data.

11.S.1.1.a. Determine and use appropriate statistical values.

11.S.1.1.b. Determine which questions can or cannot be answered from a given data set.

11.S.1.2. Comprehension: Students are able to compare multiple one-variable data sets, using range, interquartile range, mean, mode, and median.

11.S.1.3. Analysis: Represent a set of data in a variety of graphical forms and draw conclusions.

11.S.1.3.a. Make a scatterplot to draw a regression line and make predictions.

11.S.1.3.b. Make a box-and-whisker plot to model a set of one-variable data.

11.S.1.3.c. Make a histogram from a frequency distribution.

11.S.2. Apply the concepts of probability to predict events/outcomes and solve problems.

11.S.2.1. Knowledge: Students are able to distinguish between experimental and theoretical probability.

11.S.2.2. Comprehension: Students are able to predict outcomes of simple events using given theoretical probabilities.

11.S.2.2.a. Determine the sample space of an experiment.

11.A.1.A. Use procedures to transform algebraic expressions.

11.A.1.1A. Application: Students are able to write equivalent forms of rational algebraic expressions using properties of real numbers.

11.A.1.2A. Application: Students are able to extend the use of real number properties to expressions involving complex numbers.

11.A.2.A. Use a variety of algebraic concepts and methods to solve equations and inequalities.

11.A.2.1A. Analysis: Students are able to determine solutions of quadratic equations.

11.A.2.1A.a. Use the quadratic formula.

11.A.2.1A.b. Use the discriminant, b2-4ac, to describe the nature of the roots.

11.A.2.2A. Application: Students are able to determine the solution of systems of equations and systems of inequalities.

11.A.2.3A. Application: Students are able to determine solutions to absolute value statements.

11.A.3.A. Interpret and develop mathematical models.

11.A.3.1A. Analysis: Students are able to distinguish between linear, quadratic, inverse variation, and exponential models.

11.A.3.2A. Synthesis: Students are able to create formulas to model relationships that are algebraic, geometric, trigonometric, and exponential.

11.A.3.3A. Analysis: Students are able to use sequences and series to model relationships.

11.A.4.A. Describe and use properties and behaviors of relations, functions, and inverses.

11.A.4.1A. Analysis: Students are able to determine the domain, range, and intercepts of a function.

11.A.4.2A. Analysis: Students are able to describe the behavior of a polynomial, given the leading coefficient, roots, and degree.

11.A.4.3A. Analysis: Students are able to apply transformations to graphs and describe the results.

11.A.4.3A.a. Change coefficients and/or constants.

11.A.4.3A.b. Graph the inverse of a function.

11.A.4.4A. Application: Students are able to apply properties and definitions of trigonometric, exponential, and logarithmic expressions.

11.A.4.5A. Analysis: Students are able to describe characteristics of nonlinear functions and relations.

11.A.4.5A.a. Conic sections

11.A.4.5A.b. Trigonometric functions

11.A.4.5A.c. Exponential and logarithmic functions

11.A.4.6A. Application: Students are able to graph solutions to linear inequalities.

11.G.1.A. Use deductive and inductive reasoning to recognize and apply properties of geometric figures.

11.G.1.1A. Evaluation: Students are able to justify properties of geometric figures.

11.G.1.1A.a. Write a direct proof.

11.G.1.1A.b. Make conjectures.

11.G.1.2A. Application: Students are able to determine the values of the sine, cosine, and tangent ratios of right triangles.

11.G.1.3A. Application: Students are able to apply properties associated with circles.

11.G.1.4A. Analysis: Students are able to use formulas for surface area and volume to solve problems involving three-dimensional figures.

11.G.2.1A. Synthesis: Students are able to use Cartesian coordinates to verify geometric properties.

11.M.1.A. Apply measurement concepts in practical applications.

11.M.1.1A. Application: Students are able to use dimensional analysis to check answers and determine units of a problem solution.

11.M.1.2A. Analysis: Students are able to use indirect measurement in problem situations that defy direct measurement.

11.N.1.A. Analyze the structural characteristics of the real number system and its various subsystems. Analyze the concept of value, magnitude, and relative magnitude of real numbers.

11.N.1.1A. Comprehension: Students are able to describe the relationship of the real number system to the complex number system.

11.N.1.2A. Application: Students are able to apply properties and axioms of the real number system to various subsets, e.g., axioms of order, closure.

11.N.2.A. Apply number operations with real numbers and other number systems.

11.N.2.1A. Application: Students are able to add, subtract, multiply, and divide real numbers including rational exponents.

11.N.2.1A.a. Simplify numeric expressions with radicals.

11.N.3.A. Develop conjectures, predictions, or estimations to solve problems and verify or justify the results.

11.N.3.1A. Note: Skills for this indicator have been subsumed within applications to advanced skills by the time students reach advanced high school mathematics.

11.S.1.A. Use statistical models to gather, analyze, and display data to draw conclusions.

11.S.1.1A. Evaluation: Students are able to analyze and evaluate the design of surveys and experiments.

11.S.1.2A. Evaluation: Students are able to analyze and evaluate graphical displays of data.

11.S.1.3A. Analysis: Students are able to compare multiple one-variable data sets, using standard deviation and variance.

11.S.1.3A.a. Calculate the standard deviation and variance of a data set.

11.S.1.4A. Application: Students are able to describe the normal curve and use it to make predictions.

11.S.1.5A. Application: Students are able to use scatterplots, best-fit lines, and correlation coefficients to model data and support conclusions.

11.S.2.A. Apply the concepts of probability to predict events/outcomes and solve problems.

11.S.2.1A. Application: Students are able to use probabilities to solve problems.

11.S.2.1A.a. Compute combinations, permutations.

11.S.2.1A.b. Interpret tables.

11.S.2.1A.c. Create and use tree diagrams.

11.S.2.2A. Application: Students are able to determine probability of compound, complementary, independent, and mutually exclusive events.

11.S.2.3A. Application: Students are able to generate data and use the data to determine empirical (experimental) probabilities.