Explore Area and Mixed Numbers

NY Released Test - Grade 5 Math (2025)(New York Standards)

Topic 2 - Adding and Subtracting Decimals 5.NBT. 7

Topic 1 - Understand Place Value - 5.NBT.1, 2, 3 & 4

Characters: Tom and Mia Setting: Playground and nearby fields Tom: Hey Mia! Look at that flag on the pole! It’s huge! Mia: Wow! I almost can’t see the top. Hey, the map shows all the points in the playground. Let’s explore! Tom: Cool! I want to find the highest point and pretend I’m a mountain explorer. Mia: Haha! The clouds seem really close today. I think I can lie on the grass and touch them! Tom: Good idea! But careful… you might crash into a bug! Mia: Haha! Don’t worry, I brought my sack for collecting leaves and rocks. Tom: Nice! By the way, did you see that aircraft yesterday? Its flight was so long. It looked like a tiny toy in the sky! Mia: The sky looks endless today. I can’t see where it ends! Tom: Yeah! And the plains near the playground are huge. We could run forever. Mia: Tom, you look really serious. Are you thinking of a new game? Tom: Maybe… let’s clear this area and play “Treasure Explorer.” Mia: Perfect! I’ll hide the treasure in my sack first. Tom: Ready! Let’s go find it before the “aircraft” spies us from the sky!

