Math in the News: Issue 63
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In this issue of Math in the News we look at Columbus' voyages. We make some calculations based on map data. For more math resources go to www.media4math.com.
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Ponce de leon
Juan Ponce de Leon was a Spanish explorer born into a noble family in Spain but was poor. He sought fame and fortune by becoming a soldier and joining Christopher Columbus on his second voyage to the Americas in 1493. Rather than returning to Spain, he stayed in the islands near North America and decided to explore the islands off the southern tip of North America to discover riches and claim land for Spain. In 1513, his journeys brought him to what is now St. Augustine, Florida, making him the first European to reach the southeastern coast of North America and claim the land for Spain.
Explorer Biographies
The document summarizes the voyages and motivations of several early European explorers to North and South America between the 15th and early 17th centuries. It describes Christopher Columbus' four voyages for Spain seeking a route to Asia, John Cabot's voyages for England to find new lands, and Juan Ponce de Leon's exploration of Florida while seeking the fountain of youth. It also outlines expeditions by Hernan Cortes to conquer Mexico, Jacques Cartier claiming land for France along the St. Lawrence River, and Francisco Coronado's search for the Seven Cities of Gold. Later explorers mentioned include Henry Hudson sailing for the Dutch and England, Robert de la Salle establishing French settlements, and Samuel de Champl
Christopher Columbus
Rodrigo Triana spotted land on October 12, 1492 at 2:00 am, ending an era of human history without knowledge of the Americas and beginning a new era of global exploration and connection. Columbus led the expedition despite facing doubts, guided by his faith and belief that he was fulfilling prophecies. His discovery changed the world in profound ways and helped spread the gospel message across many lands rapidly, as foretold in prophecy.
Christopher columbus aoife gardnier 2 e
Christopher Columbus made four voyages to the Americas between 1492 and 1504. On his first voyage in 1492, he landed on an island in the Bahamas, believing he had reached Asia, and proceeded to explore the Caribbean. Though he did not discover North America, his voyages led to the widespread European exploration and colonization of the Americas.
Colon first voyage
Christopher Columbus was an Italian explorer who sailed across the Atlantic Ocean in 1492 hoping to find a route to Asia but instead landed in the Bahamas, believing he had reached Asia. He made four voyages to the Caribbean and South America between 1492 and 1504, establishing permanent European colonies in the Americas. His voyages marked the beginning of centuries of exploration and colonization of the Americas by European powers.
European expansion and the myth of columbus
Some maps of European expansion into the Atlantic and Pacific, and an examination of the Columbus myth
Christopher columbus victoria keogh
Christopher Columbus embarked on four voyages across the Atlantic Ocean between 1492 and 1504. He was initially sponsored by the Spanish monarchs Ferdinand and Isabella and set out to find a western route to Asia. On his first voyage in 1492, he landed in the Bahamas and believed he had reached Asia, naming the indigenous peoples "Indians." His voyages led to the European colonization of the Americas and the beginning of widespread contact between the Eastern and Western hemispheres.
Columbus
Christopher Columbus was a boy with big dreams of exploration who wanted to find a shortcut to Asia. He asked the king and queen of Spain for help, and they provided him three ships. Columbus and his crew set sail but their trip across the Atlantic Ocean was long and they began running low on food. Eventually, Columbus spotted land where he met native people, realizing his childhood dream of discovery.
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Ponce de leon
Juan Ponce de Leon was a Spanish explorer born into a noble family in Spain but was poor. He sought fame and fortune by becoming a soldier and joining Christopher Columbus on his second voyage to the Americas in 1493. Rather than returning to Spain, he stayed in the islands near North America and decided to explore the islands off the southern tip of North America to discover riches and claim land for Spain. In 1513, his journeys brought him to what is now St. Augustine, Florida, making him the first European to reach the southeastern coast of North America and claim the land for Spain.
