Underwater Ratios

Underwater Ratios

Maureen McTigue

CCLS: 6.RP.1, 3a, d

MP 1, 6

2 class sessions, or as teacher sees fit

Can cross with Literacy and Science

AIM: How do we find and construct ratios that can be used in scientific inquiry?

MOTIVATION: Students will explore whales in different settings in order to envision the true size of the blue whale in comparison to other whales and humans.

MATERIALS: videos, graph paper, color pencils, worksheets

INTRODUCTION:

We don’t think too much about whales every day of our lives, but they are out there in the ocean, and good and bad things happen to them.

VIEW Finding Nemo blue whale clip

Whales are some of the biggest mammals on Earth, and the blue whale is THE biggest animal on earth. We know they’re big but it’s hard to picture JUST how big. One way to picture it is by comparing the whale’s size to other things, like a human for instance.

EXPLICIT: I’m going to use my height. It’s best to round our heights to the nearest foot. On graph paper, one box will equal one foot, and so we can graph out own height. I’m 5-foot 7-inches, so I would round that to 6 feet, and color in 6 boxes. With a different color pencil, I’m going to compare myself to a killer whale’s length. A killer whale is about 30 feet long, so I’m going to color in 30 boxes. See the difference?

This is one way to compare different quantities. It is a type of ratio, which describes the relationship between two quantities. Once we have this visual and know these numbers, I can write the ratio comparing me to the orca three different ways:

                                    6:30

                                    6/30

                                    6 to 30

And if these numbers look like they have something in common, they do. Thinking about fraction in simplest form, you know you can reduce this, and even with ratios, you should do that. So the ratio of my height to the whale’s “height” is 1 to 5, meaning it would take 5 of me, connected head to foot, to be as long as a killer whale. That’s pretty big.

But the killer whale isn’t the biggest whale by a long shot.

IF THERE’S TIME, STUDENTS CAN DO THIS PART NOW. IF NOT, MOVE TO THE NEXT PART AND LET THEM DO THAT. THE COMPARING WITH THE GRAPH PAPER CAN COME LATER.

We’re going to do the same thing but with this graph paper with the pictures of a humpback whale and blue whale. The humpback is the smaller one. If you’ve ever gone on a whale watching boat, that’s the kind of whale you probably saw.   We’ll count units across, units being the boxes, and see the length of both whales. Go from the mouth to the furthest tail park.

*Time to do this*

We found that the humpback whale is 10 units long and the blue whale is about 20 units long. 

We can create the ratio of what?

10 to 20 or 1 to 2, when we simplify.

Now we find out that each box on this grid is worth 5 feet. How long is each whale? 

Do those numbers fit the equivalent ratio?

Realizing how big whales are, you may not realize how much help they need to survive.

View DN! clip about whaling, for background.

Watch Chapter 22 in Whale Rider

SESSION 2/or continue

Blue whale clip from Blue Planet

Blue whales are pretty awesome, you have to admit. Now, I’m going to give you a comparison chart and we’re going to set up a graph for ourselves. I can also give you the Beluga whale which is 12 feet long, and the Common Dolphin which is about 7 feet long.  So, using graph paper and color pencils, create a comparison graph of cetaceans and humans.

Once you have your numbers in place, create ratios between different creatures making sure you include human to blue whale, sperm whale to blue whale, common dolphin to blue whale, then set up three of your own. Be sure to identify what is being compared.

View Planet Earth clip of Blue Whales (44:55)

Share out and hand in.

Let’s watch a few clips about other whales. Think about the way the narrator used numbers. Why are those numbers important?

Homework: Worksheet Whale related ratios

Extension: Readings about whales

Resources:

http://www.neatorama.com/2009/03/04/blue-whale-fun-facts/

http://www.wdcs.co.uk/media/flash/whalebanner/content_pub_en.html

Dowdy, Penny. Math Make Sense. 2009. Leopard Learning. Pgs 34-35.

http://app.discoveryeducation.com/search. Wild Pacific: The Endanagerd Humpback Whale.

http://gtm-media.discoveryeducation.com/videos/47681/4B17BA67-1279-3B00-CD30AEE703FADB84.pdf

http://www.pbs.org/teachers/connect/resources/2202/preview/. Retrieved October 31, 2012.

http://www.democracynow.org/2008/1/15/headlines#11517

Homework Questions:

Identify the ratio, fraction and decimal in the following 2 problems. 

Remember to simplify where possible and show work in all problems.

1) The common dolphin is on average 8-feet long. 

The killer whale (orca) is around 30 feet long. 

What is the ratio of the dolphin’s length to the orca’s?

a) Ratio _________________

b) Fraction _______________

c) Decimal _______________

2) A human can hold his or her breath on average for one minute. 

A sperm whale can stay under water for about an hour. 

What is the ratio of human to sperm whale, using the same quantifying term? 

a) Ratio _________________

b) Fraction _______________

c) Decimal _______________

3) A blue whale is about 100 feet long. A human is about 6 feet tale. 

What is the ratio of the human to the whale?

4) A blue whale weighs up to 150 tons. If one ton equals 2,000 pounds, 

how many pounds does blue whale weigh?  

