Dona Herweck - Travel Adventures: Yosemite: Perimeter and Area

0covercover.xhtmlTravel Adventures Yosemite Perimeter and Area Dona Herweck Ricecover1page0001page0001.xhtmlMath Talk 1. Why is perimeter a measurement of length? 2. Why are square units used to measure area? 3. Jamie always finds the area of rectangles by counting each square unit. What advice would you give him to be more efficient? How can you convince him that your strategy will work? 4. How can you find the width of a rectangle if you know its length and area? What if you know its length and perimeter? 5. What do you think is the most efficient formula for finding perimeter of a rectangle? Why? 6. When might a person have to find perimeter and area in real life? Why are the measurements helpful?22page0002page0002.xhtmlTravel Adventures Yosemite Perimeter and Area33page0003page0003.xhtml44page0004page0004.xhtmlTable of Contents A Place Like No Other 4 Valley History 6 Saving Yosemite 10 "A Glitter of Green and Golden Wonder" 14 Yosemite's Wildlife 20 Worth the Effort 27 Problem Solving 28 Glossary 30 Index 31 Answer Key 3255page0005page0005.xhtmlA Place Like No Other There's green as far as the eye can see. But only in spring and summer, of course. In winter, shades of white, blue, and purple streak the mountains and valleys. Year round, there is a lake so clear you can see reflections of mountains and sky. Standing at the water's edge, it's like looking into an upside-down world. There are tree-lined trails that give hikers shady comfort on even the hottest summer days. Towering cliffs, plunging waterfalls, and ancient domes seem like the stuff of movies rather than the real world. Bears, elk, and deer roam wild. Bats dot the evening sky with flapping wings and piercing cries. Mosquitoes and stinging bugs, dragonflies and butterflies, and all manner of flying creatures are everywhere. Everywhere. This is the majestic world of Yosemite. It has a natural beauty that is not found in many places. Millions of tourists agree it is one of the most breathtaking places in the world!66page0006page0006.xhtml77page0007page0007.xhtmlValley History Long before people came to Yosemite Valley, the rocky mountain cliffs and snaking waterways were already much like we know them today. Plant life flourished. Animals settled in this thriving place. It was a rich environment. People first came to the area about 8, 000 years ago. They hunted for food with spears and gathered seeds and other plants to eat. Archaeologists (ahr-kee-AWL-uh-jists) have found some traces of their lives. Fossils and tools they used have taught us much of what we know about them. Stories have also been passed down through the ages. But, no one knows exactly when the stories began. Let's Explore Math The Yosemite Valley is only a small portion of Yosemite. But, it is the part most visited by people today. The valley is shaped like a rectangle. It is about miles long and about 1 mile wide. Suppose you want to hike the rectangular distance surrounding Yosemite Valley. How might you find the perimeter of the valley? Show your thinking.88page0008page0008.xhtmlAt some point, these people called the place they lived Ahwahnee. That was their word for "gaping mouth. " A gaping mouth is what the wide valley looked like to them. Many think it looks that way still. About 4, 000 years ago, American Indians moved into the valley. These people were called Miwok (MEE-wok). The name simply means "people. " That is what they called themselves. By the late 1700s, the valley was filled with Miwok. They thrived in this environment. It offered everything they needed to live well. A Miwok man spearfishes in a creek.99page0009page0009.xhtmlGold Rush Life in Yosemite changed greatly in 1849. That year marked the start of California's Gold Rush. Thousands of people from all over the country swooped into the area. They wanted to get rich quickly. In their frenzy for gold, miners often pushed the Miwok off their land and out of their homes. Some Miwok were killed. Some died of starvation because their resources were taken. Others fought back, trying to preserve their way of life. Miners search for gold in California in 1849.1010page0010page0010.xhtmlIn time, most Miwok who stayed adapted to western culture. They began to dress like westerners. They began to eat western types of food. They took jobs in service to the newcomers. Some served as guides for those who had just arrived. They showed the new residents how to live in Yosemite, even though their own way of life was falling away. In time, the number of Miwok dwindled. Today, fewer than 1, 000 Miwok live in the area. They have worked to maintain and restore traditions of their culture. Let's Explore Math Remember that Yosemite Valley is about miles long and about 1 mile wide. Now, consider its area. Imagine that a huge storm passed over Yosemite Valley, and the ground is all covered in snow. Use the area model to find the number of square miles of snow covering the valley. 