Nebraska State Standards for Mathematics: Grade 11

NE.MA 12.1. Students will communicate number sense concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.1.1. Number System: Students will represent and show relationships among real numbers.

MA 12.1.1.a. Demonstrate multiple equivalent forms of irrational numbers (e.g., square root of 8 = 8^1/2 = 2 square root of 2)

MA 12.1.1.b. Compare, contrast and apply the properties of numbers and the real number system, including rational, irrational, imaginary, and complex numbers

MA 12.1.2. Operations: Students will demonstrate the meaning and effects of arithmetic operations with real numbers.

MA 12.1.2.a. Use drawings, words, and symbols to explain the effects of such operations as multiplication and division, and computing positive powers and roots on the magnitude of quantities (e.g., if you take the square root of a number, will the result always be smaller than the original number? (e.g., square root of 1/4 = 1/2))

MA 12.1.2.b. Use drawings, words, and symbols to explain that the distance between two numbers on the number line is the absolute value of their difference

MA 12.1.3. Computation: Students will compute fluently and accurately using appropriate strategies and tools.

MA 12.1.3.a. Compute accurately with real numbers

MA 12.1.3.b. Simplify exponential expressions (e.g., powers of -1, 0, 1/2, 3^2 * 3^2 = 3^4)

MA 12.1.3.c. Multiply and divide numbers using scientific notation

MA 12.1.3.d. Select, apply, and explain the method of computation when problem solving using real numbers (e.g., models, mental computation, paper-pencil, or technology)

MA 12.1.4. Estimation: Students will estimate and check reasonableness of answers using appropriate strategies and tools.

MA 12.1.4.a. Use estimation methods to check the reasonableness of real number computations and decide if the problem calls for an approximation or an exact number (e.g., 10 pi is approximately 31.4, square and cube roots)

MA 12.1.4.b. Distinguish relevant from irrelevant information, identify missing information and either find what is needed or make appropriate estimates

NE.MA 12.2. Students will communicate geometric concepts and measurement concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.2.1. Characteristics: Students will analyze characteristics, properties, and relationships among geometric shapes and objects.

MA12.2.1.a. Identify and explain the necessity of and give examples of definitions and theorems

MA 12.2.1.b. Analyze properties and relationships among classes of two and three dimensional geometric objects using inductive reasoning and counterexamples

MA 12.2.1.c. State and prove geometric theorems using deductive reasoning (e.g., parallel lines with transversals, congruent triangles, similar triangles)

MA 12.2.1.d. Apply geometric properties to solve problems (e.g., parallel lines, line transversals, similar triangles, congruent triangles, proportions)

MA 12.2.1.e. Identify and apply right triangle relationships (e.g., sine, cosine, tangent, special right triangles, converse of Pythagorean Theorem)

MA 12.2.1.f. Recognize that there are geometries, other than Euclidean geometry, in which the parallel postulate is not true

MA12.2.1.g. Know the definitions and basic properties of a circle and use them to prove basic theorems and solve problems

MA 12.2.2. Coordinate Geometry: Student will use coordinate geometry to analyze and describe relationships in the coordinate plane.

MA 12.2.2.a. Use coordinate geometry to analyze geometric situations (e.g., parallel lines, perpendicular lines, circle equations)

MA 12.2.2.b. Apply the midpoint formula

MA 12.2.2.c. Apply the distance formula

MA 12.2.2.d. Prove special types of triangles and quadrilaterals (e.g., right triangles, isosceles trapezoid, parallelogram, rectangle, square)

MA 12.2.3. Transformations: Students will apply and analyze transformations.

MA 12.2.3.a. Explain and justify the effects of simple transformations on the ordered pairs of two-dimensional shapes

MA 12.2.3.b. Perform and describe multiple transformations

MA 12.2.4. Spatial Modeling: Students will use visualization, spatial reasoning, and geometric modeling to solve problems.

MA 12.2.4.a. Sketch and draw appropriate representations of geometric objects using ruler, protractor, or technology

MA 12.2.4.b. Use geometric models to visualize, describe, and solve problems (e.g., find the height of a tree; find the amount of paint needed for a room; scale model)

MA 12.2.5. Measurement: Students will apply the units, systems, and formulas to solve problems.

MA 12.2.5.a. Use strategies to find surface area and volume of complex objects

MA 12.2.5.b. Apply appropriate units and scales to solve problems involving measurement

MA 12.2.5.c. Convert between various units of area and volume, such as square feet to square yards

MA 12.2.5.d. Convert equivalent rates (e.g., feet/second to miles/hour)

MA 12.2.5.e. Find arc length and area of sectors of a circle

MA 12.2.5.f. Determine surface area and volume of three-dimensional objects (e.g., spheres, cones, pyramids)

MA12.2.5.g. Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k^2 and k^3, respectively

NE.MA 12.3. Students will communicate algebraic concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.3.1. Relationships: Students will generalize, represent, and analyze relationships using algebraic symbols.

