Mathematics

What’s the Matter with an Aquarium

Note to the adult helper:

Please look over the following material. You might want to cut some things out. Remember, you want this to be a pleasant experience for the child. If the child asks questions, maybe you’ll think of some things to add on your own. In this series, I’m giving what I’m wishing I had been given when I was in grade school starting with aquariums, but 8 year old me is not the child you’re working with.

Major points:

  1. Matter has mass and, in a gravity field, weight.
  2. Mathematics has practical uses.
  3. The aquarium will be heavy. What are the consequences?
  4. Estimation allows us to think about and check the answer.

Lesson:

For this lesson, you will need your notebook and something with which to write.

If there’s a place on the cover, write “Aquarium Notebook #1.” Beneath it, write your proper name. This is your notebook. If there’s no place on the cover, there might be on the inside. If not, write it on the first page. On the next page, write the date.

There are many different types of aquariums. An aquarium can be a lush freshwater tank with plants and fish; it can be a crystal clear saltwater tank filled with animals. Some people keep aquariums with only plants. If a fish is ill, the “hospital tank” might only contain water, medicine, and the sick fish.

There are two things that all aquariums have: the tank and the water. You need both: without the water, it’s not an aquarium. Without the tank…it’s a mess!

Let’s look at the water first.

Write this question down in your notebook: “What is water?” What are the things you think of when you think of water? Write down as many as you can before you read my suggestions.

When I think of water, some of the things that I think of are that it’s wet, it’s heavy, it can be hot or cold, it’s transparent, and it’s necessary for life. You can freeze it into a solid, you can boil it into a gas, and when you have a leak in your house, it’s a mess to clean up. You can dissolve things in water—including air!

Many of those properties of water are what make an aquarium possible. Imagine water with no weight—the water would float away, which would make keeping an aquarium very difficult. Imagine water that you couldn’t see through. You might have fish in your aquarium, but it wouldn’t be any fun.

Water is a form of matter. In very advanced science, what matter “is” can get very strange, but for everyday use, you can think of matter as being something that has mass, volume and temperature.

What is mass?

Mass is how much an unattached object resists being moved. If something is just sitting there, you have to work to move it. Once something’s moving, you have to work to stop it from moving. How much you have to work is its mass.

On everyday Earth, we treat mass and weight as the same thing. Weight is the force of an object produced by gravity pulling on it. If you’re on Earth, you can get away with saying mass and weight are the same. But if you were on the International Space Station, where things are weightless, nothing has weight but it still has mass!

There have been aquariums on space stations, but I doubt you’re creating your aquarium on a space station or on the moon. So we’ll treat mass and weight as the same. But whenever someone treats mass and weight the same, I want you to think “Yeah, but they’re not the same!” Just don’t say it out loud, because people will look at you funny.

Water, being a form of matter, has mass—and on Earth, it has weight. Milk is mostly water, and if you pick up a gallon jug of milk, you’ll realize it’s pretty heavy. A gallon of milk weighs 8.6 lbs. Now, water, which doesn’t have all the extra things of milk dissolved in it, weights 8.3 lbs.

Estimation is when you want an answer that’s “good enough.” Everyone estimates, because it makes life easier. If you want to play catch with a friend, and you say “Go about 10 yards away,” your friend doesn’t take out a tape measure and measure 10 yards exactly. Your friend might go 9 yards away or 10.1 yards away or even 15 yards away. Your friend estimates the distance. The answer is “good enough.”

We said that water is 8.3 lbs. per gallon. If you have a 20 gallon aquarium, how much does the water weigh? Can you multiply 8.3 * 20 in your head? 20 is 10 * 2, so 8.3 * 20 is the same as 8.3 * 10 * 2, which is 83 *2. 2 *3 is 6, 80 * 2 is 160, so 8.3 * 20 is 166.

What if you’d estimated by saying water is 8 lbs. per gallon? 8 * 20 is 160 and you’re done. It’s not the correct answer, but it’s only wrong by 6 / 166 which is about .036. That’s pretty small. For what we’re doing, we can estimate by saying water is 8 lbs. per gallon.

When your teacher at school asks for an answer, assume she wants an exact answer. But when you’re trying to work things out for yourself to see about how much something is, you can estimate.

Here are some other estimating tricks. In English units, we use pounds (lbs.) for weight and gallons for volume. In the metric system, we use kilograms for mass (and we’re going to use mass as if it were weight, but we know that’s not quite right, right?). 1 liter is .264 gallons, which is a little bit more than 1/4th. There are .454 kilograms in a pound, which is almost ½.

So we can estimate the number of liters in a gallon by saying there are 4 liters in a gallon and ¼ a gallon is a liter. We can estimate number of kilograms by saying it’s a half a pound and half a pound is 2 kilograms.

