New York

6 Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning.

• 1 Through systems thinking, people can recognize the commonalities that exist among all systems and how parts of a system interrelate and combine to perform specific functions.

  • 1.1 Describe the differences between dynamic systems and organizational systems.

  • 1.2 Describe the differences and similarities among engineering systems, natural systems, and social systems.

  • 1.3 Describe the differences between open-and closed-loop systems.

  • 1.4 Describe how the output from one part of a system (which can include material, energy, or information) can become the input to other parts.

• 2 Models are simplified representations of objects, structures, or systems used in analysis, explanation, interpretation, or design.

  • 2.1 Select an appropriate model to begin the search for answers or solutions to a question or problem.

  • 2.2 Use models to study processes that cannot be studied directly (e.g., when the real process is too slow, too fast, or too dangerous for direct observation).

    • Interpret ball-and-stick models (5-F.1)
    • Match chemical formulas to ball-and-stick models (5-F.2)
    • Complete chemical formulas for ball-and-stick models (5-F.3)
    • Read and construct animal life cycle diagrams (5-K.1)
    • Compare animal life cycles (5-K.2)
    • Complete chemical formulas for ball-and-stick models (6-E.4)
    • Identify chemical formulas for ball-and-stick models (7-E.3)
    • Identify chemical formulas for ball-and-stick models (8-E.3)

  • 2.3 Demonstrate the effectiveness of different models to represent the same thing and the same model to represent different things.

• 3 The grouping of magnitudes of size, time, frequency, and pressures or other units of measurement into a series of relative order provides a useful way to deal with the immense range and the changes in scale that affect the behavior and design of systems.

  • 3.1 Cite examples of how different aspects of natural and designed systems change at different rates with changes in scale.

  • 3.2 Use powers of ten notation to represent very small and very large numbers.

• 4 Equilibrium is a state of stability due either to a lack of change (static equilibrium) or a balance between opposing forces (dynamic equilibrium).

  • 4.1 Describe how feedback mechanisms are used in both designed and natural systems to keep changes within desired limits.

  • 4.2 Describe changes within equilibrium cycles in terms of frequency or cycle length and determine the highest and lowest values and when they occur.

• 5 Identifying patterns of change is necessary for making predictions about future behavior and conditions.

  • 5.1 Use simple linear equations to represent how a parameter changes with time.

  • 5.2 Observe patterns of change in trends or cycles and make predictions on what might happen in the future.

    • Use climate data to make predictions (5-T.5)

• 6 In order to arrive at the best solution that meets criteria within constraints, it is often necessary to make trade-offs.

  • 6.1 Determine the criteria and constraints and make trade-offs to determine the best decision.

  • 6.2 Use graphs of information for a decision-making problem to determine the optimum solution.