1 sq. mi. Miwok woman and her baby A Miwok tribe meets for a morning council in Yosemite Valley in 1872.1111page0011page0011.xhtmlSaving Yosemite Two men named Hutchings and Ayres went to Yosemite in 1855. They wrote and drew about the area. Then, they shared what they saw with others. Many people wanted to see it for themselves. The Wawona Hotel was built so that visitors would have a place to stay. A tunnel was carved through a giant sequoia called the Wawona Tree so they could drive right through it. The tree became a huge tourist attraction. Soon, more businesses were built. People tramped all over Yosemite. They used the land and built for commercial gain. They built homes. They took pieces as souvenirs. People exploited the beauties of Yosemite for their own gain. They didn't take action to preserve the land for the future. A group of conservationists grew worried. They wanted to protect Yosemite. These people made sure that the president of the United States knew about the problem. Abraham Lincoln joined their cause in 1864. He placed part of the land in public trust. This was the first time the government set up such protections for public land. It was an act that would mark the start of the national park movement.1212page0012page0012.xhtmlLet's Explore Math The rectangular opening to the tunnel in the Wawona Tree was 7 feet across and 9 feet tall before the tree toppled in 1969. 1. Draw a model of the tunnel opening. Label the dimensions. 2. Use the model to find the perimeter and area of the tunnel opening. Visitors drive through the Wawona Tree in 1910.1313page0013page0013.xhtmlPresident Theodore Roosevelt and John Muir visit Glacier Point in Yosemite, California.1414page0014page0014.xhtmlBecoming a National Park Yellowstone became the first national park in 1872. It was placed under the care of the U.S. government. People would still be able to enjoy the park but in ways that wouldn't harm it. Naturalist John Muir wanted the same for Yosemite. Sheep grazing had taken its toll on the land. Railroad tracks laid nearby brought many tourists. Despite the public trust, the land was overrun and overused. Yosemite was in danger. Muir spent years getting people to work with him to protect Yosemite. He wrote often about its wonders. He thought that such wild places were key to the health of the earth. He wrote, "All that the sun shines on is beautiful, so long as it is wild. " In 1890, the U.S. Congress set aside part of the area as a national park. But Muir thought more needed to be done. In 1903, he asked President Theodore Roosevelt to camp with him in Yosemite. Roosevelt was a fan of the outdoors and agreed to come. He was awed by what he saw. Muir convinced him to protect all of Yosemite. In 1906, he declared all of it a national park.1515page0015page0015.xhtml"A Glitter of Green and Golden Wonder" Ansel Adams was a famous photographer who took many photos of the park. He thought it was one of the most striking places on Earth and even lived there for a while. He called Yosemite "a glitter of green and golden wonder" a colorful caption for his black-and-white photos of the park. The park is found in the Sierra Nevada Mountains. It is 1, 169 square miles (3, 028 square kilometers). Its landscape was first formed 10 million years ago. The uplift of Earth's crust shaped the land. Then, about one million years ago, glaciers carved the mountain rock. Adams's photograph Mount Brewer, Southern Sierra Ansel Adams1616page0016page0016.xhtmlHundreds of plant species make the park their home. Giant sequoias dot the hills and valleys. Pine and cedar are also common. All types of wildflowers splash across the grassy meadows. Of the three sequoia groves, Mariposa Grove is the most visited. For a few months during the year, the road leading to the grove is closed due to weather. But, avid hikers still find their way. The Grizzly Giant may be Yosemite's most well-known tree. It stands 209 ft. (64 m) tall. Its base is 96. 5 ft. (29. 4 m) around! It's easy to see how the tree received its name. Grizzly Giant1717page0017page0017.xhtmlBridalveil Fall Besides the Grizzly Giant, another well-known site in Yosemite is Bridalveil Fall. The waterfall looks just like its name sounds. Water billows like the soft flowing fabric of a bride's veil. Its drop is 620 ft. (189 m) from top to bottom. With enough wind, the water can blow sideways, making it seem even more like a veil. Water at the fall flows all year long, although it is strongest in the spring. It is fed by Bridalveil Creek. The creek, in turn, is fed by Ostrander Lake, about 10 mi. (16 km) away. Bridalveil Fall Let's Explore Math Bridalveil Fall is about 20 meters across and about 200 meters tall. Imagine that the surface of the waterfall freezes and is made of squares of ice measuring 1 meter on each side. How many square meters of ice make up the surface of the frozen waterfall? Show your strategy for finding the solution.1818page0018page0018.xhtmlYosemite Falls Compared to Yosemite Falls, Bridalveil may seem like only a trickle. Yosemite Falls is the tallest of the park's more than 20 falls. It is 2, 425 ft. (739 m) tall. That is nearly half a mile. It is taller than almost all of the world's skyscrapers! Yosemite Falls is really made of three waterfalls. Each fall cascades into another. As with most