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The document summarizes the voyages and motivations of several early European explorers to North and South America between the 15th and early 17th centuries. It describes Christopher Columbus' four voyages for Spain seeking a route to Asia, John Cabot's voyages for England to find new lands, and Juan Ponce de Leon's exploration of Florida while seeking the fountain of youth. It also outlines expeditions by Hernan Cortes to conquer Mexico, Jacques Cartier claiming land for France along the St. Lawrence River, and Francisco Coronado's search for the Seven Cities of Gold. Later explorers mentioned include Henry Hudson sailing for the Dutch and England, Robert de la Salle establishing French settlements, and Samuel de Champl
Christopher Columbus
Rodrigo Triana spotted land on October 12, 1492 at 2:00 am, ending an era of human history without knowledge of the Americas and beginning a new era of global exploration and connection. Columbus led the expedition despite facing doubts, guided by his faith and belief that he was fulfilling prophecies. His discovery changed the world in profound ways and helped spread the gospel message across many lands rapidly, as foretold in prophecy.
Christopher columbus aoife gardnier 2 e
Christopher Columbus made four voyages to the Americas between 1492 and 1504. On his first voyage in 1492, he landed on an island in the Bahamas, believing he had reached Asia, and proceeded to explore the Caribbean. Though he did not discover North America, his voyages led to the widespread European exploration and colonization of the Americas.
Colon first voyage
Christopher Columbus was an Italian explorer who sailed across the Atlantic Ocean in 1492 hoping to find a route to Asia but instead landed in the Bahamas, believing he had reached Asia. He made four voyages to the Caribbean and South America between 1492 and 1504, establishing permanent European colonies in the Americas. His voyages marked the beginning of centuries of exploration and colonization of the Americas by European powers.
European expansion and the myth of columbus
Some maps of European expansion into the Atlantic and Pacific, and an examination of the Columbus myth
Christopher columbus victoria keogh
Christopher Columbus embarked on four voyages across the Atlantic Ocean between 1492 and 1504. He was initially sponsored by the Spanish monarchs Ferdinand and Isabella and set out to find a western route to Asia. On his first voyage in 1492, he landed in the Bahamas and believed he had reached Asia, naming the indigenous peoples "Indians." His voyages led to the European colonization of the Americas and the beginning of widespread contact between the Eastern and Western hemispheres.
Columbus
Christopher Columbus was a boy with big dreams of exploration who wanted to find a shortcut to Asia. He asked the king and queen of Spain for help, and they provided him three ships. Columbus and his crew set sail but their trip across the Atlantic Ocean was long and they began running low on food. Eventually, Columbus spotted land where he met native people, realizing his childhood dream of discovery.
Christopher columbus power point
Christopher Columbus was credited with discovering America in 1492 when he sailed west from Spain hoping to find a route to Asia. It took him 6 years to convince the Spanish royals to fund his journey. Upon landing in the Americas, Columbus referred to the native people as "Indians" believing he had reached Asia. However, later navigators like Vespucci demonstrated that the Americas were in fact a separate continent from Asia. While Columbus opened the door for exploration, historians now recognize that he never acknowledged having discovered a new continent.
Columbus
Christopher Columbus dreamed as a boy of exploring new lands and finding a shortcut from Spain to Asia. He asked the king and queen of Spain for help, who gave him three ships. Columbus and his crew set sail but their trip across the Atlantic was long and they began running low on food. Eventually, Columbus spotted land where he met native people, realizing his childhood dream of discovery and arriving in the Americas instead of Asia.
Powerpoint presentation 1 Christopher Columbus
Christopher Columbus was born in Italy in 1451 and grew up in a merchant family. He became interested in sailing as a teenager and made many voyages to Africa and Asia, gaining knowledge of ocean currents and trade routes. In 1492, Columbus received funding from the Spanish monarchs to sail west in search of a route to Asia. On his first voyage, he landed in the Bahamas instead of Asia, believing he had reached India. He established a settlement and returned to Spain with goods and native captives. His voyages opened the Americas to European colonization but had disastrous effects on native populations through disease, violence and exploitation. Columbus died in 1506 still believing he had reached Asia.
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Christopher Columbus was born in 1451 in Genoa, Italy. In 1492, he sailed from Spain with three ships and arrived in the Bahamas on October 12th, believing he had reached Asia. He explored the islands of Haiti and Cuba before returning to Spain. In 1493, he returned to the West with 14 ships and 1500 people, discovering more islands including Puerto Rico and Martinique. Columbus made three more voyages, discovering more islands and parts of South America, though he died in 1506 still convinced he had reached Asia.
