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.