Contact with the Americas In 1001, Viking sailors led by Leif Erikson reached the eastern tip of North America. Archaeologists have found evidence of the Viking settlement of Vinland in present-day Newfoundland, Canada. The Vikings did not stay in Vinland long and no one is sure why they left. However, Viking stories describe fierce battles with Skraelings, the Viking name for the Inuit. Evidence suggests that Asians continued to cross the Bering Sea into North America after the last ice age ended. Some scholars believe that ancient seafarers from Polynesia may have traveled to the Americas using their knowledge of the stars and winds. Modern Polynesians have sailed canoes thousands of miles in this way. Still others think that fishing boats from China and Japan blew off course and landed on the western coast of North or South America. Perhaps such voyages occurred. If so, they were long forgotten. Before 1492, the peoples of Asia and Europe had no knowledge of the Americas and their remarkable civilizations. The Voyages of Columbus Portuguese sailors had pioneered new routes around Africa toward Asia in the late 1400s. Spain, too, wanted a share of the riches. King Ferdinand and Queen Isabella hoped to keep their rival, Portugal, from controlling trade with India, China, and Japan. They agreed to finance a voyage of exploration by Christopher Columbus. Columbus, an Italian sea captain, planned to reach the East Indies by sailing west across the Atlantic. Finding a sea route straight to Asia would give the Spanish direct access to the silks, spices, and precious metals of Asia. The spice trade was a major cause for European exploration and a reason the Spanish rulers supported Columbus’s voyage. They also wanted wealth from any source. “Get gold,” King Ferdinand said to Columbus. “Humanely if possible, but at all hazards—get gold.” Crossing the Atlantic In August 1492, Columbus set out with three ships and about 90 sailors. As captain, he commanded the largest vessel, the Santa María. The other ships were the Niña and the Pinta. After a brief stop at the Canary Islands, the little fleet continued west into unknown seas. Fair winds sped them along, but a month passed without the sight of land. Some sailors began to grumble. They had never been away from land for so long and feared being lost at sea. Still, Columbus sailed on. On October 7, sailors saw flocks of birds flying southwest. Columbus changed course to follow the birds. A few days later, crew members spotted tree branches and flowers floating in the water. At 2 a.m. on October 12, the lookout on the Pinta spotted white cliffs shining in the moonlight. “Tierra! Tierra!” he shouted. “Land! Land!” At dawn, Columbus rowed ashore and planted the banner of Spain. He was convinced that he had reached the East Indies in Asia. He called the people he found there “Indians.” In fact, he had reached islands off the coasts of North America and South America in the Caribbean Sea. These islands later became known as the West Indies. For three months, Columbus explored the West Indies. To his delight, he found signs of gold on the islands. Eager to report his success, he returned to Spain. Columbus Claims Lands for Spain In Spain, Columbus presented Queen Isabella and King Ferdinand with gifts of pink pearls and brilliantly colored parrots. Columbus brought with him many things that Europeans had never seen before: tobacco, pineapples, and hammocks used for sleeping. Columbus also described the “Indians” he had met, the Taino (ty noh). The Taino, he promised, could easily be converted to Christianity and could also be used as slaves. The Spanish monarchs were impressed. They gave Columbus the title Admiral of the Ocean Sea. They also agreed to finance future voyages. The promise of great wealth, and the chance to spread Christianity, gave them a reason to explore further. Columbus made three more voyages across the Atlantic. In 1493, he founded the first Spanish colony in the Americas, Santo Domingo, on an island he called Hispaniola (present-day Haiti and the Dominican Republic). A colony is an area settled and ruled by the government of a distant land. Columbus also explored present-day Cuba and Jamaica. He sailed along the coasts of Central America and northern South America. He claimed all of these lands for Queen Isabella of Spain. Columbus proved to be a better explorer than governor. During his third expedition, settlers on Hispaniola complained of his harsh rule. Queen Isabella appointed an investigator, who sent Columbus back to Spain in chains. In the end, the queen pardoned Columbus, but he never regained the honors he had won earlier. He died in 1506, still convinced that he had reached Asia. The Impact of Columbus’s Voyages Columbus has long been honored as the bold sea captain who “discovered America.” Today, we recognize that American Indians had discovered and settled these lands long before 1492. We also recognize that Columbus and the Europeans who followed him treated the ancient inhabitants of the Americas brutally. Still, Columbus’s voyages did change history. They marked the beginning of lasting contact among the peoples of Europe, Africa, and the Americas. For a great many American Indians, contact had tragic results. Columbus and those who followed were convinced that European culture was superior to that of the Indians. The Spanish claimed Taino lands and forced the Taino to work in gold mines, on ranches, or in Spanish households. Many Taino died from harsh conditions or European diseases. The Taino population was wiped out. Still, the voyages of Columbus signaled a turning point for the Americas. A turning point is a moment in history that marks a decisive change. Curious Europeans saw the new lands as a place where they could settle, trade, and grow rich. Spanish Exploration Continues After the voyages of Columbus, the Spanish explored and settled other Caribbean islands that Columbus had found. They sought gold, land for crops, people to enslave, and converts to Christianity for the Spanish crown. By 1511, they had conquered Puerto Rico, Jamaica, and Cuba. They also explored the eastern coasts of North America and South America in search of a western route to Asia. In 1513, Vasco Núñez de Balboa (bal boh uh) crossed the Isthmus of Panama. American Indians had told him that a large body of water lay to the west. With a party of Spanish soldiers and Indians, Balboa reached the Pacific Ocean and claimed the ocean for Spain. The Spanish had no idea how wide the Pacific was until a sea captain named Ferdinand Magellan (muh jel un) sailed across it. The expedition—made up of five ships and about 250 crew members—left Spain in 1519. Fifteen months later, it cut through the stormy southern tip of South America by way of what is now known as the Strait of Magellan and entered the Pacific Ocean. Crossing the vast Pacific, the sailors ran out of food: Primary Source “We remained 3 months and 20 days without taking in provisions or other refreshments and ate only old biscuit reduced to powder, full of grubs and stinking from the dirt which rats had made on it. We drank water that was yellow and stinking.” —Antonio Pigafetta, The Diary of Antonio Pigafetta Magellan himself was killed in a battle with the local people of the Philippine Islands off the coast of Asia. In 1522, only one ship and 18 sailors returned to Spain. They were the first people to circumnavigate, or sail completely around, the world. In doing so, they had found an all-water western route to Asia. Europeans became aware of the true size of the Earth. How Did the Columbian Exchange Affect the Rest of the World? The encounter between the peoples of the Eastern and Western Hemispheres sparked a global exchange of goods and ideas. Because it started with the voyages of Columbus, this transfer is known as the Columbian Exchange. The Columbian Exchange refers to a biological and cultural exchange of animals, plants, human populations, diseases, food, government, technology, the arts, and languages. The exchange went in both directions. Europeans learned much from American Indians. At the same time, Europeans contributed in many ways to the culture of the Americas. This exchange also brought about many modifications, or changes, to the physical environment of the Americas, with both positive and negative results. Changing Environments Europeans introduced domestic animals such as chickens from Europe and Africa. European pigs, cattle, and horses often escaped into the wild and multiplied rapidly. Forests and grasslands were converted to pastures. As horses spread through what would become the United States, Indians learned to ride them and used them to carry heavy loads. Plants from Europe and Africa changed the way American Indians lived. The first bananas came from the Canary Islands. By 1520, one Spaniard reported that banana trees had spread “so greatly that it is marvelous to see the great abundance of them.” Oranges, lemons, and figs were also new to the Americas. In North America, explorers also brought such plants as bluegrass, the daisy, and the dandelion. These plants spread quickly in American soil and modified American grasslands. Tragically, Europeans also brought new diseases, such as smallpox and influenza. American Indians had no resistance to these diseases. Historians estimate that within 75 years, diseases from Europe had killed almost 90 percent of the people in the Caribbean Islands and in Mexico. American Indian Influences on Europe, Africa and Asia American Indians introduced Europeans to valuable food crops such as corn, potatoes, sweet potatoes, beans, tomatoes, manioc, squash, peanuts, pineapples, and blueberries. Today, almost half the world’s food crops come from plants that were first grown in the Americas. Europeans carried the new foods with them as they sailed around the world. Everywhere, people’s diets changed and populations increased. In South Asia, people used American hot peppers and chilies to spice stews. Chinese peasants began growing corn and sweet potatoes. Italians made sauces from tomatoes. People in West Africa grew manioc and corn. European settlers often adopted American Indian skills. In the North, Indians showed Europeans how to use snowshoes and trap beavers and other fur-bearing animals. European explorers learned how to paddle Indian canoes. Some leaders studied American Indian political structures. In the 1700s, Benjamin Franklin admired the Iroquois League and urged American colonists to unite in a similar way. Positive and Negative Consequences Through the Columbian Exchange, Europeans and American Indians modified their environments and gained new resources and skills. At the same time, warfare and disease killed many on both sides. Europeans viewed expansion positively. They gained great wealth, explored trade routes, and spread Christianity. Yet their farming, mining, and diseases took a toll on the physical environment and left many American Indians dead. Despite these negatives, the Columbian Exchange shaped the modern world, including what would become the United States.