Christopher Columbus
Christopher Columbus was an Italian explorer who sought to find a western sea route to Asia, with funding from the Spanish monarchs Ferdinand and Isabella. On August 3rd, 1492, Columbus departed from Spain with three ships and arrived in the Bahamas on October 12th, believing he had reached Asia. He encountered the indigenous Taíno people, explored several islands including Cuba and Hispaniola, and kidnapped some natives before returning to Spain. His voyage marked the beginning of widespread contact between Europeans and the peoples of the Americas.
Christopher Columbus
Christopher Columbus set sail from Spain in August 1492 hoping to find a western passage to India but instead discovered the Bahamas on October 12, 1492. His three ships, the Nina, Pinta and Santa Maria, faced hardships like pirate attacks, and one ship sank. Columbus made the discovery with funding from Spain, hoping to find gold, silver and spices. His discovery contributed to later European exploration and settlement of what is now New York state.
Juan ponce de leon
Juan Ponce de León discovered Florida in 1513 while searching for the Fountain of Youth. He had heard reports that the fountain was located on the island of Bimini and landed on the coast of Florida instead, naming it due to the many flowers he saw. Ponce de León went on to become the first governor of Puerto Rico after exploring the island in 1508 and finding gold deposits. He later returned to Florida in 1521 with 200 men to establish a settlement but was wounded in a Native American attack and died in Cuba from his injuries.
Christopher Columbus
Christopher Columbus was an Italian explorer who made four voyages between Spain and the Americas between 1492 and 1503. These voyages marked the beginning of European colonization of the Americas. Columbus wrongly estimated the distance between Europe and Asia and believed he had reached Asia when he landed in the Bahamas, not realizing he had discovered a new continent. While Columbus opened the door for European colonization, he faced increasing difficulties governing the colonies and was imprisoned for a year due to accusations of tyrannical rule before returning to Spain, where he died still convinced he had reached Asia.
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Juan Ponce de León was a Spanish explorer born in 1460 who led expeditions in the early 1500s hoping to find riches and the Fountain of Youth. On his first voyage in 1513, he encountered Florida while searching northwest of Hispaniola. He named Florida and became the first governor of Puerto Rico. Though he never found the Fountain of Youth, Ponce de León made important discoveries and helped expand Spain's claims in the Americas.
Christopher Columbus
Christopher Columbus was an Italian explorer who lived from 1451 to 1506. He wanted to find a new route to Asia by sailing west across the Atlantic Ocean. In 1492, he embarked on his first voyage funded by the Spanish monarchy and discovered several islands in the Bahamas which he believed were in Asia but were actually the Caribbean. Over subsequent voyages, he explored more islands in the Caribbean and parts of Central and South America, though he never realized he had found a new continent. He died in Spain in 1506 still believing he had reached Asia.
The first travel of Christopher Columbus
Christopher Columbus made his first voyage across the Atlantic Ocean in 1492. He set sail from Palos, Spain on August 3rd with three ships: the Pinta, the Niña, and the Santa Maria. After stopping at the Canary Islands, Columbus arrived in the Bahamas on October 12th, becoming the first European to discover the Americas since the Vikings. He later explored additional islands in the Caribbean, such as modern-day Santo Domingo and Cuba, before returning to Spain and arriving in Lisbon on March 4th and Palos on March 15th, 1493.
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The document is from an algebra library and summarizes rational numbers. It provides examples of numbers and asks the reader to identify which are rational. The numbers -1, -1/3, 1/2, 0, 5, -7, and 0.001 are rational while π, -√2, i, e, and x are not. It also presents an expression of a/b and asks the reader to check which properties are true of rational numbers, that both a and b must be integers, and the value of b cannot be zero.
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James Littech Ha3 Christopher Columbus
Christopher Columbus was an explorer who lived in the 15th century. He believed that the world was round, unlike many others at the time who thought you could fall off the edge. Columbus wanted to find a western route to Asia and sought funding from Ferdinand and Isabella of Spain. In 1492, Columbus set sail with three ships - the Nina, Pinta and Santa Maria - and landed in the Bahamas, believing he had reached Asia but had actually discovered the Americas.
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Christopher Columbus was credited with discovering America in 1492 when he sailed west from Spain hoping to find a route to Asia. It took him 6 years to convince the Spanish royals to fund his journey. Upon landing in the Americas, Columbus referred to the native people as "Indians" believing he had reached Asia. However, later navigators like Vespucci demonstrated that the Americas were in fact a separate continent from Asia. While Columbus opened the door for exploration, historians now recognize that he never acknowledged having discovered a new continent.
