Standard 7: Computation and Estimation

In grades 5-8, the mathematics curriculum should develop the concepts underlying computation and estimation in various contexts so that students can:

• Compute with whole numbers, fractions, decimals, integers, and rational numbers

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 3-5, page 290
Add, subtract, multiply, and divide whole numbers mentally, on paper, and with a calculator.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 6-8, page 291
Use ratios and proportions, including constant rates, in appropriate problems.
 

• Develop, analyze, and explain procedures for computation and techniques for estimation

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 3-5, page 290
State the purpose of each step in a calculation.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 3-5, page 296
Make sketches to aid in explaining procedures or ideas.

Benchmarks 12D (Habits of Mind: Communication Skills)
Grades 3-5, page 296
Write instructions that others can follow in carrying out a procedure.
 

• Develop, analyze, and explain methods for solving proportions

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 6-8, page 291
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.

 
• Select and use an appropriate method for computing from among mental arithmetic, paper-and-pencil, calculator, and computer methods

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 3-5, page 290
Read and follow step-by-step instructions in a calculator or computer manual when learning new procedures.

Benchmarks 12C (Habits of Mind: Manipulation and Observation)
Grades 3-5, page 290
Use calculators to determine area and volume from linear dimensions, aggregate amounts of area, volume, weight, time, and cost, and find the difference between two quantities of anything.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 6-8, page 291
Insert instructions into computer spreadsheet cells to program arithmetic calculations.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 6-8, page 291
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.

 
• Use computation, estimation, and proportions to solve problems

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 6-8, page 291
Estimate distances and travel times from maps and the actual size of objects from scale drawings.

Benchmarks 12C (Habits of Mind: Manipulation and Observation)
Grades 6-8, page 294
Use calculators to compare amounts proportionally.
 

• Use estimation to check the reasonableness of results

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Grades 3-5, page 290
Judge whether measurements and computations of quantities such as length, area, volume, weight, or time are reasonable in a familiar context by comparing them to typical values.