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A. Systems
By the end of 12th grade, students should know that:
- 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.
- The successful operation of a designed system usually involves feedback.
- Even in some very simple systems, it may not always be possible to predict accurately the result of changing some part or connection.
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B. Models
By the end of 12th grade, students should know that:
- 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.
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C. Constancy and Change
By the end of 12th grade, students should know that:
- A system in equilibrium may return to the same state of equilibrium if the disturbances it experiences are small.
- Along with the theory of atoms, the concept of the conservation of matter led to revolutionary advances in chemical science.
- Things can change in detail but remain the same in general (the players change, but the team remains; cells are replaced, but the organism remains).
- Graphs and equations are useful (and often equivalent) ways for depicting and analyzing patterns of change.
- In many physical, biological, and social systems, changes in one direction tend to produce opposing (but somewhat delayed) influences, leading to repetitive cycles of behavior.
- In evolutionary change, the present arises from the materials and forms of the past, more or less gradually, and in ways that can be explained.
- Most systems above the molecular level involve so many parts and forces and are so sensitive to tiny differences in conditions that their precise behavior is unpredictable, even if all the rules for change are known.
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D. Scale
By the end of 12th grade, students should know that:
- Representing large numbers in terms of powers of ten makes it easier to think about them and to compare things that are greatly different.
- Because different properties are not affected to the same degree by changes in scale, large changes in scale typically change the way that things work in physical, biological, or social systems.
- As the number of parts of a system increases, the number of possible interactions between pairs of parts increases much more rapidly.
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