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Core Ideas
- Core Idea 1: Functions
- Understand patterns, relations, and functions.
- Understand and perform transformations on functions.
- Understand and compare the properties of classes of functions, including linear, quadratic, reciprocal, and exponential functions.
- Identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships.
- Core Idea 2: Mathematical Reasoning and Proofs
- Employ forms of mathematical reasoning and proof appropriate to the solution of the problem at hand, including deductive and inductive reasoning, making and testing conjectures and using counter examples and indirect proof.
- Show mathematical reasoning in solutions in a variety of ways, including words, numbers, symbols, pictures, charts, graphs tables, diagrams, and models.
- Explain the logic inherent in a solution process.
- Identify, formulate, and confirm conjectures.
- Use synthetic, coordinate, and /or transformational geometry in direct or indirect proof of geometric relationships.
- Establish the validity of geometric conjectures using deduction; prove theorems, and critique arguments made by others.
- Core Idea 3: Algebraic Properties and Representations
- Represent and analyze mathematical situations and structures using algebraic symbols.
- Develop fluency in operations with real numbers and simple vectors and matrices.
- Solve equations involving radicals and exponents in contextualized problems such as use of Pythagorean Theorem.
- Recognize and use equivalent graphical and algebraic representations of lines with their geometric characteristics, such as slope, intercepts, parallelism, and perpendicularity.
- Use coordinate geometry to find measures of geometric figures
- Core Idea 4: Geometry and Measurement
- Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; and apply appropriate techniques, tools, and formulas to determine measurements.
- Understand and use formulas for the area, surface area, and volume of geometric figures, including spheres and cylinders.
- Explore relationships among classes of two- and three-dimensional geometric objects, make and test conjectures about them, and solve problems involving them.
- Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, and function notation.
- Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools.
- Visualize three-dimensional objects from different perspectives and analyze their cross-sections.
- Core Idea 5: Data Analysis
- Select and use appropriate statistical methods to analyze data and understand and apply concepts of probability.
- Find, use, and interpret measures of center and spread, including standard deviation.
- For bivariate measurement data, be able to display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools.
- Evaluate studies that are based on data by examining the design of the study, the appropriateness of the data analysis, and the validity of conclusions.
- Apply the concept of expected value in problem situations.
- Use and interpret problems involving probability in terms of areas of geometric figures.
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Tools for Educators