Highly Recommended
Like all our Science Reasoning Center activities, the completion of the Modeling Roller Coasters activity requires that a student use provided information about a phenomenon, experiment, or data presentation to answer questions. Three of our five parts involve the use of such information. This information is accessible by tapping on the small thumbnails found on the bottom right of every question. However, it may be considerably easier to have a printed copy of this information or to display the information in a separate browser window. You can access this information from this page

The Standards
The Modeling Roller Coasters In an NGSS-inspired task in which students are presented numerous question types that target their ability to develop and use energy models to explain how energy is transformed between kinetic and potential energy. Exercises within the task include three Matching Pair exercises, three Paragraph Completion exercises, a Ranking Task exercise, a Table Completion exercise, and a Law Breaker exercise.

Modeling Roller Coasters consists of five parts. Each part involves a different type of skill or understanding. Collectively, the five parts were designed to address the following NGSS performance expectation:

HS-PS3-2:
Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative positions of particles (objects).

As a whole, the questions in this task address a wide collection of disciplinary core idea (DCI), crosscutting concepts (CCC), and science and engineering practices (SEP). There are 33 questions (many multi-part) organized into 15 Question Groups and spread across the five activities. Each question is either a 2D or (preferrably) a 3D question. That is, the task of answering the question requires that the student utilize at least two of the three dimensions of the NGSS science standards - a DCI, a CCC, and/or an SEP.

The following DCI, SEPs, and CCCs are addressed at some point within Modeling Roller Coasters:

DCI:  PS3.A: Definitions of Energy
• 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.
• At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy.
• These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration (relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space.

SEP 2.3:  Developing and Using Models
Develop, revise, and/or use a model based on evidence to illustrate and/or predict the relationships between systems or between components of a system.

SEP 2.6:  Developing and Using Models
Develop and/or use a model (including mathematical and computational) to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems.

SEP 5.3: Using Mathematics and Computational Thinking
Use mathematical, computational, and/or algorithmic representations of phenomena or design solutions to describe and/or support claims and/or explanations.

SEP 6.4: Constructing Explanations and Designing Solutions
Apply scientific reasoning, theory, and/or models to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion.

CCC 1.2Patterns
Empirical evidence is needed to identify patterns.

CCC 3.1: Scale, Proportion, and Quantity
The significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs.

CCC 3.2: Scale, Proportion, and Quantity
Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth).

CCC 5.4: Energy and Matter
Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems.

Here is our NGSS-based analysis of each individual activity of the Modeling Roller Coasters Science Reasoning task. The core ideas, crosscutting concepts, and science and engineering practices that we reference in our analysis are numbered for convenience. You can cross-reference the specific notations that we have used with the listings found on the following pages:

#### Part 1: Matching Energy Pairs

This activity consists of three matching pair exercises. In each exercise, students are given eight words or phrases on a grid and must group them into pairs based upon similarity of meaning. They are given instant feedback each time they match a pair. If they mismatch a pair of words or phrases on any of the three exercises, the grid for that exercise resets and students must begin again from the beginning without penalty. Students earn the Trophy for this activity once they successfully complete all three matching pair exercises.

NGSS Claim Statement: Apply scientific ideas about the conservation of energy to explain how energy is transferred into, out of, and within a system.

 Target DCI(s) Target SEP(s) Target CCC(s) Definitions of Energy PS3.A 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. At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration (relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space. Constructing Explanations and Designing Solutions SEP 6.4 Apply scientific reasoning, theory, and/or models to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion. Energy and Matter CCC 5.4 Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems.

#### Part 2: Energy Charts

This activity consists of 12 forced-choice questions organized into four Question Groups. Students are presented a roller coaster design with four labeled locations along the design. An accurate energy bar chart or an energy pie chart is provided for one of the locations. Bar charts or pie charts are proposed for the other three locations. Two are accurate and one is not. They must determine which one is not accurate. Students earn the trophy for this activity once they have accurately completed all four Question Groups.

NGSS Claim StatementAnalyze and use energy models based on evidence to identify a diagram that is inconsistent with other models and/or does not follow the conservation of energy principle.

 Target DCI(s) Target SEP(s) Target CCC(s) Definitions of Energy PS3.A 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. At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. ​ These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration (relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space. Developing and Using Models SEP 2.3 Develop, revise, and/or use a model based on evidence to illustrate and/or predict the relationships between systems or between components of a system. Energy and Matter CCC 5.4 Energy cannot be created or destroyed—it only moves between one place and another place, between objects and/or fields, or between systems.

