- Core Idea 1: Number and Operations
- Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
- Develop meaning for percents greater than 100 and less than 1.
- Develop an understanding of large numbers and recognize and appropriately use exponential, scientific, and calculator notation.
- Understand and use the inverse relationships of squaring and finding square roots to simplify computations and solve problems.
- Demonstrate how and when to use the operations of exponents and roots.
- Compare and contrast the properties of rational and irrational numbers.
- Core Idea 2: Mathematical Reasoning
- Employ forms of mathematical reasoning and justification appropriate to the solution of a problem.
- Extract pertinent information from situations and determine what additional information is needed.
- Formulate conjectures and test them for validity.
- Invoke problem-solving strategies.
- Verify and interpret results of a problem.
- Use mathematical language in representations to make complex situations easier to understand.
- Core Idea 3: Algebra and Functions
- Understand relations and functions, analyze mathematical situations, and use models to solve problems involving quantity and change.
- Identify functions as linear or nonlinear, and contrast their properties from tables, graphs, or equations.
- Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.
- Recognize and generate equivalent forms of simple algebraic expressions and solve linear equations.
- Model and solve contextualized problems involving inequalities.
- Use graphs to analyze the nature of changes on quantities in linear relationships
- Recognize, represent and solve contextualized problems involving polynomials and their factors.
- Core Idea 4: Geometry and Measurement
- Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; apply transformations and use symmetry to analyze mathematical situations; and apply appropriate techniques, tools, and formulas to determine measurements.
- Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.
- Understand relationships among the angles, side lengths, perimeter, areas, and volumes of similar objects.
- Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
- Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.
- Core Idea 5: Data Analysis
- Formulate questions that can be addressed with data and collect, organize, analyze, and display relevant data to answer them.
- Formulate questions, design studies, and collect data about a characteristic shared by two populations or different characteristics within one population.
- Select, create, and use appropriate graphical representations of data, including box plots and scatterplots.
- Find, use, and interpret measures of center and spread, including interquartile range.
- Discuss and understand the correspondence between data sets and their graphical representations, especially box plots and scatterplots.
- Make conjectures about possible relationships between two characteristics of a population on the basis of scatterplots of the data, including correlations and approximate lines of fit.
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