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Christopher Columbus dreamed as a boy of exploring new lands and finding a shortcut from Spain to Asia. He asked the king and queen of Spain for help, who gave him three ships. Columbus and his crew set sail but their trip across the Atlantic was long and they began running low on food. Eventually, Columbus spotted land where he met native people, realizing his childhood dream of discovery and arriving in the Americas instead of Asia.
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Christopher Columbus was born in Italy in 1451 and grew up in a merchant family. He became interested in sailing as a teenager and made many voyages to Africa and Asia, gaining knowledge of ocean currents and trade routes. In 1492, Columbus received funding from the Spanish monarchs to sail west in search of a route to Asia. On his first voyage, he landed in the Bahamas instead of Asia, believing he had reached India. He established a settlement and returned to Spain with goods and native captives. His voyages opened the Americas to European colonization but had disastrous effects on native populations through disease, violence and exploitation. Columbus died in 1506 still believing he had reached Asia.
Trabalho de itália powerpoint projecto comenius - inglês
Christopher Columbus was born in 1451 in Genoa, Italy. In 1492, he sailed from Spain with three ships and arrived in the Bahamas on October 12th, believing he had reached Asia. He explored the islands of Haiti and Cuba before returning to Spain. In 1493, he returned to the West with 14 ships and 1500 people, discovering more islands including Puerto Rico and Martinique. Columbus made three more voyages, discovering more islands and parts of South America, though he died in 1506 still convinced he had reached Asia.
Christopher Columbus
Christopher Columbus was an Italian explorer who sought to find a western sea route to Asia, with funding from the Spanish monarchs Ferdinand and Isabella. On August 3rd, 1492, Columbus departed from Spain with three ships and arrived in the Bahamas on October 12th, believing he had reached Asia. He encountered the indigenous Taíno people, explored several islands including Cuba and Hispaniola, and kidnapped some natives before returning to Spain. His voyage marked the beginning of widespread contact between Europeans and the peoples of the Americas.
Christopher Columbus
Christopher Columbus set sail from Spain in August 1492 hoping to find a western passage to India but instead discovered the Bahamas on October 12, 1492. His three ships, the Nina, Pinta and Santa Maria, faced hardships like pirate attacks, and one ship sank. Columbus made the discovery with funding from Spain, hoping to find gold, silver and spices. His discovery contributed to later European exploration and settlement of what is now New York state.
Juan ponce de leon
Juan Ponce de León discovered Florida in 1513 while searching for the Fountain of Youth. He had heard reports that the fountain was located on the island of Bimini and landed on the coast of Florida instead, naming it due to the many flowers he saw. Ponce de León went on to become the first governor of Puerto Rico after exploring the island in 1508 and finding gold deposits. He later returned to Florida in 1521 with 200 men to establish a settlement but was wounded in a Native American attack and died in Cuba from his injuries.
Christopher Columbus
Christopher Columbus was an Italian explorer who made four voyages between Spain and the Americas between 1492 and 1503. These voyages marked the beginning of European colonization of the Americas. Columbus wrongly estimated the distance between Europe and Asia and believed he had reached Asia when he landed in the Bahamas, not realizing he had discovered a new continent. While Columbus opened the door for European colonization, he faced increasing difficulties governing the colonies and was imprisoned for a year due to accusations of tyrannical rule before returning to Spain, where he died still convinced he had reached Asia.
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Juan Ponce de León was a Spanish explorer born in 1460 who led expeditions in the early 1500s hoping to find riches and the Fountain of Youth. On his first voyage in 1513, he encountered Florida while searching northwest of Hispaniola. He named Florida and became the first governor of Puerto Rico. Though he never found the Fountain of Youth, Ponce de León made important discoveries and helped expand Spain's claims in the Americas.
Christopher Columbus
Christopher Columbus was an Italian explorer who lived from 1451 to 1506. He wanted to find a new route to Asia by sailing west across the Atlantic Ocean. In 1492, he embarked on his first voyage funded by the Spanish monarchy and discovered several islands in the Bahamas which he believed were in Asia but were actually the Caribbean. Over subsequent voyages, he explored more islands in the Caribbean and parts of Central and South America, though he never realized he had found a new continent. He died in Spain in 1506 still believing he had reached Asia.
