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.