#### Part 3: Predicting Energy Values

This activity requires that students complete a table of energy values for four locations along a roller coaster track. Given mass, height, and speeds, they perform calculations of kinetic energy, potential energy, and total mechanical energy. They are provided immediate feedback to their answers and can correct wrong answers an unlimited number of times. They receive the trophy once the table is accurately completed.

NGSS Claim StatementUse algebraic thinking and a mathematical model of conservation of energy to predict how changes in one variable affects another.

 Target DCI(s) Target SEP(s) Target CCC(s) Definitions of Energy PS3.A 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. At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. ​ These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration (relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space. Developing and Using Models SEP 2.3 Develop and/or use a model (including mathematical and computational) to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems. Scale, Proportion, and Quantity CCC 3.2 Algebraic thinking is used to examine scientific data and predict the effect of a change in one variable on another (e.g., linear growth vs. exponential growth).

This activity consists of eight forced-choice questions organized into four Question Groups. Students are provided two diagrams of two different-massed cars descending a hill between two different inital and final heights. They must use relative numbers to rank the kinetic energy, potential energy, total mechanical energy, and speeds for four different locations along the two hills. Students earn the Trophy for this activity once they demonstrate mastery of all four Question Groups.

NGSS Claim StatementUse mathematical models of mechanical energy to rank various quantities related to energy its conservation

 Target DCI(s) Target SEP(s) Target CCC(s) Definitions of Energy PS3.A 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. At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. ​ These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration (relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space. Using Mathematics and Computational Thinking SEP 5.3 Use mathematical, computational, and/or algorithmic representations of phenomena or design solutions to describe and/or support claims and/or explanations. Patterns CCC 1.2 Empirical evidence is needed to identify patterns.

#### Part 5: Looking a Bit Closer

This activity includes three different paragraph completion exercises. Students select words and phrases from a word bank to complete a paragraph associated with energy from a macroscopic and microscopic perspective. Students earn the Trophy for this activity once they accurate complete all three paragraphs.

NGSS Claim StatementApply models to construct explanations that the energy of a system can be better understood at the microscopes scale in terms of the motion of particles and through the relative position of particles which can be thought of as stored in fields.

 Target DCI(s) Target SEP(s) Target CCC(s) Definitions of Energy PS3.A 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. At the macroscopic scale, energy manifests itself in multiple ways, such as in motion, sound, light, and thermal energy. ​ These relationships are better understood at the microscopic scale, at which all of the different manifestations of energy can be modeled as a combination of energy associated with the motion of particles and energy associated with the configuration (relative position of the particles). In some cases the relative position energy can be thought of as stored in fields (which mediate interactions between particles). This last concept includes radiation, a phenomenon in which energy stored in fields moves across space. Constructing Explanations and Designing Solutions SEP 6.4 Apply scientific reasoning, theory, and/or models to link evidence to the claims to assess the extent to which the reasoning and data support the explanation or conclusion. Scale, Proportion, and Quantity CCC 3.1 The significance of a phenomenon is dependent on the scale, proportion, and quantity at which it occurs.

Complementary and Similar Resources
The following resources at The Physics Classroom website complement the Modeling Roller Coasters Science Reasoning Activity. Teachers may find them useful for supporting students and/or as components of lesson plans and unit plans.

The Physics Classroom Tutorial, Work, Energy and Power Chapter

Physics Video Tutorial, Work, Energy, and Power: Mechanical Energy Conservation

Physics Video Tutorial, Work, Energy, and Power: Force and System Analysis

Physics Interactives, Work and Energy: Roller Coaster Model

Physics Interactives, Work and Energy: It's All Uphill

Physics Interactives, Work and Energy: Chart That Motion

Concept Builders, Work and Energy: Words and Charts

Concept Builders, Work and Energy: LOL Charts

Concept Builders, Work and Energy: Energy Analysis 1

Minds On Physics, Work and Energy Module: Mission WE6, Energy Bar Charts

Minds On Physics, Work and Energy Module: Mission WE8, Energy Analysis

Minds On Physics, Work and Energy Module: Mission WE9, Work and Energy Conversions

Minds On Physics, Work and Energy Module: Mission WE9, Work and Energy Analysis

The Calculator Pad, Work, Energy, and Power: Problem Sets WE12 - WE19