The first travel of Christopher Columbus
Christopher Columbus made his first voyage across the Atlantic Ocean in 1492. He set sail from Palos, Spain on August 3rd with three ships: the Pinta, the Niña, and the Santa Maria. After stopping at the Canary Islands, Columbus arrived in the Bahamas on October 12th, becoming the first European to discover the Americas since the Vikings. He later explored additional islands in the Caribbean, such as modern-day Santo Domingo and Cuba, before returning to Spain and arriving in Lisbon on March 4th and Palos on March 15th, 1493.
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The document is from an algebra library and summarizes rational numbers. It provides examples of numbers and asks the reader to identify which are rational. The numbers -1, -1/3, 1/2, 0, 5, -7, and 0.001 are rational while π, -√2, i, e, and x are not. It also presents an expression of a/b and asks the reader to check which properties are true of rational numbers, that both a and b must be integers, and the value of b cannot be zero.
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James Littech Ha3 Christopher Columbus
Christopher Columbus was an explorer who lived in the 15th century. He believed that the world was round, unlike many others at the time who thought you could fall off the edge. Columbus wanted to find a western route to Asia and sought funding from Ferdinand and Isabella of Spain. In 1492, Columbus set sail with three ships - the Nina, Pinta and Santa Maria - and landed in the Bahamas, believing he had reached Asia but had actually discovered the Americas.
Columbus
Christopher Columbus was born in 1451 in Genoa, Italy. He believed the world was round and proposed sailing west to reach Asia, hoping to find a trade route for spices. In 1492, King Ferdinand and Queen Isabella of Spain funded Columbus' expedition, providing him with three ships: the Nina, Pinta and Santa Maria. On October 12, 1492, Columbus landed in the Bahamas, believing he had reached Asia, but had actually discovered the Americas. Over his four voyages, Columbus explored the Caribbean islands and parts of Central and South America, claiming the lands for Spain. Columbus died in 1506, still believing he had reached Asia.
Christopher Columbus Enrichment Book
Columbus set sail from Spain in 1492 with the goal of reaching Asia by sailing west across the Atlantic. After over two months at sea, land was spotted on October 12, 1492, though it was not Asia but a Bahamian island. Columbus made three subsequent voyages, exploring and establishing colonies in the Caribbean and along the Central and South American coasts. However, he never found the riches he promised and died disgraced, though he had succeeded in opening the door for European exploration and colonization of the Americas.
Christopher columbus
Christopher Columbus made four trips to the Caribbean and South America between 1492 and 1504 in an attempt to find a route to India to trade for spices. On his first trip in 1492, Columbus led an expedition of three ships and landed on an island he named San Salvador. Columbus established a colony on Hispaniola during his second trip in 1493-1496 and explored Cuba and other islands. During his third trip from 1498-1500, Columbus explored South America, becoming the first European since the Vikings to reach the mainland of North America. Columbus's fourth and final trip from 1502-1504 took him to Central America and Jamaica before he returned to Spain.
The Columbian Exchange
This document discusses Christopher Columbus and the consequences of his voyages to the Americas in the late 15th century. It describes Columbus' upbringing and experiences at sea that convinced him the world was round and could be sailed around to access eastern trade routes. It details his voyage in 1492 with three small ships, during which he discovered the West Indies and landed in the Americas, though he did not realize he had found a new world. It also discusses the devastating impacts on indigenous populations from European colonization and diseases, with populations declining rapidly in the decades following first contact.
Abinash Baniya - 5p ppt project on columbus
Christopher Columbus made four voyages across the Atlantic Ocean from Spain between 1492 and 1502. While seeking a direct route to Asia, he instead encountered the Americas. His journeys marked the beginning of centuries of European colonization in the Americas. However, Columbus and his men also subjected the native inhabitants to violence and brutality, enslaving many and imposing forced labor policies. Today, Columbus remains a controversial figure who is both celebrated for initiating the Columbian Exchange and criticized for the devastating impacts on indigenous populations.
Columbus
Early explorers like Christopher Columbus used map skills to explore new lands. In 1492, Columbus set sail from Spain across the Atlantic Ocean hoping to find a western route to Asia, but instead became the first European to discover the Americas. He convinced the King and Queen of Spain to fund his expedition and they provided three ships. After a difficult voyage, Columbus landed on an island in the Caribbean that he mistakenly believed was India, naming the native people "Indians" though he had actually reached a new continent.