So how many liters are in a 20 gallon aquarium? There’s about 80 liters. Now, the fun thing about the Metric system is, water weighs 1 kilogram per liter. So how much does an 80 liter aquarium weigh? It weighs 80 kilograms.

Your friend bought a 5 gallon aquarium. What does it weigh in lbs? How many liters is it? How much does it mass in kilograms? Write down in your notebook “A 5 gallon aquarium is approximately”. Below that, write down approximately how many pounds it is, how many liters and how many kilograms. Try to do the calculations in your head. Don’t move on until you do.

What did you get for the answers? Did you write “40 lbs, 20 liters and 20 kilograms”?

Now, write down A 5 gallon aquarium is exactly”. Below that, multiply 5 by 8.3 to get the exact number of pounds. Divide the number of gallons by .264 to get the exact number of liters. Once you have the number of liters, you’ll know how many kilograms it is. You can do these calculations with a calculator, or, if you’re feeling adventurous, do it using a pencil and paper. Write those answers down.

Again, what were your answers? Did you get 41.5 lbs? 18.9 liters and 18.9 kilograms?

Which way was easier to solve the problem?

Let’s say another friend bought a 55 gallon aquarium. Write down “A 55 gallon aquarium is approximately” and below it write down how many lbs., liters and kilograms. See if you can do the calculations in your head. Then write down “A 55 gallon aquarium is exactly” and below it write down how many lbs., liters and kilograms.

Did you get 440 lbs, 220 liters and 220 kilograms for the approximation? Did you get 456 lbs., 208 liters and 208 kilograms?

Now, let’s think about our results a little bit. Is 160 lbs and 80 kilograms—the weight of the water in a 20 gallon aquarium—a lot? Scientists estimate the mass of an adult man at 75 kilograms. 80 is a bit more than 75 kilograms. 80 kilograms not a tremendous amount, but it’s more than a gallon of milk. What do you think would happen if you put a 160 lb. aquarium on one end of a table? Have you ever seen someone sit on a table and the table move or even get tipped over? Would you put an 80 liter aquarium on top of a cardboard box? It might be possible to make a stand out of cardboard that would safely hold 80 kilograms. But what happens to cardboard when it gets wet? Do you think working on an aquarium might get the cardboard wet? Even if you were careful, the aquarium could leak. A leak would be a problem by itself, but imagine what would happen if the cardboard stand got soggy!

You have to put your aquarium on a piece of furniture so you can see it easily. What do you think that piece of furniture should be like?

With permission of an adult, jump up and down in the middle of a room. Does it make a lot of noise and do things vibrate a bit? Now, go jump near a wall. What kind of noise does it make and how do things vibrate? Finally, go jump up and down in a corner. What happens? Write down in your notebook what you did and what you observed.

Next, stand in the middle of the room on one foot. How easy is it to stand on one foot? Go over to the wall, lean slightly on it, and see if you can stand longer on one foot than you could in the middle of a room. Finally, lean in the corner and stand on one foot. Where is it easiest to stand? Write down in your notebook what you did and what you observed.

You want the aquarium to be stable. You don’t want it to vibrate, you don’t want it to fall over, and you don’t want it to fall through the floor. There’s not much danger of a 20 gallon aquarium falling through the floor, but what if you had a 100 gallon aquarium? About how much would that weigh? Could it cause problems in the middle of a room?

Where do you think the best place to put an aquarium is based on your jumping up and down and trying to stand on one leg? Write down in your notebook how you would rank places to put your aquarium.

Next, what if you had to put the aquarium in the worst place in the room? What can you think of doing to give your aquarium the best chance to survive if you put it there. Write that down in the notebook. Drawing pictures will help explain what you’re saying. You can also talk to the person helping you. Can they think of other things that could be done to make the aquarium safe? If you don’t have to, would you want to do these things? Do you think they would be more or less expensive?
By estimating, you were able to figure out how much different size aquariums would weigh (or mass). Estimation lets you think about things without investing effort you don’t need to make. If you had done the exact calculations, would it have made any difference in the answer as to where you’d put an aquarium? If you had a 5 gallon aquarium, do you think you could get away with putting the aquarium in the worst possible place? What if it were a 55 gallon aquarium? Would you be worried if you had to put it in the worst possible place?

Estimation lets you know if it’s worth doing the full calculations!

When I was writing this, I did the multiplication in my head and got an answer for the weight of a 20 gallon aquarium of 8.3 * 20 as “246 lbs.” I multiplied the 8 by 30, not 20. Because I estimated the weight at 160 lbs., I knew something was wrong. Now, I didn’t know whether my estimation was wrong or my full calculation was wrong, so I pulled out a piece of paper and did the calculation carefully. I got the correct answer of 166. Because I had estimated, I avoided a significant mistake.