Why should mankind explore space? Why should money, time and effort be spent exploring, investigating and researching something with so few apparent benefits? Why should resources be spent on space rather than on conditions and people on Earth? These are questions that, understandably, are very often asked. Perhaps the best answer lies in our genetic makeup as human beings. What drove our distant ancestors to move from the trees into the plains, and on into all possible areas and environments? It appears that we are driven to ensure the success and continuation of not just our own genes, but of the species as a whole. The wider the distribution of a species, the better its chance of survival. Perhaps the best reason for exploring space is this genetic predisposition to expand wherever possible. Nearly every successful civilisation has explored, because by doing so, any dangers in surrounding areas can be identified and prepared for. These might be enemies in neighbouring cultures, physical features of the area, a change in the area which might affect food supplies, or any number of other factors. They all pose a real danger, and all can be made less threatening if certain preparations are made. Without knowledge, we may be completely destroyed by the danger. With knowledge, we can lessen its effects. Exploration also allows minerals and other potential resources to be located. Additional resources are always beneficial when used wisely, and can increase our chances of survival. Even if we have no immediate need of them, they will perhaps be useful later. Resources may be more than physical assets. Knowledge or techniques acquired through exploration, or preparing to explore, filter from the developers into society at large. The techniques may have medical applications which can improve the length or quality of our lives. Techniques may be social, allowing members of society better to understand those within or outside the culture. Better understanding may lead to more efficient use of resources, or a reduction in competition for resources. We have already benefited from other spin-offs, including improvements in earthquake prediction – which has saved many lives – in satellites used for weather forecasting and in communications systems. Even non-stick saucepans and mirrored sunglasses are by-products of technological developments in the space industry! While many resources are spent on what seems a small return, the exploration of space allows creative, brave and intelligent members of our species to focus on what may serve to save us. While space may hold many wonders and explanations of how the universe was formed or how it works, it also holds dangers. The chances of a large comet or asteroid hitting the Earth are small, but it could happen in time. Such strikes in the past may account for the extinction of dinosaurs and other species. Human technology is reaching the point where it might be able to detect the possibility of this happening, and enable us to minimise the damage, or prevent it completely, allowing us as a species to avoid extinction. The danger exists, but knowledge can help human beings to survive. Without the ability to reach out across space, the chance to save ourselves might not exist. In certain circumstances, life on Earth may become impossible: over-population or epidemics, for instance, might eventually force us to find other places to live. While Earth is the only planet known to sustain life, surely the adaptive ability of humans would allow us to inhabit other planets and moons. It is true that the lifestyle would be different, but human life and cultures have adapted in the past and surely could in the future. The more a culture expands, the less chance there is that it will become extinct. Space allows us to expand and succeed: for the sake of everyone on the Earth, now and in the future, space exploration is essential.

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