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Age of Awareness

# The Conservation of Money Game

## A big upgrade to your science class’s conservation of energy lesson

In the fall of 2008, I was a senior in college. Lehman had just collapsed and financial havoc abounded. At the time I lacked a framework to understand what was breaking and why.

As a physicist, my mental models were always built on conservation laws — that is, quantities whose total amounts never change. The Law of Conservation of Energy says that the total energy in the universe is constant, although energy can transfer between different types. For example: when a plant photosynthesizes, the light energy from the sun is converted into chemical energy in the plant. The energy changes from solar to chemical, but the total amount of energy stays the same.

Back in 2008, as I learned more about the subprime mortgage crisis, I began to wonder if conservation of money was a thing. I kept reading about how there used to be so much money and now it’s all gone. What did that mean? How can money just disappear? Perhaps money is not, after all, the economic analog of energy in science.

I was perplexed at the time because money seemed to be a conserved quantity. When you buy sunglasses for \$17.50, you give seventeen dollars and fifty cents of your money to the store. So you have \$17.50 less than before, and the store has \$17.50 more. For daily transactions, it’s easy to ignore things like interest rates and asset pricing, and to just think about money as a substance-like quantity that can change hands but doesn’t get created or destroyed. As we see time and again in history, money is not actually conserved through economic transactions; real wealth is. But the conservation of money analogy worked too well with my ninth grade students to let this technical inaccuracy stop me from teaching it this way.

So what is the Conservation of Money Game? It was born from my desire to build students’ intuition about conservation laws in science. For years, I used Richard Feynman’s Dennis the Menace analogy (chapter 4–1) to explain energy conservation to my physics classes. I first encountered Feynman’s delightful essay through the AMTA. The basic idea is that Dennis the Menace has a bunch of toy blocks in his room. The total number of blocks remains the same, even though the blocks can change location. If we have trouble finding all the blocks we had previously counted, then perhaps we forgot to look in a certain place, or someone removed it from the room, or we miscounted in the first place — but it can never be the case that the block literally disappeared. Similarly, we may have lost track of the energy in our science experiment, but we know it has not just disappeared. The same reasoning works for an excess of toy blocks (in Feynman’s analogy) or energy (in real life) — that is, energy cannot be created so it must be that there was mismeasurement or a failure to account for something in the experimental design.

Feynman’s analogy never really resonated for my students. My ninth graders are not in the habit of counting toy blocks and then moving them around and counting again. I needed a different analogy to make it meaningful. Thus the Conservation of Money Game.

Here’s how it works:

1. I tell the class that each student has a certain amount of money to start with, say \$10. I say that there’s going to be a series of hypothetical transactions, and if they get the totals all correct at the end then there will be a prize.
2. I announce monetary transactions one by one while students do their accounting with pen and paper.
3. Students share their final answers and compare to each other.
4. We discuss how this game applies to conservation of energy.
5. We use the game to launch energy pie charts as a tool for energy accounting in physics problems.

Here’s how it went with my 3rd period Physics First class. I made up this story and read it aloud: “Evan, Theresa, Jonathan, Allen, Raquel, and Erik each had \$10. First, Raquel gave Allen \$1. Then Theresa gave Erik \$2. Then Evan gave Allen \$3. Then Jonathan gave Raquel \$5. Then Allen spent all his money, dividing it evenly between Theresa and Jonathan. Then Raquel gave Allen \$5.” All the students individually did their accounting. We put some of their results on the board, which you can see in the photo above: one student’s answers are in orange, one in brown, and one in red.

I asked the class, “Is there a quick check we can do on these final numbers to rule out answers that are definitely wrong?” Almost every student inferred immediately: you can add up the numbers and see if the total remained unchanged. In this particular case there was \$60 total to start (6 people with \$10 each), so we could immediately eliminate the first two answers. We discussed that this check will not identify the correct answer, but it can be used to identify incorrect answers.

In each transaction, money flows from one person to another person. When Raquel gave Allen \$1, the amount of “Raquel money” decreased from \$10 to \$9, and the amount of “Allen money” increased from \$10 to \$11. You can see how the individual amounts changed while the total remained the same in these pie charts.

The last component of the Conservation of Money Game is to discuss how we might actually end up with a different total at the end. I pose to the class: “Let’s say the person who computed \$66 total was actually correct — that there really was \$66 at the end of the game. What may have happened to cause this?” Students’ answers are creative. Perhaps another teacher came in the room and gave someone \$6 while the transactions were happening. Perhaps there was \$6 on the floor of the classroom or in someone’s pocket that we forgot to count at the beginning of the exercise. Perhaps we just made a mistake in tallying up the totals before the transactions began.

Students readily agree that there’s got to be an explanation for ending up with a different amount of money at the end: it cannot be that the money just appeared or disappeared from thin air. I then tell students that energy works the same way. Calories (or Joules) of energy cannot be created or destroyed. As Feynman said, it’s a surprising and not-necessarily-expected fact, but it’s the way our universe works (as far as we can tell): this thing we call energy is a conserved quantity.

My students could then quickly transfer this knowledge to energy pie charts. We had already discussed the types of energy that may be present in a system, and they could see that “Evan money,” “Theresa money,” and “Jonathan money” were analogous to kinetic (motion) energy, thermal (heat) energy, and light (electromagnetic) energy.

Here’s a typical energy pie chart question: how can we explain the energy transfer that takes place when a slow-moving car is halfway up a hill and then accelerates to get to the top? First, we identify the energies present “before” and “after.” In the “before” state, the car has chemical energy from its gasoline, as well as kinetic (motion) energy because it’s moving, and also gravitational energy because it’s above the ground. In the “after” state, the car has more kinetic energy because it’s moving faster, more gravitational energy because it’s higher up, and less chemical energy because of the gasoline that’s been used up. Thermal (heat) energy has also been produced by all the friction and chemical reactions. The size of the pie stays the same because the total energy stays the same — just like money in the Conservation of Money Game.

Energy pie charts are powerful, because they enable students to identify when they’re missing a piece of the energy story when explaining a phenomenon. My favorite example to do with students is air conditioners or refrigerators: my students use pie charts to discover that these devices that were engineered to cool things down actually (on net) produce heat! I’ll save that analysis for another post.

Play the Conservation of Money Game with your students. It won’t explain the subprime mortgage crisis, but it will explain conservation of energy. There are other resources you can use to teach students what happened when all that money disappeared in 2008.

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## Elissa Levy

I teach physics and computer science in East Harlem, New York. I aim to engage.