MA 12.3.1.a. Represent, interpret, and analyze functions with graphs, tables, and algebraic notation and convert among these representations (e.g., linear, non-linear)

MA 12.3.1.b. Identify domain and range of functions represented in either symbolic or graphical form (e.g., linear, non-linear)

MA 12.3.1.c. Identify the slope and intercepts of a linear relationship from an equation or graph

MA 12.3.1.d. Identify characteristics of linear and non-linear functions

MA 12.3.1.e. Graph linear and non-linear functions

MA 12.3.1.f. Compare and analyze the rate of change by using ordered pairs, tables, graphs, and equations

MA 12.3.1.g. Graph and interpret linear inequalities

MA 12.3.1.h. Represent, interpret, and analyze functions and their inverses

MA 12.3.1.i. Determine if a relation is a function

MA 12.3.2. Modeling in Context: Students will model and analyze quantitative relationships.

MA 12.3.2.a. Model contextualized problems using various representations (e.g., graphs, tables, one variable equalities, one variable inequalities, linear equations in slope intercept form, inequalities in slope intercept form, system of linear equations with two variables)

MA 12.3.2.b. Represent a variety of quantitative relationships using linear equations and one variable inequalities

MA 12.3.2.c. Analyze situations to determine the type of algebraic relationship (e.g., linear, nonlinear)

MA 12.3.2.d. Model contextualized problems using various representations for non-linear functions (e.g., quadratic, exponential, square root, and absolute value)

MA 12.3.3. Procedures: Students will represent and solve equations and inequalities.

MA 12.3.3.a. Explain/apply the reflexive, symmetric, and transitive properties of equality

MA 12.3.3.b. Simplify algebraic expressions involving exponents (e.g., (3x^4)^2)

MA 12.3.3.c. Add and subtract polynomials

MA 12.3.3.d. Multiply and divide polynomials (e.g., divide x^3 - 8 by x - 2, divide x^4 - 5x^3 - 2x by x^2)

MA 12.3.3.e. Factor polynomials

MA 12.3.3.f. Identify and generate equivalent forms of linear equations

MA 12.3.3.g. Solve linear equations and inequalities including absolute value

MA 12.3.3.h. Identify and explain the properties used in solving equations and inequalities

MA 12.3.3.i. Solve quadratic equations (e.g., factoring, graphing, quadratic formula)

MA 12.3.3.j. Add, subtract, and simplify rational expressions

MA 12.3.3.k. Multiply, divide, and simplify rational expressions

MA 12.3.3.l. Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified values of their variables

MA 12.3.3.m. Derive and use the formulas for the general term and summation of finite arithmetic and geometric series

MA 12.3.3.n. Combine functions by composition, as well as by addition, subtraction, multiplication, and division

MA 12.3.3.o. Solve an equation involving several variables for one variable in terms of the others

MA 12.3.3.p. Analyze and solve systems of two linear equations in two variables algebraically and graphically

NE.MA 12.4. Students will communicate data analysis/probability concepts using multiple representations to reason, solve problems, and make connections within mathematics and across disciplines.

MA 12.4.1. Display and Analysis: Students will formulate a question and design a survey or an experiment in which data is collected and displayed in a variety of formats, then select and use appropriate statistical methods to analyze the data.

MA 12.4.1.a. Interpret data represented by the normal distribution and formulate conclusions

MA 12.4.1.b. Compute, identify, and interpret measures of central tendency (mean, median, mode) when provided a graph or data set

MA 12.4.1.c. Explain how sample size and transformations of data affect measures of central tendency

MA 12.4.1.d. Describe the shape and determine spread (variance, standard deviation) and outliers of a data set

MA 12.4.1.e. Explain how statistics are used or misused in the world

MA 12.4.1.f. Create scatter plots, analyze patterns, and describe relationships in paired data

MA 12.4.1.g. Explain the impact of sampling methods, bias, and the phrasing of questions asked during data collection and the conclusions that can rightfully be made

MA 12.4.1.h. Explain the differences between randomized experiment and observational studies

MA 12.4.2. Predictions and Inferences: Students will develop and evaluate inferences to make predictions.

MA 12.4.2.a. Compare data sets and evaluate conclusions using graphs and summary statistics

MA 12.4.2.b. Support inferences with valid arguments

MA 12.4.2.c. Develop linear equations for linear models to predict unobserved outcomes using regression line and correlation coefficient

MA 12.4.2.d. Recognize when arguments based on data confuse correlation with causation

MA 12.4.3. Probability: Students will apply and analyze concepts of probability.

MA 12.4.3.a. Construct a sample space and a probability distribution

MA 12.4.3.b. Identify dependent and independent events and calculate their probabilities

MA 12.4.3.c. Use the appropriate counting techniques to determine the probability of an event (e.g., combinations, permutations)

MA 12.4.3.d. Analyze events to determine if they are mutually exclusive

MA 12.4.3.e. Determine the relative frequency of a specified outcome of an event to estimate the probability of the outcome