Standard 14: Mathematical Structure

In grades 9-12, the mathematics curriculum should include the study of mathematical structure so that all students can:
• Compare and contrast the real number system and its various subsystems with regard to their structural characteristics
• Benchmarks 9A (The Mathematical World: Numbers)
Comparison of numbers of very different size can be made approximately by expressing them as nearest powers of 10.

Benchmarks 9A (The Mathematical World: Numbers)
When calculations are made with measurements, a small error in the measurements may lead to a large error in the results.

Benchmarks 9A (The Mathematical World: Numbers)
The effects of uncertainties in measurements on a computed result can be estimated.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Express and compare very small and very large numbers using powers-of-ten notation.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Trace the source of any large disparity between an estimate and the calculated answer.

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Recall immediately the relations among 10, 100, 1000, 1 million, and 1 billion (knowing, for example that 1 million is a thousand thousands).

Benchmarks 12B (Habits of Mind: Computation and Estimation)
Consider the possible effects of measurement errors on calculations.

• Understand the logic of algebraic procedures
• Benchmarks 9B (The Mathematical World: Symbolic Relationships)