MA 12.1.1: Students will represent and show relationships among real numbers.
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: 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 12.2.1: Students will analyze characteristics, properties, and relationships among geometric shapes and objects.
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.g: Know the definitions and basic properties of a circle and use them to prove basic theorems and solve problems
MA 12.2.2: 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.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: 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: 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: 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.f: Determine surface area and volume of three-dimensional objects (e.g., spheres, cones, pyramids)
MA 12.2.5.g: Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively
MA 12.3.1: 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: 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: 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 to the 4th power)²)
MA 12.3.3.c: Add and subtract polynomials
MA 12.3.3.d: Multiply and divide polynomials (e.g., divide x³ ? 8 by x ? 2, divide x to the 4th power ? 5x³ ? 2x by x²)
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.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
MA 12.4.1: 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.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.f: Create scatter plots, analyze patterns, and describe relationships in paired data
MA 12.4.2: 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.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: 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.e: Determine the relative frequency of a specified outcome of an event to estimate the probability of the outcome
Correlation last revised: 3/29/2010