NATIONAL STANDARDS

Benchmark 2061

1. The Nature of Science

B. Scientific Inquiry
- Sometimes, scientists can control conditions in order to obtain evidence. When that is not possible for practical or ethical reasons, they try to observe as wide a range of natural occurrences as possible to be able to discern patterns.

C. Scientific Enterprise
- Scientists can bring information, insights, and analytical skills to bear on matters of public concern. Scientists help people understand the likely causes of events and estimate their possible effects.

5. The Living Environment

A. Diversity of Life
- The variation of organisms within a species increases the likelihood that at least some members of the species will survive under changed environmental conditions.B. Heredity
- Some new gene combinations make little difference, some can produce organisms with new and perhaps enhanced capabilities, and some can be deleterious.D. Interdependence of Life
- Ecosystems can be reasonably stable over hundreds or thousands of years. As any population of organisms grows, it is held in check by one or more environmental factors: depletion of food, increased loss to increased numbers of predators, or parasites.E. Flow of Matter and Energy
- The amount of life any environment can support is limited by the available energy, water, oxygen, and minerals.F. Evolution of Life
- Natural selection provides the following mechanisms for evolution: some variation in heritable characteristics exists within every species, some of these give individuals an advantage over others in surviving and reproducing, and the advantaged offspring, in turn, are more likely than others to survive and reproduce.
- Natural selection leads to organisms that are well suited for survival in particular environments.

9. The Mathematical World

B. Symbolic Relationships
- In some cases, the more of something there is, the more rapidly it may change. In other cases, the rate of change of something depends on how much there is of something else.
- Any mathematical model, graphic or algebraic, is limited in how well it can represent how the world works.
- Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.D. Uncertainty
- A physical or mathematical model can be used to estimate the probability of real-world events.

11. Common Themes

A. Systems
- A system usually has some properties that are different from those of its parts, but appear because of the interaction of those parts.
- Understanding how things work and designing solutions to problems of almost any kind can be facilitated by systems analysis. In defining a system, it is important to specify its boundaries and subsystems, indicate its relation to other systems, and identify what its input and its output are expected to be.B. Models
- The basic idea of mathematical modeling is to find a mathematical relationship that behaves in the same ways as the objects or processes under investigation.
- Computers have greatly improved the power and use of mathematical models by performing computations that are very long, very complicated, or repetitive.
- The usefulness of a model can be tested by comparing its predictions to actual observations in the real world.C. Consistency and Change
- Graphs and equations are useful ways for depicting and analyzing patterns of change.
- In many physical, biological, and social systems, changes in one direction tend to produce opposing influences, leading to repetitive cycles of behavior.