falls in the park, water flows freely in the spring but can dry up by late summer. Autumn rain and winter snow return the falls to flowing. Yosemite Creek feeds the falls, which then flow into the Merced River. Yosemite Falls1919page0019page0019.xhtmlHalf Dome Half Dome is one of the most famous domes in the world. Rising 5, 000 ft. (1, 524 m) over Yosemite Valley, its rocky face glints in the sun. People come from all around the world to hike the tough trail. Just when they think they've reached their goal, they have to climb the last 400 ft. (122 m) with only two metal cables to help them. Looking down may make hikers nervous as they ascend. But, they are safe if they are careful. Most injuries are just blisters and twisted ankles. After completing the 10-to-12-hour round-trip, hikers return with a great story to tell. Half Dome Hikers climb Half Dome.2020page0020page0020.xhtmlEl Capitan El Capitan is the world's largest granite monolith. It is 13, 114 ft. (3, 997 m) tall. That's about 21/2 mi. (4 km)! Its height makes it a popular spot to climb. Climbers usually take between two and three days to reach the summit, or top. More advanced climbers can reach it in 24 hours. Known as El Cap, it is also popular for BASE jumps. BASE stands for building, antenna, span, and earth. These are fixed structures from which jumpers take their leaps. Many people have climbed or jumped from El Cap and have lived to tell the tale. But, that's not true for everyone. El Capitan2121page0021page0021.xhtmlYosemite's Wildlife John Muir was a naturalist who seemed to have the heart of a poet. Speaking of Yosemite's wildlife, he wrote, "How many hearts with warm red blood in them are beating under cover of the woods, and how many teeth and eyes are shining !" He went on, "A multitude of animal people, intimately related to us, but of whose lives we know almost nothing, are as busy about their own affairs as we are about ours ." Muir studied the animals of Yosemite almost like he studied the land. It was easy to do! Animals are everywhere you turn. Visitors can see them day and night. They come in all shapes and sizes. Mule deer, bobcats, and black bears live there in large numbers. Bats fill the night sky. Spotted owls and falcons take to the air as well. Foxes and skinks skitter along the ground. Rivers and lakes are filled with fish. Muir certainly was right; Yosemite is alive with its "animal people"! peregrine falcon2222page0022page0022.xhtmlbobcat skink2323page0023page0023.xhtmlBats As the sun sets on Yosemite, many visitors are struck by fluttering shadows overhead. During the day, bats are often found roosting and foraging in the sequoia groves. At night, they emerge to hunt and eat insects. There are 17 species of bat that call Yosemite home. The state of California only has 25 species, making the park a bat paradise! The big brown bat is the most common species there. brown bats2424page0024page0024.xhtmlBlack Bear Bears can also be found in the park. However, only about 300 to 500 black bears live there. It's not unheard of to see a bear, but it's not a common sight either. Bears generally don't like to walk among people. But, campers must be careful where they leave food. Hungry bears are known to raid tents. Bears can even smell food inside locked cars. It doesn't take much for them to break in! When bears can't find human food, they eat mainly berries, grasses, and acorns. They may eat meat, but it's not their typical diet. It's important for campers to help ensure that bears eat what nature provides. Human food is not healthy for them! Let's Explore Math Imagine that rangers measure the rectangular floor of a black bear's den in Yosemite. They discover that the den is 6 feet long and has a perimeter of 20 feet. How can they find the width of the den floor? Show your strategy. den black bear2525page0025page0025.xhtmlSierra Nevada Bighorn Sheep Sierra Nevada bighorn sheep once roamed Yosemite in huge numbers. Adept at climbing rocky hillsides, they thrived in the park's high ranges. But disease and hunting wiped out the bighorn population in the park's first 25 years. In time, conservationists were able to protect the species. They relocated sheep outside of Yosemite but still within the Sierra Nevada mountains. Later, they returned a few herds to the park. After nearly a century-long absence, the bighorn may return to the numbers they once had. Sierra Nevada bighorn sheep2626page0026page0026.xhtmlMule Deer Mule deer are the most easily spotted mammal in Yosemite. They are named for their big ears that look like a mule's. These deer communicate with their ears. They point them forward when they sense danger. They flatten them to their heads when angry. Mule deer eat shrubs and herbs. But they are a main food source for many predators, too. Visitors to Yosemite often try to feed mule deer. They are fooled by the deers' gentle looks. But the deer are wild animals. Many people are kicked or butted. Good thing, too. Human food can make the deer sick or dependent on humans. mule deer2727page0027page0027.xhtml2828page0028page0028.xhtmlWorth the Effort "Between every two pine trees there is a door leading