published by
the Integrated Teaching and Learning Program: Teach Engineering
supported by
the National Science Foundation

This is a multi-day instructional unit for middle school science on kinetic and potential energy. Through investigations of waterwheels, roller coasters, bouncing balls, and a pendulum, students get a feel for energy transformation in a mechanical interaction and build accurate concepts about the Law of Conservation of Energy. The unit also introduces static and kinetic friction, drag, elastic/inelastic collision, and students learn to calculate frictional force. Lessons are all aligned to AAAS Benchmarks, and may be conducted separately or in concert.

Editor's Note: Understanding mechanical energy is at the root of many engineering applications in our world. This set of lessons provides inquiry-based exploration, while also introducing simple calculations in the context of real-life situations. It is developmentally appropriate for middle school, but will definitely challenge students.

TeachEngineering is a Pathway project of the National Science Digital Library. It provides a large collection of teacher-tested, research-based content for K-12 teachers to connect real-world experiences with curricular content.

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.

4. The Physical Setting

4E. Energy Transformations

6-8: 4E/M1. Whenever energy appears in one place, it must have disappeared from another. Whenever energy is lost from somewhere, it must have gone somewhere else. Sometimes when energy appears to be lost, it actually has been transferred to a system that is so large that the effect of the transferred energy is imperceptible.

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/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.

4F. Motion

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H4. Whenever one thing exerts a force on another, an equal amount of force is exerted back on it.

9-12: 4F/H7. In most familiar situations, frictional forces complicate the description of motion, although the basic principles still apply.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

9. The Mathematical World

9B. Symbolic Relationships

6-8: 9B/M2. Rates of change can be computed from differences in magnitudes and vice versa.

6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.

9-12: 9B/H1b. Sometimes the rate of change of something depends on how much there is of something else (as the rate of change of speed is proportional to the amount of force acting).

11. Common Themes

11A. Systems

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.

Next Generation Science Standards

Motion and Stability: Forces and Interactions (MS-PS2)

Students who demonstrate understanding can: (6-8)

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)

Energy (MS-PS3)

Students who demonstrate understanding can: (6-8)

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)

Construct, use, and present arguments to support the claim that when the motion energy of an object changes, energy is transferred to or from the object. (MS-PS3-5)

Engineering Design (MS-ETS1)

Students who demonstrate understanding can: (6-8)

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)

Disciplinary Core Ideas (K-12)

Forces and Motion (PS2.A)

The patterns of an object's motion in various situations can be observed and measured; when that past motion exhibits a regular pattern, future motion can be predicted from it. (Boundary: Technical terms, such as magnitude, velocity, momentum, and vector quantity, are not introduced at this level, but the concept that some quantities need both size and direction to be described is developed.) (3)

For any pair of interacting objects, the force exerted by the first object on the second object is equal in strength to the force that the second object exerts on the first, but in the opposite direction (Newton's third law). (6-8)

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)

All positions of objects and the directions of forces and motions must be described in an arbitrarily chosen reference frame and arbitrarily chosen units of size. In order to share information with other people, these choices must also be shared. (6-8)

Definitions of Energy (PS3.A)

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)

Conservation of Energy and Energy Transfer (PS3.B)

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

Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems. (9-12)

Relationship Between Energy and Forces (PS3.C)

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)

Crosscutting Concepts (K-12)

Cause and Effect (K-12)

Cause and effect relationships may be used to predict phenomena in natural or designed systems. (6-8)

Systems and System Models (K-12)

Models can be used to represent systems and their interactions—such as inputs, processes and outputs— and energy, matter, and information flows within systems. (6-8)

Energy and Matter (2-12)

Energy may take different forms (e.g. energy in fields, thermal energy, energy of motion). (6-8)

Within a natural or designed system, the transfer of energy drives the motion and/or cycling of matter. (6-8)

Scientific Knowledge Assumes an Order and Consistency in Natural Systems (1-12)

