Core Ideas
 Core Idea 1: Functions and Relations Understand patterns, relations, and functions. Generalize patterns using explicitly defined functions. Understand relations and functions and select, convert flexibly among, and use various representations for them. Analyze functions of one variable by investigating local and global behavior, including slopes as rates of change, intercepts, and zeros. Core Idea 2: Mathematical Reasoning Employ forms of mathematical reasoning and proof appropriate to the solution of the problem, including deductive and inductive reasoning, making and testing conjectures, and using counterexamples and indirect proof. Show mathematical reasoning in a variety of ways, including words, numbers, symbols, pictures, charts, graphs, tables, diagrams, and models. Explain the logic inherent in a solution process. Use induction to make conjectures and use deductive reasoning to prove conclusions. Draw reasonable conclusions about a situation being modeled. Core Idea 3: Algebraic Properties and Representations Represent and analyze mathematical situations and structures using algebraic symbols. Compare and contrast the properties of numbers and number systems including real numbers. Understand the meaning of equivalent forms of expressions, equations, inequalities, or relations. Write equivalent forms of equations, inequalities, and systems of equations and solve them. Use symbolic algebra to represent and explain mathematical relationships. Judge the meaning, utility, and reasonableness of results of symbolic manipulations. Use symbolic expressions to represent relationships arising from various contexts. Approximate and interpret rates of change from graphic and numeric data. Core Idea 4: Geometry and Measurement Describe spatial relationships using coordinate geometry; develop mathematical arguments about geometric relationships; understand measurable attributes of objects; and understand the units, systems, and process of measurement. Investigate conjectures and solve problems involving two-dimensional objects represented with Cartesian coordinates. Solve problems that involve measurement units and scale factors. Use geometric models to gain insights into, and answer questions in, other areas of mathematics. Core Idea 5: Data Analysis Select and use appropriate statistical methods to analyze data and understand and apply basic concepts of probability. Understand the relationship between two sets of data (bivariate), display such data in a scatterplot, and describe trends and shape of the plot including correlations (positive, negative, or no) and lines of best fit. Make inferences based on the data and evaluate the validity of conclusions drawn. Compute and interpret the expected value of random variables in simple cases. Understand the concepts of conditional probability and independent events and compute the probability of a compound event.