# Polar Bear Math: Learning About Fractions from Klondike and Snow

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ISBN-13: 9780312377496 Square Fish 12/26/2007 Animal Math Series First Edition 32 828,761 7.92(w) x 9.99(h) x 0.06(d) 4 - 8 Years

Ann Whitehead Nagda is the author of Tiger Math, Chimp Math, Polar Bear Math, and Panda Math, as well as several other books about wildlife. Her love of wild animals grew during her visits to national parks and wildlife reserves in Asia and Africa, and today she is a docent at the Denver Zoo. Her newest book, Cheetah Math: Learning About Division from Baby Cheetahs, was released in Fall 2007 by Henry Holt. Ms. Nagda lives in Boulder, Colorado, with her husband.

Cindy Bickel has worked at the Denver Zoo for more than thirty years. During her career, she has hand-raised hundreds of babies for the zoo, using math every day in her job as a veterinary assistant. Ms. Bickel helped write Chimp Math, Tiger Math, and Klondike and Snow: The Denver Zoo's Remarkable Story of Raising Two Polar Bear Cubs.

CHAPTER 1

Early one November morning at the Denver Zoo, a polar bear named Ulu gave birth to two baby bears. She cleaned them off, then left them lying on the cold cement floor of the hallway that led to her den. When Gary, the polar bear keeper, came to work, he heard soft crying. Gary could see that Ulu was in her den, but there were two small shapes in the hallway. When he looked closer, he found the newborn polar bear twins that Ulu had abandoned. Gary tucked the babies inside his jacket and rushed them to the zoo hospital.

COMMON DENOMINATORS

Fractions that have the same denominators are said to have common denominators. It is easy to add fractions if they have common denominators — you can simply add the numerators (the denominator does not change). In the example below, the two fractions from Hereare added together.

In the resulting fraction, both the numerator and the denominator are 3. When the numerator and the denominator are the same, a fraction is equal to 1, or one whole set.

Dr. Kenny, the zoo veterinarian, examined the cubs. They had fine white hair covering their pink skin, and their eyes were closed. They weighed slightly over one pound each, a typical weight for newborn polar bears. Gary, the keeper, named the male cub Klondike and the female cub Snow. Klondike had a cut on his head, possibly caused by Ulu picking him up in her mouth to move him. Both cubs were frail and very cold. Dr. Kenny didn't think they would live.

However, he asked Cindy, a veterinary technician, to take care of the bears, because she had raised many baby animals. The bears were put in a human infant incubator to raise their body temperatures. Several hours later, when Klondike had warmed up, Dr. Kenny stitched the cut on his head.

MAKING POLAR BEAR MILK

Cindy used a recipe to make polar bear milk. She mixed 1 cup of puppy milk with 2 cups of half-and-half to create a whole amount of 3 cups.

Since the whole amount was in three equal parts, you could say:

One part, or 1/3, was puppy milk. Two parts, or 2/3, were half-and-half.

After the milk was mixed, cod-liver oil and vitamins were added.

Because the cubs were very weak, Cindy fed them sugar water at first. Soon they would need milk. But what formula would be just right for polar bear cubs? Cindy did some research and learned that polar bear milk looks like heavy cream, smells fishy, and is high in fat. When zoos have to make milk for a baby bear, they use puppy milk formula because it's most like mother bear's milk. So Cindy mixed puppy milk with half-and-half (half milk and half cream) for extra fat, then added cod-liver oil and vitamins.

That night Cindy took the twins home with her. She didn't sleep at all — she was too busy tube-feeding milk to the cubs, cleaning them, and checking on every little cry. When dawn came, the small bears were still clinging to life.

DIVIDING A MONTH INTO THREE PARTS

To figure out how many times a month Cindy took the bears home with her, we can circle every third day on the calendar below. By counting the circled days, we can see that Cindy took the bears home ten times in a month that is thirty days long.

The chart below shows that this month can be divided into three equal parts of ten days each. Each part is equal to 1/3, or one-third of the month. So Cindy, Denny, and Dr. Kenny each spend 1/3, or one-third, of the month taking care of the bears at night.

At first the cubs needed to eat every two hours, or twelve times a day. Dr. Kenny, Cindy, and Denny (another veterinary technician) took turns bringing them home at night. Every third night, it was Cindy's turn. At five o'clock she put the two bears into a box padded with fleece to keep them warm, packed lots of bottles of milk, and loaded the cubs, their food, and a portable incubator into her car. Once home, she unpacked, made dinner, then fed and cleaned the bears. Snow was no trouble. She drank her bottle and went right back to sleep. But Klondike screamed a lot.

TWELFTHS AND THIRDS

When Klondike and Snow were two weeks old, they each drank twelve bottles of milk in one full day. Since one bear's daily portion of milk — the set — was twelve bottles, each bottle was 1/12, or one-twelfth, of the set.

