- demonstrating an understanding of the real number system;
- demonstrating that a number can be expressed in many forms, and selecting an appropriate form for a given situation (e.g., fractions, decimals, percents, and scientific notation);
- using number sense to estimate and determine if solutions are reasonable;
- determining whether an exact or approximate answer is necessary;
- selecting and using appropriate computational methods and tools for given situations (e.g., estimation, or exact computation using mental arithmetic, calculator, symbolic manipulator, or paper and pencil);
- applying ratios and proportional thinking in a variety of situations (e.g., finding a missing term of a proportion);
- justifying reasonableness of solutions and verifying results.
- demonstrating the ability to translate real-world situations (e.g., distance versus time relationships, population growth, growth functions for diseases, growth of minimum wage, auto insurance tables) into algebraic expressions, equations, and inequalities and vice versa;
- recognizing the relationship between operations involving real numbers and operations involving algebraic expressions;
- using tables and graphs as tools to interpret algebraic expressions, equations, and inequalities;
- solving algebraic equations and inequalities using a variety of techniques with the appropriate tools (e.g., hand-held manipulatives, graphing calculator, symbolic manipulator, or pencil and paper).
- selecting and using appropriate units, techniques, and tools to measure quantities in order to achieve specified degrees of precision, accuracy, and error (or tolerance) of measurements;
- demonstrating an intuitive sense of measurement (e.g., estimating and determining reasonableness of results as related to area, volume, mass, rate, and distance);
- estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures, surface area and volume of solids presented in real-world situations);
- demonstrating the concept of measurement as it applies to real-world experiences.
- identifying, describing, comparing, constructing, and classifying geometric figures in two and three dimensions using technology where appropriate to explore and make conjectures about geometric concepts and figures;
- representing and solving problems using geometric models and the properties of those models (e.g., Pythagorean Theorem or formulas involving radius, diameter, and circumference);
- solving problems using coordinate methods, as well as synthetic and transformational methods (e.g., transform on a coordinate plane a design found in real-life situations);
- using inductive reasoning to predict, discover, and apply geometric properties and relationships (e.g., patty paper constructions, sum of the angles in a polygon);
- classifying figures in terms of congruence and similarity and applying these relationships;
- demonstrating deductive reasoning and mathematical justification (e.g., oral explanation, informal proof, and paragraph proof).
- designing and conducting statistical experiments that involve the collection, representation, and analysis of data in various forms (Analysis should reflect an understanding of factors such as: sampling, bias, accuracy, and reasonableness of data.);
- recognizing data that relate two variables as linear, exponential, or otherwise in nature (e.g., match a data set, linear or non-linear, to a graph and vice versa);
- using simulations to estimate probabilities (e.g., lists and tree diagrams);
- demonstrating an understanding of the calculation of finite probabilities using permutations, combinations, sample spaces, and geometric figures;
- recognizing events as dependent or independent in nature and demonstrating techniques for computing multiple-event probabilities;
- recognizing and answering questions about data that are normally or non-normally distributed;
- making inferences from data that are organized in charts, tables, and graphs (e.g., pictograph; bar, line, or circle graph; stem-and-leaf plot or scatter plot);
- using logical thinking procedures, such as flow charts, Venn diagrams, and truth tables;
- using discrete math to model real-life situations (e.g., fair games or elections, map coloring).
- modeling the concepts of variables, functions, and relations as they occur in the real world and using the appropriate notation and terminology;
- translating between tabular, symbolic, or graphic representations of functions;
- recognizing behavior of families of elementary functions, such as polynomial, trigonometric, and exponential functions, and, where appropriate, using graphing technologies to represent them;
- analyzing the effects of changes in parameters (e.g., coefficients and constants) on the graphs of functions, using technology whenever possible;
- analyzing real-world relationships that can be modeled by elementary functions.

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