Science assumes that objects and events in natural systems occur in consistent patterns that are understandable through measurement and observation. (6-8)

Science and Engineering Practices (K-12)

Analyzing and Interpreting Data (K-12)

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 provide evidence for phenomena. (6-8)

Asking Questions and Defining Problems (K-12)

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)

Ask questions that can be investigated within the scope of the classroom, outdoor environment, and museums and other public facilities with available resources and, when appropriate, frame a hypothesis based on observations and scientific principles. (6-8)

Constructing Explanations and Designing Solutions (K-12)

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)

Apply scientific ideas or principles to design, construct, and test a design of an object, tool, process or system. (6-8)

Construct an explanation that includes qualitative or quantitative relationships between variables that describe phenomena. (6-8)

Planning and Carrying Out Investigations (K-12)

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)

Plan an investigation individually and collaboratively, and in the design: identify independent and dependent variables and controls, what tools are needed to do the gathering, how measurements will be recorded, and how many data are needed to support a claim. (6-8)

Scientific Knowledge is Based on Empirical Evidence (K-12)

Science knowledge is based upon logical connections between evidence and explanations. (6-8)

Using Mathematics and Computational Thinking (5-12)

Mathematical and computational thinking at the 6–8 level builds on K–5 and progresses to identifying patterns in large data sets and using mathematical concepts to support explanations and arguments. (6-8)

Use mathematical representations to support scientific conclusions and design solutions. (6-8)

Common Core State Standards for Mathematics Alignments

Standards for Mathematical Practice (K-12)

MP.1 Make sense of problems and persevere in solving them.

Ratios and Proportional Relationships (6-7)

Understand ratio concepts and use ratio reasoning to solve
problems. (6)

6.RP.3.a Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

6.RP.3.b Solve unit rate problems including those involving unit pricing and constant speed.

Analyze proportional relationships and use them to solve real-world
and mathematical problems. (7)

7.RP.2.a Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Expressions and Equations (6-8)

Apply and extend previous understandings of arithmetic to algebraic
expressions. (6)

6.EE.2.c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Reason about and solve one-variable equations and inequalities. (6)

6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Solve real-life and mathematical problems using numerical and
algebraic expressions and equations. (7)

7.EE.4.a Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach.

Analyze and solve linear equations and pairs of simultaneous linear
equations. (8)

8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

Functions (8)

Define, evaluate, and compare functions. (8)

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Use functions to model relationships between quantities. (8)

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.

<a href="http://www.compadre.org/portal/items/detail.cfm?ID=10952">National Science Foundation. Teach Engineering: Energy of Motion. Boulder: Integrated Teaching and Learning Program: Teach Engineering, January 31, 2011.</a>

Teach Engineering: Energy of Motion (Integrated Teaching and Learning Program: Teach Engineering, Boulder, 2004), <http://www.teachengineering.org/view_curricularunit.php?url=http://www.teachengineering.org/collection/cub_/curricular_units/cub_energy/cub_energy_curricularunit.xml>.

Teach Engineering: Energy of Motion. (2011, January 31). Retrieved April 19, 2014, from Integrated Teaching and Learning Program: Teach Engineering: http://www.teachengineering.org/view_curricularunit.php?url=http://www.teachengineering.org/collection/cub_/curricular_units/cub_energy/cub_energy_curricularunit.xml

National Science Foundation. Teach Engineering: Energy of Motion. Boulder: Integrated Teaching and Learning Program: Teach Engineering, January 31, 2011. http://www.teachengineering.org/view_curricularunit.php?url=http://www.teachengineering.org/collection/cub_/curricular_units/cub_energy/cub_energy_curricularunit.xml (accessed 19 April 2014).

@misc{
Title = {Teach Engineering: Energy of Motion},
Publisher = {Integrated Teaching and Learning Program: Teach Engineering},
Volume = {2014},
Number = {19 April 2014},
Month = {January 31, 2011},
Year = {2004}
}

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