The chart below shows that one-twelfth is a smaller fraction than one-third. When the denominator is a bigger number, the whole amount is divided into more parts, so each part is smaller. You can also see that the fraction four-twelfths, or 4/12, is equal to one-third, or 1/3. These two equal fractions are called equivalent fractions.

After two weeks, the cubs' weight had doubled. Snow was doing well, but Klondike had a tight, swollen belly. He didn't seem to be digesting the milk he was being fed.

Dr. Kenny ran some tests and consulted with other doctors. They decided not to add cod-liver oil to the milk anymore, but to use safflower oil instead. The doctors also felt that the bears were drinking too much milk.

With a smaller amount of the new milk, Klondike started to feel better. He was still fussy at night, so sometimes Cindy put him in a sleeping bag with her and let him suck on her finger. As the cubs' fur grew thicker, their bodies stayed warm enough outside the incubator. Both of them liked to sleep on Cindy's pillow.

EIGHTHS AND TWELFTHS

By the time Klondike and Snow were one month old, they drank more milk but they were fed less often. In a full day each bear drank eight bottles of milk. For each bear the whole amount, or set, was eight bottles, so one bottle was 1/8, or one-eighth, of the set.

You can see on the chart below that 1/12, or one-twelfth, is a smaller fraction than 1/8, or one-eighth.

When the bears were one month old, they slept in a wooden box together. Klondike liked to be near Snow. He pulled himself over to his sister and sucked on her paw. Then he would continue moving around, climbing on top of Snow or burrowing underneath her.

Sometimes Snow acted like she was in pain, crying out between feedings. She didn't like it when Klondike touched her. Cindy began to worry that Snow was too quiet and inactive. Dr. Kenny took X rays of the bears. The X rays showed that both bears had tiny breaks in many of their bones. Klondike and Snow had a disease called rickets.

FRACTIONS OF A 24-HOUR DAY

Klondike and Snow were at the zoo hospital every day from eight in the morning until five o'clock at night. They spent nine hours at the zoo. The next fifteen hours they spent at the home of Cindy, Denny, or Dr. Kenny.

Since there are twenty-four hours in a day, you can see from the chart below that three hours is equal to 1/8, or one-eighth, of a day. Nine hours is three times that much. It is equal to 3/8, or three-eighths, of a day. Fifteen hours is equal to 5/8, or five-eighths, of a day.

So the bears spent three-eighths of every day at the zoo and five-eighths of the day at a caretaker's house.

Rickets is caused by a lack of vitamin D, which the body needs in order to absorb calcium and build strong bones. Right away both cubs were given an injection of vitamin D, and their milk was once again made with cod-liver oil, because it has a lot of vitamin D in it. This time the milk didn't bother Klondike's stomach.

Since Snow had been growing faster than Klondike, her bones were more affected by the rickets. The two bears were separated so that Snow could rest without having her brother bumping her or climbing over her. Snow had trouble getting comfortable and often whimpered to be held. Cindy comforted the small bear and hoped the new milk would make her feel better.

MAKING POLAR BEAR MILK USING HALVES

When Klondike and Snow were two months old, the zoo staff decided that the bears needed more protein in their milk to help them grow faster. The original recipe had 1/3, or one-third, puppy milk.

Because puppy milk has more protein than half-and-half, Cindy knew she had to use a bigger fraction of puppy milk in the recipe.

So she increased the amount of puppy milk in the recipe to 1/2, or one-half, of the whole amount. The chart below shows that 1/2, or one-half, is bigger than 1/3, or one-third.

Cindy mixed 2 cups of puppy milk with 2 cups of half-and-half.

Since the whole amount was in four equal parts you could say:

Two parts, or 2/4, were puppy milk. Two parts, or 2/4, were half-and-half.

But the puppy milk is supposed to be 1/2, or one-half, of the whole amount, not 2/4, or two-fourths. The chart below shows that 1/2 and 2/4 are equivalent, or equal, fractions.

After the milk was mixed, cod-liver oil and vitamins were added.

Both bears got better quickly with cod-liver oil in their milk. A week later, an X ray showed that the cubs' bones had begun to heal. Snow often lay still on the nursery floor like a small bear rug. A physical therapist who had worked with animal patients for a local vet was called in to help Snow strengthen her muscles. Slowly she got stronger.

The cubs started to get their baby teeth, and they fussed because their gums hurt. Cindy soaked towels in water, rolled them up, and put them in the freezer. The bears liked chewing on the frozen towels. Later, Cindy gave them large ice blocks to suck on. Klondike and Snow used the ice as a pillow when they took their naps.

