Mathematical Skills and Tools
 Elementary School The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, books, or other students, perhaps working to reconstruct a method; that is, the student: a Adds, subtracts, multiplies, and divides whole numbers correctly; that is: • knows single digit addition, subtraction, multiplication, and division facts; • adds and subtracts numbers with several digits; • multiplies and divides numbers with one or two digits; • multiplies and divides three digit numbers by one digit numbers. b Estimates numerically and spatially. c Measures length, area, perimeter, circumference, diameter, height, weight, and volume accurately in both the customary and metric systems. d Computes time (in hours and minutes) and money (in dollars and cents). e Refers to geometric shapes and terms correctly with concrete objects or drawings, including triangle, square, rectangle, side, edge, face, cube, point, line, perimeter, area, and circle; and refers with assistance to rhombus, parallelogram, quadrilateral, polygon, polyhedron, angle, vertex, volume, diameter, circumference, sphere, prism, and pyramid. f Uses +, -, x, ÷, /, , \$, ¢, %, and . (decimal point) correctly in number sentences and expressions. g Reads, creates, and represents data on line plots, charts, tables, diagrams, bar graphs, simple circle graphs, and coordinate graphs. h Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions; that is, uses measuring devices, graded appropriately for given situations, such as rulers (customary to the 1¼8 inch; metric to the millimeter), graph paper (customary to the inch or half-inch; metric to the centimeter), measuring cups (customary to the ounce; metric to the milliliter), and scales (customary to the pound or ounce; metric to the kilogram or gram).

 Middle School The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task (perhaps referring to notes, or books, perhaps working to reconstruct a method); that is, the student: a Computes accurately with arithmetic operations on rational numbers. b Knows and uses the correct order of operations for arithmetic computations. c Estimates numerically and spatially. d Measures length, area, volume, weight, time, and temperature accurately. e Refers to geometric shapes and terms correctly. f Uses equations, formulas, and simple algebraic notation appropriately. g Reads and organizes data on charts and graphs, including scatter plots, bar, line, and circle graphs, and Venn diagrams; calculates mean and median. h Uses recall, mental computations, pencil and paper, measuring devices, mathematics texts, manipulatives, calculators, computers, and advice from peers, as appropriate, to achieve solutions.

 High School The student demonstrates fluency with basic and important skills by using these skills accurately and automatically, and demonstrates practical competence and persistence with other skills by using them effectively to accomplish a task, perhaps referring to notes, or books, perhaps working to reconstruct a method; that is, the student: a Carries out numerical calculations and symbol manipulations effectively, using mental computations, pencil and paper, or other technological aids, as appropriate. b Uses a variety of methods to estimate the values, in appropriate units, of quantities met in applications, and rounds numbers used in applications to an appropriate degree of accuracy. c Evaluates and analyzes formulas and functions of many kinds, using both pencil and paper and more advanced technology. d Uses basic geometric terminology accurately, and deduces information about basic geometric figures in solving problems. e Makes and uses rough sketches, schematic diagrams, or precise scale diagrams to enhance a solution. f Uses the number line and Cartesian coordinates in the plane and in space. g Creates and interprets graphs of many kinds, such as function graphs, circle graphs, scatter plots, regression lines, and histograms. h Sets up and solves equations symbolically (when possible) and graphically. i Knows how to use algorithms in mathematics, such as the Euclidean Algorithm. j Uses technology to create graphs or spreadsheets that contribute to the understanding of a problem. k Writes a simple computer program to carry out a computation or simulation to be repeated many times. l Uses tools such as rulers, tapes, compasses, and protractors in solving problems. m Knows standard methods to solve basic problems and uses these methods in approaching more complex problems.