When you’re done with a test, go back through and look to see if your answers are reasonable. Where appropriate, estimate the answer—does the estimate match the answer you put? Estimating is a way to check your work!

Finally, draw a line under the last thing you wrote in your notebook. That’s all for today, and the line lets you know where that day’s data ends!

Science in 80 Liters (20 Gallons)

In 1967, I was in third grade and got a book by Beverly Cleary titled “Henry Huggins.” In the book, Henry goes to a pet store and buys a pair of guppies. The two guppies had babies. Soon Henry’s room and life are over-run with jars of fish. This story disaster inspired me to ask my parents to let me have an aquarium. My parents agreed, and soon there were three aquariums in our new house.
Recently, I looked back on those experiences with tropical fish and realized just how much science I learned from them. Making the water safe for the fish taught me a lot of chemistry. Learning about the fish, keeping a balanced tank the fish could live in, and breeding them introduced me to topics in biology long before I had them in my classes. Even mathematics, physics and a touch of engineering came into play.

Today, scientists and educators are making a deliberate attempt to interest children in science, technology, engineering and mathematics—it’s abreviated STEM. In the past, such activities tended to be aimed mostly at boys. Now, the goal is to interest everyone, no matter their gender.

I learned through books. My first book on aquariums taught me how to set up a small 5 gallon tank. As I got bigger books, I got bigger tanks. My Dad was an engineer, but for the most part, he stuck to lifting heavy objects, curbing some of my excesses, and suggesting how to look up an answer. It worked for me.

Part of me would love to write a book for third through fifth graders explaining the science as they set up a modern aquarium. Unfortunately, my wife and I weren’t blessed with children. I’m not sure if I’d know how to write for third to fifth graders.

As I thought about it, I realized I don’t want to write for those third to fifth graders. I want to write for their parents. The parents can guide their children, pick and choose the topics that are appropriate, and interpret the lessons for their children’s level of understanding. With any luck, the parents and children have fun together with the tank.

And who knows? Maybe the parents will gain a little more understanding and appreciation for science.

As I see it now, I’ll write a lesson about once a week, focusing on the particular topic involved with that stage of the aquarium setup. That might seem slow, and, as I get a feel for it, perhaps the frequency of the posts will increase. But one of the tricks to setting up an aquarium is to take it slowly. If, in a single day, you purchase an aquarium, set it up, and put the fish in, there’s a high probability that you’ll waste a lot of money and kill the fish.

If anyone is going to follow along, I would appreciate getting feedback. What was clear? What wasn’t clear? What was too difficult for your child to understand? What was too simple? What was too expensive? What better ways are there to do this? A comment section is available at the end of each article. I’ll make every effort to answer questions and learn from any suggestions.

Weather Wars

Weather Wars

There’s an interesting exchange beginning at 41:08 on the YouTube video of the recording of the NASA Hangout: Ask A Climate Scientist on 30 September 2013. The video starts a few seconds before the 41:08 mark:

NASA Hangout: Ask a Climate Scientist

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Forbes’ Embarrassing Op-Ed on Climate Change

I wasn’t looking to pick a fight. A link on Facebook pointed out the very good Forbes article on how “US Scientists Are Leaving The Country And Taking The Innovation Economy With Them”. But there was an advertisement for an opinion/editorial (op-ed) by Dr. Mark W. Hendrickson titled “The Palpable Politicization Of Science By Global Warming Alarmists” that I just had to check out. It’s a shame Dr. Hendrickson or Forbes or someone didn’t fact-check the op-ed piece. Early in the opinion piece, there’s an egregious error of fact.

Continue Reading…

Dealing with Feral Cats

Our neighborhood has two feral cats that we know of. (1) The question is, what should we do with them?

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  1. Whether they’re truly feral or strays that have learned to survive in the wild, I don’t know. []

The Problems with Computer Models (Part 1)

Dr. Katharine Hayhoe (@KHayhoe on Twitter) repeatedly pointed out in a recent excellent Infrastructure and Climate Network webinar (1), that climate models can’t predict what will happen on a particular day in the future. Well, living here in Pittsburgh, where the weather forecast for much of this summer was “Possibility of sunshine, clouds, rain and severe storms,” there’s no surprise that a climate model can’t predict the weather next year. (2) But why do these models fail?

Years ago, I created a simple computer model for weight loss. By looking at that model, you’ll see what that model could and couldn’t do–and why.

Let’s do a science!

Continue Reading…

  1. “High-resolution climate projectioncs: Where do they come from and what can we do with them?”–by Dr. Katharine Hayhoe on September 18, 2013 []
  2. It’s possible all the weather forecasters went on vacation at the same time and put up a generic forecast that would cover any situation. I can’t rule that out. []