At two months, the bears weighed ten pounds each. But hand-raised polar bears at other zoos had weighed fifteen pounds at two months. Klondike and Snow weren't growing fast enough.

MAKING POLAR BEAR MILK USING FIFTHS

At two and a half months, Klondike and Snow still weren't growing as fast as the zoo staff thought they should be. Cindy needed to change the recipe for bear milk again. She needed to use a formula that had more puppy milk than one-half of the whole amount.

From the chart below, you can see that the fraction 1/5, or one-fifth, is smaller than 1/2, or one-half. This goes along with our rule that the bigger the denominator, the smaller the fraction. But when you add three of the one-fifth parts together, you get the fraction 3/5, or three-fifths, which is bigger than the fraction 1/2, or one-half.

Cindy mixed 3 cups of puppy milk with 2 cups of half-and-half to make a whole set of 5 cups.

Since the whole amount was in five equal parts, you could say:

Three parts, or 3/5, were puppy milk. Two parts, or2/5 , were half-and-half.

The last change to the milk recipe was made at two and a half months, and after that the bears grew rapidly. At three months, Klondike finally weighed a lot more than his sister and could pull himself around on the floor with his front paws. He still had trouble rolling from his back to his stomach. He would paw the air and struggle until he could flip over. Normally a baby bear can walk when he's two months old. Because they had had rickets, Klondike and Snow were late in their development.

With each week that passed, the bears got stronger. One week Klondike was walking around slowly. The next week he could run across the room. Cindy kept working with Snow, helping her stand against a red ball to strengthen her legs. Finally Snow began to walk.

FOURTHS AND EIGHTHS

At three months, the bears were drinking only four bottles of milk a day (though they also got some milk mixed into their solid food). For each bear the whole amount, or set, was four bottles, so one bottle was 1/4, or one-fourth, of the whole set.

Instead of drinking eight bottles a day, or one bottle every three hours, as they did when they were one month old, the bears were now drinking four bottles a day, or one every six hours. From the chart below, you can see that 1/4, or one-fourth, is a bigger fraction than 1/8, or one-eighth. In fact one-fourth is twice as big as one-eighth. One-fourth and two-eighths are equivalent, or equal, fractions.

When the cubs were about three months old, Cindy began to mix canned dog food with the bears' milk. Klondike liked to turn his bowl over and dump the mixture on the floor. Sometimes Snow would crawl through the spilled milk. Then her brother would lick the food off her fur.

The bears were now old enough to learn to swim. Cindy and Denny set up a swimming pool in the nursery. Klondike got right in the pool, but Snow was cautious. She watched Klondike swim underwater, like a furry submarine. Denny had to pick her up and put her in the pool.

When the bears were five months old, they were big enough to leave the nursery and go to a regular zoo exhibit. At first they were afraid to go in the large outdoor pool. Cindy and Dr. Kenny wore wet suits and swam in the pool, coaxing the bears to join them. Before long, however, the bears grew so big and powerful that it was too dangerous for humans to be with them anymore.

Both bears grew a lot in their first year of life. During the next few years, Klondike grew much bigger than Snow. Adult male polar bears are usually much bigger than female polar bears.

When Snow was full-grown, she weighed about 450 pounds, while Klondike weighed about 900 pounds. If you want to compare Snow's weight to Klondike's weight using a fraction, it would look like this:

In the chart below, you can see that 450 pounds is 1/2, or one-half, of 900 pounds.

So Snow weighs one half as much as Klondike.

Shortly after their first birthday, Klondike and Snow went to SeaWorld in Orlando, Florida. Cindy and Dr. Kenny flew with them on the plane from Colorado to Florida. The bears settled into their new home quickly and were soon catching the trout that swam around in their new pool.

When Cindy went to visit the bears a few years later, she watched them play and wrestle in the water. Klondike and Snow had grown into beautiful, healthy adult animals. After a time, the bears got out of the pool. Klondike went to the back of the exhibit to wait for his dinner, but Snow came toward the glass where the visitors were watching. Suddenly she got very excited, stood on her hind legs, and pounded on the glass with her paws. Even after all the time that had passed, Snow still recognized Cindy.

(Continues…)

Excerpted from "Polar Bear Math"
by .
Excerpted by permission of Henry Holt and Company.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

INTRODUCTION,
MOTHER POLAR BEARS,
Polar Bear Math,
COMMON DENOMINATORS,
MAKING POLAR BEAR MILK,
DIVIDING A MONTH INTO THREE PARTS,
TWELFTHS AND THIRDS,
EIGHTHS AND TWELFTHS,
FRACTIONS OF A 24-HOUR DAY,
MAKING POLAR BEAR MILK USING HALVES,
MAKING POLAR BEAR MILK USING FIFTHS,
FOURTHS AND EIGHTHS,

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