The blue whale’s heart weighs about 2000 pounds. 

What is the ratio of heart to whale in a blue whale in both units?

5) A blue whale’s tongue weighs about as much as an elephant, 

and about 100 people can fit in a blue whale’s mouth. 

An average weight for an elephant is 11,000 pounds. 

What’s the ratio of blue whale to blue whale tongue?

6) Written response:  All kinds of numbers are used when dealing with studies of animals and 

even in environmental studies. 

Why is it good to understand how ratios are found when learning about a subject? 

How can ratios be used in different ways, especially in dealing with populations of animals, 

like whales? How can they be used in positive and negative ways? 

What do you find most important when working on this project?

The following story is a reading that can be added to enhance the theme of the lesson.  

It is from National Geographic's Educational material found at 

http://education.nationalgeographic.com/education/?ar_a=1

Whale Tales

Research biologist reveals blue whales' striking characteristics

By Stuart Thornton

Sunday, January 16, 2011

The largest animal that has ever lived, blue whales can grow to 100 feet (30 meters) long, which is longer than the length of a basketball court. They can weigh as much as 200 tons (181 metric tons), about the weight of 15 school buses.



So when a blue whale does an ordinary act that is necessary for its own survival—even just breathing or gliding through the ocean—it can be an awe-inspiring event.



“I think it’s humbling,” says John Calambokidis, a marine mammal research biologist who studies blue whales. “Often, we are working in boats 18 feet long, and these animals we are approaching can be five times larger.”



Calambokidis is co-founder of Cascadia Research, a nonprofit organization based in the U.S. state of Washington that studies marine mammals in an attempt to help protect them. Calambokidis has traveled all over the Pacific Ocean—from off the coast of Costa Rica, where he was funded by expedition grants from the National Geographic Society, to the Queen Charlotte Islands in British Columbia, Canada. He travels to research blue whales. Having observed about 5,000 blue whales in the wild, Calambokidis has witnessed the behaviors of the enormous creatures up close and personal.



The scientist can easily recall the first time he heard the geyser-like explosion of air from a blue whale breathing nearby. 

“Here’s this massive animal exhaling virtually all of the air in its lungs in a fraction of a second,” he says. “It comes out with an explosive force. It literally made me jump in the boat.”

Calambokidis says a blue whale’s call, which the animal uses to communicate with other members of its pod and possibly to sonar-navigate the oceans, is a far cry from the sounds emitted by other marine organisms. 

“The calls they make underwater are some of the loudest sounds any animal makes,” he says.

But the low-frequency sound is normally below a human’s hearing range. Calambokidis never heard a blue whale’s call during the first decade he was studying the animal. Eventually, with the help of a hydrophone, a microphone that picks up noises underwater, he was able to hear the deep, pulsating sound.

“Hearing that reverberate through was one of the more impressive times I’ve heard an animal call,” he says.


Just as impressive as its call is the noticeable mark a blue whale leaves behind as it sinks into the sea. The phenomenon is called a flukeprint. 

“The flukeprint is created by the upward motion of water coming off the trailing edge of the fluke [the whale’s tail] as the animal basically begins its acceleration downward,” Calambokidis says. “So what it ends up looking like is basically an upwelling mass of water that starts as a small circle and spreads outward.”



There is one striking aspect of a blue whale that has nothing to do with the animal’s enormous size—its appearance underwater. 

“Especially in the sunlight, when they are traveling just below the surface, they can get this almost shimmering light, an almost turquoise glow,” Calambokidis says. “They can almost seem to glow underwater.”



While blue whales dwarf their adversaries in the sea, the large marine mammals are surprisingly timid, Calambokidis says. 

“Their response to killer whales is to flee at high speed,” he says. “People might not expect that from the largest animal that has ever lived.”

Though a blue whale’s tongue can weigh as much as an elephant, the giant ocean creature survives almost exclusively on a diet of two-inch shrimp-like organisms called krill. During certain periods of the year, a blue whale can eat as much as 4 tons of krill in a single day. It then expels the processed food in a defecation trail, which Calambokidis describes as a brick-red cloud that colors the water.



The world population of the docile creatures dwindled severely from 1900 to the mid-1960s, when blue whales were being hunted extensively for whale oil. Whale oil is a substance made from whale’s fat, or blubber. Whale oil can be used as a heating and lighting fluid. It is estimated that 360,000 blue whales were killed during that period. In 1966, the killing of blue whales was banned by the International Whaling Commission. 

                             

Scientists believe there are between 10,000 and 25,000 blue whales left in the Earth’s oceans. 

Even though whale hunting no longer threatens the endangered species, Calambokidis says there are other dangers facing the blue whale today. Underwater sounds from ships and sonar might affect the animals. Many scientists worry that climate change could alter the whales’ ecosystems. One definite cause of blue whale deaths occurs when large ocean vessels inadvertently strike the marine mammals. In fall 2007, four blue whales were killed by ships off the coast of Southern California.



With Cascadia Research, Calambokidis is trying to learn more about blue whales in an effort to ensure their population doesn’t dwindle any more. 

“They do represent one of the more magnificent animals that we have on the planet,” he says.

© National Geographic Society