Christopher Columbus Powerpoint
It seems that some of the things within my presentation got moved around a little bit when I uploaded it to here! I'm sorry I tried to fix it a couple of times but I just don't know why the format keeps changing around on me.
Christopher Columbus projecto comenius - inglês
Christopher Columbus was born in 1451 in Genoa, Italy. In 1492, he sailed from Spain with three ships and came upon land in the Bahamas, believing he had reached Asia. He explored the islands of Haiti and Cuba before returning to Spain. In 1493, he returned to the West with 14 ships and 1500 people, discovering more islands including Puerto Rico and Martinique. Though he never knew it, Columbus had in fact reached a "New World" and not Asia as he believed.
The myth of columbus
Columbus' voyages were not as difficult as commonly portrayed. He had experienced crews and well-equipped ships. While he never reached North America, landing in the Caribbean instead, his voyages did connect Europe and the Americas, leading to immense changes including the near-extinction of the native Taino people from disease and violence within decades. Columbus profited from his discoveries but was an ineffective governor, though he lived comfortably in Spain until his death from disease.
Colonial america
The Age of Discovery began in the 15th century as European powers sought new trade routes and lands. Portugal, Spain, England, France and the Netherlands launched explorations led by figures like Columbus, Vespucci, Cabot and Verrazano. These explorations resulted in contact with indigenous peoples in the Americas and led to the beginning of European colonization and exploitation of resources. The Treaty of Tordesillas divided control of newly discovered lands between Spain and Portugal. Significant explorations included those by Columbus, Cortes-Real, Cabot, Vespucci, Magellan and others. Indigenous populations declined sharply due to disease and conflict with European colonizers.
The discovery of america
North and South America were discovered by Christopher Columbus in 1492. Columbus was born in Genoa, Italy but lived in Spain, where he convinced King Ferdinand and Queen Isabella to fund his expedition. In August 1492, Columbus set sail from Spain with three ships - the Niña, Pinta, and Santa Maria - and arrived in the Bahamas after over a month at sea, believing he had found a new route to Asia but had actually discovered the Americas. He claimed the land for Spain and named the native peoples "Indians," establishing the permanent European presence in the Western Hemisphere.
American history 1492 1776
1) The first people to arrive in North and South America were hunting bands from Asia who crossed over a land bridge between Siberia and Alaska over 25,000 years ago.
2) Christopher Columbus completed four voyages across the Atlantic Ocean in the late 15th century, which led to European awareness of the Americas and initiated the Spanish colonization of the New World.
3) Although Columbus was not the first person to discover the Americas, his voyages are seen as initiating widespread European exploration and colonization of the region.
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Math in the News: Issue 107
This document discusses using mathematical models to represent the thawing of frozen turkeys. It introduces logarithmic functions as a model for thawing curves, as the temperature increases over time in a way similar to the inverse of an exponential cooling curve. The document provides guidelines from the USDA for safely thawing turkeys either in the refrigerator over several days or in a water container over several hours, and shows how to construct a logarithmic model to fit starting and ending temperature points for a turkey thawing in the refrigerator.
Tutorials--Cube Root Functions in Tabular and Graph Form
This document provides 40 examples of tutorials that construct function tables and graphs for cube root functions of the form y=cuberoot(ax+b)+c. Each tutorial varies the values of a, b, and c to illustrate different forms of cube root functions.
Tutorials--Square Root Functions in Tabular and Graph Form
This document provides 40 examples of tutorials for constructing tables and graphs of square root functions. Each tutorial examines a square root function of the form y = sqrt(ax + b) + c or y = d * sqrt(ax + b) + c, varying the values of a, b, c, and d to demonstrate different forms of square root functions.
Tutorials--Logarithmic Functions in Tabular and Graph Form
This document contains 120 examples of tutorials that construct function tables and graphs for logarithmic functions in tabular and graph form. The tutorials vary the base of the logarithm (base 10 or base 2), the characteristics of the logarithmic function (values of a, b, c for the function y = log(ax + b) + c), and whether the function has a single logarithm or a scaled logarithm (with coefficient d).
