- Core Idea 1: Number and Operation
- Understand number systems, the meanings of operations, and ways of representing numbers, relationships, and number systems.
- Develop, analyze, and explain methods for solving problems involving proportional reasoning, such as scaling and finding equivalent ratios.
- Develop meaning of integers and represent and compare quantities with them.
- Understand the meaning and effects of operations with rational numbers.
- Understand and use the inverse relationships of a series of operations to simplify computations and solve problems.
- Develop and analyze algorithms for computing with rational numbers.
- Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with rational numbers.
- Develop and use strategies to estimate the results of rational number computations, and judge the reasonableness of results.
- Work flexibly with fractions, decimals, and percents to solve problems.
- Core Idea 2: Probability
- Apply and deepen their understanding of theoretical and empirical probability.
- Represent the sample space for simple and compound events in an organized way (table, diagram, organized list, and tree diagram) and express the theoretical probability of each outcome.
- Use data to estimate the probability of future events (e.g., batting averages or number of accidents per mile driven).
- Know the relationship between the probability of an event and its complement (i.e., if the probability of an event is P, then the probability of the event not occurring is 1 - P).
- Identify data that represent sampling errors and explain why the sample and the display might be biased.
- Core Idea 3: Algebra and Functions
- Understand relations and functions, analyze mathematical situations, and use models to solve problems involving quantity and change.
- Represent, analyze, and generalize a variety of functions including linear and simple exponential relationships.
- Relate and compare different forms of representation for a relationship including words, tables, graphs in the coordinate plane, and symbols.
- Express mathematical relationships using expressions and equations.
- Develop conceptual understanding of different uses of variables.
- Use symbolic algebra to represent situations to solve problems.
- Identify and describe situations with constant or varying rates of change and compare them.
- Core Idea 4: Geometry and Measurement
- Analyze characteristics and properties of two- and three-dimensional geometric shapes; develop mathematical arguments about geometric relationships; apply congruence and similarity to analyze mathematical situations; and apply appropriate techniques, tools, and formulas to determine measurements.
- Understand relationships among the angles, side lengths, perimeters, and areas of similar objects.
- Develop and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence and similarity.
- Solve problems involving similarity and scale factors, using proportional reasoning.
- Core Idea 5: Statistics
- Deepen their understanding of statistical methods used to display, analyze, compare, and interpret different data sets.
- Make predictions, justify conclusions that are based on data, and design studies to further investigate the predictions and conclusions.
- Construct the most appropriate graph, including frequency distribution, stem and leaf, and scatterplot, for a given set of data and justify the choice.
- Analyze data, including finding measures of center and spread presented in a frequency distribution.
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