- 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.