Tutorials--Secant Functions in Tabular and Graph Form
This document describes 65 tutorials that provide examples of constructing tables and graphs for secant functions of the form y = sec(ax + b) + c, where a, b, and c can have various values. Each tutorial examines a different combination of values for a, b, and c to demonstrate secant functions with different periodic behaviors and shifts.
Tutorials--Cosecant Functions in Tabular and Graph Form
This document describes 65 tutorials that provide examples of constructing tables and graphs for cosecant functions. Each tutorial examines a cosecant function of the form y = csc(ax + b) or y = a * csc(bx + c) + d with different values for the variables a, b, c, and d. The tutorials demonstrate how changing the values of these variables affects the shape of the cosecant function graph and its table of values.
Tutorials--Tangent Functions in Tabular and Graph Form
This document provides 65 examples of tutorials that construct function tables and graphs for tangent functions of the form y = tan(ax + b) + c. Each tutorial varies the values of a, b, and c to illustrate different characteristics of tangent graphs.
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Math in the News: Issue 112--Back-to-School Purchases
Math in the News: Issue 112--Back-to-School Purchases
Tutorials--The Language of Math--Variable Expressions--Multiplication and Sub...
Tutorials--The Language of Math--Variable Expressions--Multiplication and Sub...
Tutorials--The Language of Math--Variable Expressions--Multiplication and Add...
Tutorials--The Language of Math--Variable Expressions--Multiplication and Add...
Tutorials--The Language of Math--Numerical Expressions--Grouping Symbols
Tutorials--The Language of Math--Numerical Expressions--Grouping Symbols
Tutorials--The Language of Math--Numerical Expressions--Multiplication
Tutorials--The Language of Math--Numerical Expressions--Multiplication
Tutorials--The Language of Math--Numerical Expressions--Division
Tutorials--The Language of Math--Numerical Expressions--Division
Tutorials--The Language of Math--Numerical Expressions--Subtraction
Tutorials--The Language of Math--Numerical Expressions--Subtraction
Tutorials--Language of Math--Numerical Expressions--Addition
Tutorials--Language of Math--Numerical Expressions--Addition
Tutorials--Cube Root Functions in Tabular and Graph Form
Tutorials--Cube Root Functions in Tabular and Graph Form
Tutorials--Square Root Functions in Tabular and Graph Form
Tutorials--Square Root Functions in Tabular and Graph Form
Tutorials--Logarithmic Functions in Tabular and Graph Form
Tutorials--Logarithmic Functions in Tabular and Graph Form
Tutorials--Secant Functions in Tabular and Graph Form
Tutorials--Secant Functions in Tabular and Graph Form
Tutorials--Cosecant Functions in Tabular and Graph Form
Tutorials--Cosecant Functions in Tabular and Graph Form
Tutorials--Tangent Functions in Tabular and Graph Form
Tutorials--Tangent Functions in Tabular and Graph Form
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Math in the News: Issue 63
- 1. Math in the News Christopher Columbus requesting funds for his voyage from Queen Isabella and King Ferdinand of Spain Christopher Columbus is known for discovering America, but that wasn’t his original plan. He was looking for sugar, spices, and other riches east of Japan. He believed that he could reach those places by traveling west. In this issue of Math in the News, we discover the routes Christopher Columbus traveled during his four famous voyages. We use map data to draw some conclusions.
- 2. Math in the News This is a map of Columbus‘ first voyage. It took him 40 days to reach San Salvador, an island in the Bahamas. If he traveled 150 miles a day, how many miles in total did he travel?
- 3. Math in the News Columbus made three more voyages to the New World. Here is a map of all four voyages. Can you calculate the number of miles he traveled during voyages 2 through 4?
- 4. Math in the News The map on the right is Columbus’ third voyage. This trip took longer because Columbus was waylaid in the Doldrums, an area with little wind off the coast of Africa. What other ways was the third voyage different from the other three?
- 5. Math in the News The bottom map shows Columbus’ final voyage, which he completed in 21 days. If this trip was about 3,500 miles, how many miles did he travel each day? Columbus was considered a master of the seas. Can you see why?
- 6. Math in the News The bottom map shows Columbus’ final voyage, which he completed in 21 days. If this trip was about 3,500 miles, how many miles did he travel each day? Columbus was considered a master of the seas. Can you see why?