• compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals;
• select and use appropriate forms of rational numbers to solve real-life problems including those involving proportional relationships;
• approximate (mentally [and with calculators]) the value of irrational numbers as they arise from problem situations (such as fÎ, ã2);
• express numbers in scientific notation, including negative exponents, in appropriate problem situations.
• select appropriate operations to solve problems involving rational numbers and justify the selections;
• use appropriate operations to solve problems involving rational numbers in problem situations;
• evaluate a solution for reasonableness;
• use multiplication by a constant factor (unit rate) to represent proportional relationships.
• compare and contrast proportional and non-proportional linear relationships;
• estimate and find solutions to application problems involving percents and other proportional relationships such as similarity and rates.
• generate a different representation of data given another representation of data (such as a table, graph, equation, or verbal description).
• predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations;
• find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change).
• generate similar figures using dilations including enlargements and reductions;
• graph dilations, reflections, and translations on a coordinate plane.
• draw three-dimensional figures from different perspectives;
• use geometric concepts and properties to solve problems in fields such as art and architecture;
• use pictures or models to demonstrate the Pythagorean Theorem;
• locate and name points on a coordinate plane using ordered pairs of rational numbers.
• find the probabilities of dependent and independent events;
• use theoretical probabilities and experimental results to make predictions and decisions.
• select the appropriate measure of central tendency or range to describe a set of data and justify the choice for a particular situation;
• draw conclusions and make predictions by analyzing trends in scatterplots;
• select and use an appropriate representation for presenting and displaying relationships among collected data, including line plots, line graphs, [stem and leaf plots,] circle graphs, bar graphs, box and whisker plots, histograms, and Venn diagrams, [with and] without the use of technology.
• evaluate methods of sampling to determine validity of an inference made from a set of data;
• recognize misuses of graphical or numerical information and evaluate predictions and conclusions based on data analysis.
• identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines, and with other mathematical topics;
• use a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness;
• select or develop an appropriate problem-solving strategy from a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.
• communicate mathematical ideas using language, efficient tools, appropriate units, and graphical, numerical, physical, or algebraic mathematical models.
• make conjectures from patterns or sets of examples and non-examples;
• validate his/her conclusions using mathematical properties and relationships.