Next Generation Science Standards

Performance Expectation

Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known.

• Clarification Statement: Emphasis is on explaining the meaning of mathematical expressions used in the model.
• Assessment Boundary: Assessment is limited to basic algebraic expressions or computations; to systems of two or three components; and to thermal energy, kinetic energy, and/or the energies in gravitational, magnetic, or electric fields.

In this performance expectation, your little human calculators will be hard at work crunching numbers and taking names. That's right, there's math in this task. We'll wait for you to stop cheering before we go on.

Okay, so maybe you weren't cheering so much as weeping, but don't fret, this math is different. Instead of memorizing equations (or programming them into their graphing calculators), your students are going to be the ones coming up with the computational models. As long as they remember a few key relationships, they'll be good to go creating their own custom models of the scenarios they come across.

These equations will help them do some basic algebra to figure out how the energy of one part of a system changes when they know the changes in energy of the other parts. We (almost) made that sound fun, didn't we?

Warm up your calculator, it's computation time. Here are some high-energy activities ideas:

• Provide small groups of students with a small toy car and a ramp. Have them experiment with releasing the car from different heights on the ramp to determine the difference in the resulting kinetic energy of the car. Try to keep the collisions to a minimum.
• Have students fill two beakers with the same amount of water. They will place each beaker on a hot plate, but set the hot plates to different temperatures and observe how the temperature input affects the time it takes the water to boil.
• Take a field trip out to the school pool and have students figure out the gravitational potential energy of a diver standing on the high dive, low dive, and deck of the pool. Don't have diving boards? Or a pool? Use the roof of the building and a cell phone as your example instead.
• Have students calculate the kinetic energy of two skydivers of different masses before they open their parachutes. You can have them use their lab partners as examples or provide them with examples, like The Rock and Sheldon Cooper.

Disciplinary Core Ideas

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.

There are a couple of ideas here that students need to get comfy with. First of all, they need to know that energy is a property that we can measure quantitatively, even though we can't always see it. No imagination necessary.

They should also know that we've got a buffet of different forms of energy. There's kinetic energy, potential energy, radiation energy, thermal energy, and the energy found in force fields. All of these different forms of energy come and go depending on how the objects in a system are interacting.

For example, if you have a car stopped at the top of a hill, it has potential energy. As it starts to roll down the hill, that potential energy becomes kinetic energy. As the driver presses the brakes, that kinetic energy is changed into thermal energy and the car comes to a stop.

This one is a biggie: students need to know that the energy in a system is conserved, which means it hangs out within the system. It might change forms and it might get transferred between the different parts of the system, but the energy doesn't pull any disappearing acts. This handy fact is what allows us to actually calculate the energy of an entire system.

Some of these ideas are really abstract when you see them written on paper, so students may feel a little squirmy at first. This is where models, simulations, and real-life examples come in to save the day. Also, stick to the basic forms of energy, simple algebra, and systems with two or three components. Otherwise they might end up switching schools just to get away from your class.

PS3.B – Conservation of Energy and Energy Transfer: Conservation of energy means that the total change of energy in any system is always equal to the total energy transferred into or out of the system.

This idea sounds really fancy and complicated, but it's really, dare we say, simple? Students should know that energy is conserved, so it just bounces around a system like a pinball. Thus, we can assume that if nothing in the system changes, the total energy in the system will stay the same.

For example, let's say we're baking cupcakes. (They're chocolate and we're going to put vanilla frosting on them, in case you were wondering.) We're baking cupcakes and they're in the oven doing their thing. We can consider the oven a closed system and the total energy is the energy of the stuff inside. If we keep the door closed and the oven set to a specific temperature, the total energy isn't going to change.

Now, what if we open the oven door (we just needed to, um, check on the cupcakes, see how they're doing, give them some encouraging words, you know…)? As warm air rushes out, we have a decrease in the total energy of the system. However, because energy is always conserved, we know that the decrease in total energy inside the oven is equal to the energy transferred to the air outside the oven when we opened the door. No energy is really lost; it just moved someplace else.

Like we said, this idea sounds really intimidating, but if your students can add and subtract with reasonable accuracy, they're going to pick up on it pretty quickly. Obviously, energy is a somewhat slippery concept to grasp so that may be tricky, but once you start relating it to food, they'll get the hang of it pretty quickly.

PS3.B – Conservation of Energy and Energy Transfer: Energy cannot be created or destroyed, but it can be transported from one place to another and transferred between systems.

Even if your students can't remember to bring a pencil to class or write their name on their paper, make sure they remember this: energy cannot be created or destroyed. So how do we charge our phones or turn on the lights or run the blender to make a peanut butter kale smoothie?

Lucky for us, it's pretty easy to move energy around. We can transport it from one place to another like a hot potato. Energy can also be transported into or out of a system, like when you open the oven to retrieve your hot potato and a wall of hot air smacks you in the face.

It may be tricky for students to understand the whole "energy can't be created or destroyed" concept and we're sure they'll have lots of deep questions, like "Where did it come from, then?" If you want to bring the Big Bang Theory into it, we don't want to be the ones to stop you.

If you'd rather stay the course, or your students are more accepting of this information than you thought they'd be, just focus on the fact that energy doesn't just appear or disappear, it gets transferred from one object to another or in between systems.

Also, be sure to keep the quantum stuff out of it; just stick to simple systems with two or three components. They also don't need to worry about every type of energy out there—the basic thermal, kinetic, and force field energies are enough to keep their wheels turning. Calculus is another no-no for this standard. Simple algebraic equations are all they need to know. We'll give you a minute to celebrate.

