• Graphs and charts can be used to identify patterns in data. (6-8)

• Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data. (9-12)
  • Analyze data using computational models in order to make valid and reliable scientific claims. (9-12)

• Modeling in 6–8 builds on K–5 and progresses to developing, using and revising models to describe, test, and predict more abstract phenomena and design systems. (6-8)
  • Develop and use a model to describe phenomena. (6-8)
• Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)
  • Use a model to provide mechanistic accounts of phenomena. (9-12)

• Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)
  • Create or revise a simulation of a phenomenon, designed device, process, or system. (9-12)
  • Use mathematical or computational representations of phenomena to describe explanations. (9-12)

• Analyzing data in 9–12 builds on K–8 and progresses to introducing more detailed statistical analysis, the comparison of data sets for consistency, and the use of models to generate and analyze data. (9-12)

• Modeling in 6–8 builds on K–5 and progresses to developing, using and revising models to describe, test, and predict more abstract phenomena and design systems. (6-8)
• Modeling in 9–12 builds on K–8 and progresses to using, synthesizing, and developing models to predict and show relationships among variables between systems and their components in the natural and designed worlds. (9-12)

• Mathematical and computational thinking at the 9–12 level builds on K–8 and progresses to using algebraic thinking and analysis, a range of linear and nonlinear functions including trigonometric functions, exponentials and logarithms, and computational tools for statistical analysis to analyze, represent, and model data. Simple computational simulations are created and used based on mathematical models of basic assumptions. (9-12)

• 6-8: 4B/M3. Everything on or anywhere near the earth is pulled toward the earth's center by gravitational force.

• 9-12: 4G/H1. Gravitational force is an attraction between masses. The strength of the force is proportional to the masses and weakens rapidly with increasing distance between them.

• 6-8: 11B/M1. Models are often used to think about processes that happen too slowly, too quickly, or on too small a scale to observe directly. They are also used for processes that are too vast, too complex, or too dangerous to study.
• 6-8: 11B/M2. Mathematical models can be displayed on a computer and then modified to see what happens.

• A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

• A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

• F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

We like the simplicity of this model for introducing free fall and gravitational acceleration. Students can control the initial height, set initial velocity from -20 to 20 m/s and change the gravitational constant. The free fall is displayed as a motion diagram, while graphs are simultaneously displayed showing position, velocity, and acceleration vs. time.

• Physical Sciences K-8 Modeling Motion Unit
• Physics First Modeling Motion Unit
• Conceptual Physics Modeling Motion Unit
• Algebra-Based Physics Modeling Motion Unit
• AP/Calculus-Based Physics Modeling Motion Unit