Michaels, Sarah, Shouse, Andrew W., Schweingruber, Heidi A.. "3 Foundational Knowledge and Conceptual Change." Ready, Set, SCIENCE!: Putting Research to Work in K-8 Science Classrooms. Washington, DC: The National Academies Press, 2007.
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Ready, Set, Science!: Putting Research to Work in K-8 Science Classrooms
brought them back to the situation in the aquarium. “So even if the surface area of the water is huge, what matters is how many and with how much force the air molecules pound each square inch of the surface of the water. Wherever you are, at sea level or in the mountains, you don’t have to calculate the surface area in a container, or in a swimming pool, or in a huge lake, because at the same elevation, every single square inch has exactly the same amount of air pressure on it.”
After a moment, Monica asked, “How tall a glass could we pull out of the aquarium? How far could the column of water be pushed up, by air?”
“Could it go all the way up into space?” someone else asked.
Salizar quickly responded, ”It couldn’t go that far up because there’s only 14.7 pounds per square inch pushing down. If the water weighed more than 14.7 pounds per square inch, it wouldn’t stay up. The water would win in the battle of the forces!”
“So how far can the air push the water up?” Monica asked again.
“I don’t know the answer to that question,” Ms. Faulkner admitted. “But I’m sure we can figure it out. Any ideas about how to get started? What would we need to know?”
There was silence. Finally, Tanika said, “How many cubic inches of water does it take … um, to weigh more than the air pressure—like 14.7 pounds?”
As if finishing Tanika’s sentence, Monica continued, “Like how many cubic inches of water can push down on that spot to outweigh the air pressure that’s forcing the water up?”
Phuong said, “I think I get it. It’s like the air pressure is pressing down on the surface of the aquarium, everywhere, like a piece of plywood pressing down with a lot of force, like a lot of force. And then we cut a hole in the plywood, like a one-square-inch hole. And right there, on that square inch, there’s no air, no nothing, I mean no pressure pushing the water down. So the water would squirt up through the hole! If we had the one-inch glass there, the bud vase thingy, then the water would squirt up into it. When the water column goes higher and higher it gets heavier and heavier, and at some point, eventually, the water will weigh as much—down—as the air is pushing up. That’s as far as it could go.” After a long pause he said, “So how many of Salizar’s little cubic inches could we pile up on top of one another? How many would equal up to 14.7 pounds?”
“Phuong’s on the right track when she asks how many of Salizar’s little cubic inches could we pile up on top of one another to equal the air pressure at 14.7 pounds per square inch,” Ms. Faulkner said. “It’s really a question of balancing forces. It’s like a seesaw. We’ve got someone on one side who weighs 14.7 pounds. That’s the air pressure. On the other side, we’ve got a one-inch-square column of water. With what we’ve figured out already, see if you can figure out how tall that column of water could be. And, even more interesting, see if you can figure out a way we could test it to see if our calculations are right. Think about it tonight, and we’ll talk about it tomorrow.”
By the next day, the class had calculated that the air could hold up a column of water 34 feet tall. They had come up with many different methods, but the simplest was building on Salizar’s fact that a cubic inch of water weighs 0.036 pounds. They divided 14.7 pounds by 0.036 pounds (per cubic inch) and came up with 408.3 cubic inches. That’s how many cubic inches of water could be piled on top of each other to equal 14.7 pounds. They then divided that by 12 to determine the feet and got 34.03 feet.
Ms. Faulkner applauded her students’ hard work and amazing results—they had truly changed their conceptual thinking in many ways.