PS3.B – Conservation of Energy and Energy Transfer: Mathematical expressions, which quantify how the stored energy in a system depends on its configuration (e.g. relative positions of charged particles, compression of a spring) and how kinetic energy depends on mass and speed, allow the concept of conservation of energy to be used to predict and describe system behavior.

We're going to talk about math real quick, but we promise it will be relatively painless (just be thankful we're not talking about the life cycle of a barnacle). First of all, "mathematical expressions" is just a fancy name for equations. Students should know that we get to use these equations to predict and describe what happens when they roll a shopping cart down a hill because we know that the energy in a system is conserved.

Equations tell us all sorts of stuff, and they're pretty useful when it comes to figuring out how different components of a system are related to one another in terms of energy. For example, we have equations that tell us how much energy is in a squished spring or the energy of a roller coaster sprinting through a loop.

Students should know that these equations didn't just appear on the pyramid walls. They were developed to help give a numerical value to the energy within a given system and that energy can change depending on the configuration of the parts of the system.

For example, we use the equation K = ½ mv² to talk about the kinetic energy of an object as it scurries around. We have other equations to help us quantify stored energy in a system and those depend on what kind of objects we're looking at. For example, we use one equation to talk about gravitational potential energy and another to talk about elastic potential energy.

The really groovy thing is we can set it up so different equations are equal to one another in "before" and "after" scenarios, thanks to that whole conservation of energy thing. So, for example, if we have someone jump off the high dive, their gravitation potential energy before jumping is equal to their kinetic energy as they hit the surface of the water. How's that for a splash?

Hopefully your students don't run away screaming when they hear you'll be introducing them to some math. Remind them that it's not scary math, just a little algebra, and you won't be dealing with complex, twelve-part systems, just systems with two or three components. Peer teaching is a great tool to use here—your students will benefit from it, and your teacherly heart will get all warm and fuzzy watching them work together.

PS3.B – Conservation of Energy and Energy Transfer: The availability of energy limits what can occur in any system.

Today marks the six hundred and fifty-seventh day that we repeatedly hit the snooze button instead of going to the gym. We know we're slackers, but the gym requires more energy than we have at five a.m.

Just like how our available energy supply limits what we can accomplish for the day (much to the detriment of our waistlines), it also limits what can happen in any other system. Energy is what makes things move or glow or heat up—and without that energy, that stuff may as well be the gym because it's not gonna happen.

This concept shouldn't be terribly foreign to students. They know they need energy to skateboard, build homes for displaced hedgehogs, and maybe do some homework in between. They know they have to put gas in their car and wood on a fire.

Applying this idea to other systems should be easy for them, and maybe even fun (you can dream, right?). Just remember to stick to basic algrebra and simple systems of three or fewer components, and your energy executives will be experts in no time.

Science and Engineering Practices

Using Mathematics and Computational Thinking: Create a computational model or simulation of a phenomenon, designed device, process, or system.

Math is sort of like the really scary-looking kid in gym class who actually turns out to be pretty cool. Your students probably think they don't like math, but once they get to know it, they'll see its softer, incredibly useful side and they'll be BFFL's (Best Friends For Life, duh).

Scientists and engineers know all about math's secret friendliness. They use math almost as much as they use oxygen, because it helps them understand stuff better. Even though computational models, i.e. equations, use numbers (gasp!) and variables (gasp!), they are the perfect way to sum up something really complex, like the potential energy in a rubber chicken at the top of the Empire State Building. And they're way easier than writing a paragraph about it.

In this performance expectation, students will get a taste of the awesomeness of computational models as they create their own equations to calculate the energy change in various components of a system. The key to coming up with them will be remembering that energy is conserved, meaning we can set up before and after scenarios with our various energy equations. For instance, if students know how to find the gravitational potential energy and kinetic energy of a duck riding a roller coaster at various points in time, then they can set up their own equations relate those pieces to each other.

Who knows, maybe by the end of this, the students will run around calling themselves mathemagicians. Watch out, Harry Potter!

Crosscutting Concepts

Systems and System Models: Models can be used to predict the behavior of a system, but these predictions have limited precision and reliability due to the assumptions and approximations inherent in models.

Models are probably one of the most important tools a scientist has in their toolbox. That's right. Step aside, pipette. Move over, Erlenmeyer flask. Make room for the model.

Models are so important because most of the best stuff to study is too small or too big or too fast or too slow or even too dangerous to observe directly. Thus, models allow us to study these systems that we can't observe directly on our own.

Unfortunately, scientific models aren't perfect. Students should understand that we have to make a lot of assumptions and cut some realistic corners here and there to make them work, which means we lose some of the accuracy that comes with studying the real deal. In real life, for example, friction is constantly ebbing away energy from our otherwise perfect conservation of energy models. It would be great if roller coasters never lost any of their initial potential energy, but friction is a greedy animal, and our loop-de-loops suffer because of it.

Scientific Knowledge Assumes an Order and Consistency in Natural Systems: Science assumes the universe is a vast single system in which basic laws are consistent.

Ah, the universe. So starry. So galaxy-y. So…vast. Unless you've got a really awesome secret project going on in your garage, there's no way we're going to be able to explore the entire universe anytime soon.

For the time being, we'll have to assume that it's just one giant system and that the laws we have been able to observe in Earth's neck-of-the-woods apply exactly the same as they do out in the far reaches of space. It doesn't do much for the imagination, but it does wonders for your sanity when you're trying to perform calculations involving gravity.