• Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object. (MS-PS2-2)

• Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object. (MS-PS3-1)

• Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions. (MS-ETS1-1)
• Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem. (MS-ETS1-2)
• Analyze data from tests to determine similarities and differences among several design solutions to identify the best characteristics of each that can be combined into a new solution to better meet the criteria for success. (MS-ETS1-3)
• Develop a model to generate data for iterative testing and modification of a proposed object, tool, or process such that an optimal design can be achieved. (MS-ETS1-4)

• The motion of an object is determined by the sum of the forces acting on it; if the total force on the object is not zero, its motion will change. The greater the mass of the object, the greater the force needed to achieve the same change in motion. For any given object, a larger force causes a larger change in motion. (6-8)

• Motion energy is properly called kinetic energy; it is proportional to the mass of the moving object and grows with the square of its speed. (6-8)
• A system of objects may also contain stored (potential) energy, depending on their relative positions. (6-8)
• Energy is a quantitative property of a system that depends on the motion and interactions of matter and radiation within that system. That there is a single quantity called energy is due to the fact that a system's total energy is conserved, even as, within the system, energy is continually transferred from one object to another and between its various possible forms. (9-12)

• When the motion energy of an object changes, there is inevitably some other change in energy at the same time. (6-8)

• When two objects interact, each one exerts a force on the other that can cause energy to be transferred to or from the object. (6-8)

• The more precisely a design task's criteria and constraints can be defined, the more likely it is that the designed solution will be successful. Specification of constraints includes consideration of scientific principles and other relevant knowledge that is likely to limit possible solutions. (6-8)

• A solution needs to be tested, and then modified on the basis of the test results, in order to improve it. (6-8)
• Sometimes parts of different solutions can be combined to create a solution that is better than any of its predecessors. (6-8)
• Models of all kinds are important for testing solutions. (6-8)
• When evaluating solutions it is important to take into account a range of constraints including cost, safety, reliability and aesthetics and to consider social, cultural and environmental impacts. (9-12)

• Although one design may not perform the best across all tests, identifying the characteristics of the design that performed the best in each test can provide useful information for the redesign process—that is, some of the characteristics may be incorporated into the new design. (6-8)

• Analyzing data in 6–8 builds on K–5 and progresses to extending quantitative analysis to investigations, distinguishing between correlation and causation, and basic statistical techniques of data and error analysis. (6-8)
  • Analyze and interpret data to determine similarities and differences in findings. (6-8)

• Asking questions and defining problems in grades 6–8 builds from grades K–5 experiences and progresses to specifying relationships between variables, and clarifying arguments and models. (6-8)
  • Define a design problem that can be solved through the development of an object, tool, process or system and includes multiple criteria and constraints, including scientific knowledge that may limit possible solutions. (6-8)

• Constructing explanations and designing solutions in 6–8 builds on K–5 experiences and progresses to include constructing explanations and designing solutions supported by multiple sources of evidence consistent with scientific ideas, principles, and theories. (6-8)
  • Undertake a design project, engaging in the design cycle, to construct and/or implement a solution that meets specific design criteria and constraints. (6-8)
  • Apply scientific ideas or principles to design, construct, and test a design of an object, tool, process or system. (6-8)

• Planning and carrying out investigations to answer questions or test solutions to problems in 6–8 builds on K–5 experiences and progresses to include investigations that use multiple variables and provide evidence to support explanations or design solutions. (6-8)
  • Collect data to produce data to serve as the basis for evidence to answer scientific questions or test design solutions under a range of conditions. (6-8)

• 6-8: 3A/M3. Engineers, architects, and others who engage in design and technology use scientific knowledge to solve practical problems. They also usually have to take human values and limitations into account.
• 9-12: 3A/H4. Engineers use knowledge of science and technology, together with strategies of design, to solve practical problems. Scientific knowledge provides a means of estimating what the behavior of things will be even before they are made. Moreover, science often suggests new kinds of behavior that had not even been imagined before, and so leads to new technologies.

• 6-8: 3B/M3a. Almost all control systems have inputs, outputs, and feedback.
• 6-8: 3B/M4a. Systems fail because they have faulty or poorly matched parts, are used in ways that exceed what was intended by the design, or were poorly designed to begin with.
• 6-8: 3B/M4b. The most common ways to prevent failure are pretesting of parts and procedures, overdesign, and redundancy.

• 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/H1. Although the various forms of energy appear very different, each can be measured in a way that makes it possible to keep track of how much of one form is converted into another. Whenever the amount of energy in one place diminishes, the amount in other places or forms increases by the same amount.
• 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.

• 6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.
• 6-8: 4F/M3b. If a force acts towards a single center, the object's path may curve into an orbit around the center.
• 9-12: 4F/H7. In most familiar situations, frictional forces complicate the description of motion, although the basic principles still apply.

• 6-8: 8B/M2. Manufacturing usually involves a series of steps, such as designing a product, obtaining and preparing raw materials, processing the materials mechanically or chemically, and assembling the product. All steps may occur at a single location or may occur at different locations.

• 6-8: 11A/M2. Thinking about things as systems means looking for how every part relates to others. The output from one part of a system (which can include material, energy, or information) can become the input to other parts. Such feedback can serve to control what goes on in the system as a whole.
• 9-12: 11A/H1. A system usually has some properties that are different from those of its parts, but appear because of the interaction of those parts.
• 9-12: 11A/H2. 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 output are expected to be.
• 9-12: 11A/H4. Even in some very simple systems, it may not always be possible to predict accurately the result of changing some part or connection.

• 6-8: 12D/M6. Present a brief scientific explanation orally or in writing that includes a claim and the evidence and reasoning that supports the claim.

A four-day lesson that explores the same physics concepts as roller coaster design, but breaks the learning into two distinct segments to ensure that beginners understand the basics. In Part I, kids build a very simple curved track to explore kinetic and potential energy for a gumball moving downhill. Part II becomes more complex: build and test a gumball machine with loops and specific design constraints.

• Physical Sciences K-8 The Case of Roller Coasters Unit
• Physics First The Case of Roller Coasters Unit
• Conceptual Physics The Case of Roller Coasters Unit