Benchmark 12B: Habits of Mind - Computation and Estimation

• Find the mean and median of a set of data. (4 of 10)
• Standard 10-1, page 105, Grades 5-8
Systematically collect, organize, and describe data
• Estimate distances and travel times from maps and the actual size of objects from scale drawings. (5 of 10)
• Standard 7-6, page 94, Grades 5-8
Use computation, estimation, and proportions to solve problems
• Insert instructions into computer spreadsheet cells to program arithmetic calculations. (6 of 10)
• Standard 7-4, page 94, Grades 5-8
Select and use an appropriate method for computing from among mental arithmetic, paper-and-pencil, calculator, and computer methods

Standard 12-3 page 176, Grades 9-12
Develop and analyze algorithms

• Determine what unit (such as seconds, square inches, or dollars per tankful) an answer should be expressed in from the units of the inputs to the calculations, and be able to convert compound units (e.g., yen per dollar into dollar per yen, or miles/hour into feet/sec. (7 of 10)
• Standard 7-3, page 94, Grades 5-8
Develop, analyze, and explain methods for solving proportions

Standard 13-6, page 116, Grades 5-8
Develop the concepts of rates and other derived and indirect measurements

Standard 13-7, page 116, Grades 5-8
Develop formulas and procedures for determining measures to solve problems

• Decide what degree of precision is adequate and round off the result of calculator operations to enough significant figures to reasonably reflect those of the inputs. (8 of 10)
• Standard 12-1 page 57, Grades K-4
Develop concepts of fractions, mixed numbers, and decimals

Standard 12-2 page 57, Grades K-4
Develop number sense for fractions and decimals

Standard 7-4, page 94, Grades 5-8
Select and use an appropriate method for computing from among mental arithmetic, paper-and-pencil, calculator, and computer methods

• Estimate probabilities of outcomes in familiar situations, on the basis of history or the number of possible outcomes (10 of 10)
• Standard 11-4, page 109, Grades 5-8
Make predictions that are based on experimental or theoretical probabilities

Standard 11-5, page 109, Grades 5-8
Develop an appreciation for the pervasive use of probability in the real world

Standard 11-1 page 171, Grades 9-12
Use experimental or theoretical probability, as appropriate, to represent and solve problems involving uncertainty

Standard 12-4 page 176, Grades 9-12
Solve enumeration and finite probability problems

Standard 11-4 page 171, Grades 9-12
Create and interpret discrete probability distributions