to a new way of life. " John Muir wrote these words in the margin of his notebook. He was speaking of Yosemite. Muir found the beauty of Yosemite's landscape and wildlife inspiring. Countless visitors to Yosemite agree. Although visits are governed and the park is protected, people still come to Yosemite in droves. They hike its mountains. They explore its valley. They wade in its rivers and bike its trails. They camp in the forest or look out at the wild terrain from the window of a lodge. For just a little while, they make Yosemite their home, too. "It is good for everybody, " Muir also wrote about Yosemite. "None can escape its charms. Its natural beauty cleans and warms like a fire, and you will be willing to stay forever in one place like a tree. " Many people wish they could. They'd dig in their roots, sprout their leaves, and stand with the Grizzly Giant watching over the beautiful landscape known as Yosemite.2929page0029page0029.xhtmlProblem Solving Yosemite National Park is a popular place to vacation. Imagine you have been asked to build cabins for tourists. You must design four different cabins. Each cabin, no matter the size, should have a rectangle-shaped living area and a perimeter of 60 feet.3030page0030page0030.xhtml1. What is the length and width of the living areas of each of your four cabin designs? Sketch each design on graph paper, and label the dimensions. 2. How many square feet make up each cabin design? Explain your thinking. 3. What pattern do you notice in your strategies for finding the perimeter of each of your designs? 4. What pattern do you notice in your strategies for finding the area of each of your designs?3131page0031page0031.xhtmlGlossary archaeologists scientists who study humans of the past and their activities through the items they leave behind area the amount of space covered by square units inside a two-dimensional shape ascend to go up commercial having to do with earning money conservationists people who work to protect and preserve the natural world and its resources culture the belief, practices, customs, language, art, and music of a group of people living at the same time in the same place exploited used someone or something in a way that helped you unfairly foraging looking for food gaping spread wide open monolith a tall and narrow stone formation naturalist person who studies and explores nature perimeter the distance around the outside of a shape public trust system by which lands are held for use by all roosting making a home in a nest skinks type of lizard summit the top, or highest point, of a mountain3232page0032page0032.xhtmlIndex Adams, Ansel, archaeologists, area, BASE jumping, bats, bears, bighorn sheep, Bridalveil Fall, conservationists, El Capitan, Grizzly Giant, Half Dome, Lincoln, Abraham, Mariposa Grove, Miwok, Muir, John, mule deer, perimeter, Roosevelt, Theodore, sequoia, Sierra Nevada, Wawona Tree, Yosemite Falls,3333page0033page0033.xhtmlAnswer Key Let's Explore Math page 7 : 17 miles; + 1 + + 1 = 17; Answers will vary, but may include drawing a sketch of the rectangle, labeling the dimensions, and adding all four measurements. page 8 : 71/2 square miles; count the number of squares page 11 : 1. Model should be labeled as a 7 foot 9 foot rectangle 2. Perimeter = 32 ft.; Area = 63 sq. ft. page 16 : 4, 000 square meters; Strategies will vary, but may include drawing a sketch and multiplying the length and width. page 23 : 4 ft.; Answers will vary. Possible strategy : 6 + 6 = 12; 20 12 = 8; 8 2 = 4 Problem Solving 1. Answers may vary. Possible answers : 10 ft. 20 ft., 12 ft. 18 ft., 15 ft. 15 ft., and 16 ft. 14 ft. 2. Answers may vary. Possible answers : 10 ft. 20 ft. = 200 sq. ft.; 12 ft. 18 ft. = 216 sq. ft.; 15 ft. 15 ft. = 225 sq. ft.; 16 ft. 14 ft. = 224 sq. ft. 3. Answers will vary, but may include that the perimeter can be found by multiplying the length by 2, multiplying the width by 2, and adding the products; or, by adding the length and width and multiplying the sum by 2; or, by adding all sides. 4. Answers will vary, but may include that the area can be found by multiplying the length and width.3434page0034page0034.xhtmlMath Talk 1. Why is perimeter a measurement of length? 2. Why are square units used to measure area? 3. Jamie always finds the area of rectangles by counting each square unit. What advice would you give him to be more efficient? How can you convince him that your strategy will work? 4. How can you find the width of a rectangle if you know its length and area? What if you know its length and perimeter? 5. What do you think is the most efficient formula for finding perimeter of a rectangle? Why? 6. When might a person have to find perimeter and area in real life? Why are the measurements helpful?3535page0035page0035.xhtmlTravel Adventures Yosemite Perimeter and Area The landscapes of Yosemite have astounded people for thousands of years. Now, they are one reason why Yosemite is one of the most visited national parks in the world. Tourists are awed by the size, scope, and sweeping views. Reason with perimeter and area while touring one of the United States' national treasures! Measurement36