• 6-8: 4E/M2. Energy can be transferred from one system to another (or from a system to its environment) in different ways: 1) thermally, when a warmer object is in contact with a cooler one; 2) mechanically, when two objects push or pull on each other over a distance; 3) electrically, when an electrical source such as a battery or generator is connected in a complete circuit to an electrical device; or 4) by electromagnetic waves.
• 6-8: 4E/M4. Energy appears in different forms and can be transformed within a system. Motion energy is associated with the speed of an object. Thermal energy is associated with the temperature of an object. Gravitational energy is associated with the height of an object above a reference point. Elastic energy is associated with the stretching or compressing of an elastic object. Chemical energy is associated with the composition of a substance. Electrical energy is associated with an electric current in a circuit. Light energy is associated with the frequency of electromagnetic waves.
• 9-12: 4E/H9. Many forms of energy can be considered to be either kinetic energy, which is the energy of motion, or potential energy, which depends on the separation between mutually attracting or repelling objects.

• 9-12: 4F/H1. The change in motion (direction or speed) of an object is proportional to the applied force and inversely proportional to the mass.
• 9-12: 4F/H4. Whenever one thing exerts a force on another, an equal amount of force is exerted back on it.

• 6-8: 11B/M4. Simulations are often useful in modeling events and processes.
• 9-12: 11B/H1a. A mathematical model uses rules and relationships to describe and predict objects and events in the real world.

• 6-8: 12E/M5b. Notice and criticize the reasoning in arguments in which the claims are not consistent with the evidence given.

• 7.RP.2.b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

• 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

• F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^?
• F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
• F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context.

• 5-8: Motion & Forces
• 9-12: Motions & Forces
• 9-12: Conservation of Energy & Increase in Disorder

This two-hour activity was created to accompany the PhET simulation Masses & Springs. In the first lesson, students use the simulation to explore how displacement of a spring is mathematically related to the load applied to it. On Day 2, learners analyze the energy interactions by observing distribution and transfer of kinetic, elastic potential, and gravitational potential energy. Includes explicit directions for use of the simulation, homework problems, and answer key. Note: Only registered users have access to the PhET teacher-contributed materials, but registration is free and easy.

• Conceptual Physics Conservation of Energy and Forces on a Spring Unit
• Algebra-Based Physics Conservation of Energy and Forces on a Spring Unit
• AP/Calculus-Based Physics Conservation of Energy and Forces on a Spring Unit