Benjamin's Praxis Blog

Praxis Elementary Education: Math (5003)

The following are my study notes for the PLT exam, the outline is created using the Praxis official scope outline. Definitions and sample questions have been added. This outline is useful for keeping information organized, though the presentation here lacks polish, it tries to cover the most important theories and concepts.

expression - no equals sign

equation - has an equals sign

inequality - ><

Algebraic expression -

numerical expression -

statistic - a statistical question is one that can be answered by collecting data and where there will be variability in the data collected.

box plots - see diagram

Quadrants

  • A monomial is an algebraic expression that consists of one term that is a number (2), a variable (y), or a product of a number and a variable(2+y), where all exponents are whole numbers. (also, 2y)
  • binomial is a polynomial that is the sum of two terms, each of which is a monomial. (a+b)²
  • coefficient a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).
  • factor a number or quantity that when multiplied with another produces a given number or expression. "an amount that exceeds it by a factor of 1000 or more"
  • Independent variable in r= 5b Since the formula investigates how the number of roses r used increases depending on the number of bouquets b, the dependent variable is r and the independent variable is b.
  • dependent variable
CAT MAT Educational Android Aps

II. Geography, Anthropology, and Sociology

A. Knows world and regional geography (e.g., spatial terms, places, regions)

The Lowest Point The Dead Sea (Its surface and shores are 430.5 metres (1,412 ft) below sea level )

The Highest Point Mount Everest (in the Himalayas in Nepal and China)

The Largest Lake The Caspian Sea

The Longest River The Nile River

The Coldest Land Antarctica

The Driest Land Atacama Desert Chile

The Largest Island Greenland

The Hottest Land Ethiopia

The Wettest Land India

The Largest Waterfall Angel Falls (Venezuela)

The Largest Desert Sahara (NE Northern Africa)

Largest Canyon Grand Canyon

The Largest Reef Great Barrier Reef (Australia)

Deepest point/trench in the world Challenger Deep, Mariana Trench, Philippine Sea, Pacific Ocean

7 Continents: Europe, Africa, South America, North America, Asia, Oceania (Australia and Pacific Islands), and Antarctica.

The 10 Largest Lakes

1. Caspian Sea, Azerbaijan-Russia-Kazakhstan-Turkmenistan-Iran (salt water)

2. Superior, U.S.-Canada

3. Victoria, Tanzania-Uganda

4. Huron, U.S.-Canada

5. Michigan, U.S.

6. Aral, Kazakhstan-Uzbekistan

7. Tanganyika, Tanzania-Congo

8. Baikal, Russia

9. Great Bear, Canada

10. Nyasa, Malawi-Mozambique-Tanzania

The 10 Largest Rivers

1. Nile, Africa

2. Amazon, South America

3. Mississippi-Missouri-Red Rock, United States

4. Chang Jiang (Yangtze), China

5. Ob, Russia

6. Huang Ho (Yellow), China

7. Yenisei, Russia

8. Parana, South America

9. Irtish, Russia

10. Zaire (Congo), Congo

Largest Seas by area (seems to vary depending on source used)

1. Philippine sea 5.69 million km2

2. Coral Sea 4.79 million Km2

3. Arabian Sea 3.86 Km2

4. South China Sea 3.5 million Km2

5. Weddell Sea 8.8 million km2

B. Understands the interaction of physical and human systems (e.g., how humans change the environment, how the environment changes humans, importance of natural and human resources)


C. Knows the uses of geography (e.g., apply geography to interpret past, to interpret present, to plan for future)


D. Knows how people of different cultural backgrounds interact with their environment, family, neighborhoods, and communities

III. World History and Economics

A. Knows the major contributions of classical civilizations (e.g., Egypt, Greece, Rome)

Sumerians

The people who dominated southern Mesopotamia through the end of the third millennium B.C.E. They were responsible for the creation of many fundamental elements of Mesopotamian culture-such as irrigation technology, cuneiform, and religious conceptions.

Chinese Empire

(2100 BCE - 1911 CE)

Since the end of the Warring States Period in 221 BC, China has functioned as an Empire. Although the Dynasties have changed several times, the basic government structure remained the same until the 20th century. The Chinese also have extensive written record of their culture, which heavily empathizes history, philosophy, and a common religion.

Indian Empire

(7600 BCE - 1858 CE)

The subcontinent was seldom unified in terms of government until the British Empire controlled the area in the 19th and 20th centuries. In terms of culture, India has had persistent institutions and religions that have loosely united the people, such as the caste systems and guilds. These have regulated daily life more than any government.

Egyptians

the first true developers of a solar calendar, the decimal system, and made significant contributions to the development of religion, geometry, and astronomy

Indus Valley

C.3000-C.1750 BCE


A civilization extending from what today is now Pakistan to northwest India and northeast Afghanistan. It flourished in the basins of the Indus River. At its peak it had a population of over five million. The Indus cities are noted for their urban planning, baked brick houses, elaborate drainage systems, water supply systems, and clusters of large non-residential buildings.

Ancient Greece

A civilization that lasted from the 8th/6th century BCE to 600 AD. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine Era. Because of conquests by Alexander the Great of Macedonia, Hellenistic civilization flourished from Central Asia to the western end of the Mediterranean Sea. Classical Greek culture, especially philosophy, had a powerful influence on the Roman Empire, which carried a version of it to many parts of the Mediterranean Basin and Europe, for which Classical Greek is generally considered to be the seminal culture which provided the foundation of modern Western culture.

Ancient Mesopotamia

A religion in and around the Tigris-Euphrates river system in which some of the earliest known civilization formed. it includes Sumer, Assyria, and Babylonia.

Ancient Rome

A civilization that began on the Italian Peninsula as early as the 8th century BCE. During its 12 centuries of existence Roman civilization shifted from a monarchy to a classical republic and then to an increasingly autocratic empire. Through conquest and assimilation it came to dominate Southern and Western Europe, Asia Minor, North Africa, and parts of Northern and Eastern Europe. Ancient Roman society has contributed to modern government, law, politics, engineering, art, literature, and society. It achieved impressive technological and architectural feats, such as the construction of an extensive system of aqueducts and roads, as well as large monuments, palaces, and public facilities.

B. Understands twentieth-century developments and transformations in world history

World War 1

(1914-1918) First time all European Countries are engulfed in one war (Italy, Austria-Hungry, and Germany, against France, Russia, Great Britain) as a result of Industrial Revolution, scramble for Africa, and alliance systems. At least 20 million people died. The assignation of Archduke Ferdinand was the breaking point. The war ended the Empire system throughout the world.

Great Depression

(1929-1939) The dramatic decline in the world's economy due to the United State's stock market crash of 1929, the overproduction of goods from World War I, and decline in the need for raw materials from non industrialized nations. Results in millions of people losing their jobs as banks and businesses closed around the world. Many people were reduced to homelessness, and had to rely on government sponsored soup kitchens to eat. World trade also declined as many countries imposed protective tariffs in an attempt to restore their economies.

Cold War

(1945-1991) The period after the Second World War marked by rivalry and tension between the two nuclear superpowers, the United States and the communist government of the Soviet Union. The Cold War ended when the Soviet government collapsed in 1991.

The Korean War was a war between North Korea and South Korea. The war began on 25 June 1950 when North Korea invaded South Korea.

Vietnam War after World War II and the French withdrawal from its former colony, on 21 July 1954, Vietnam became partitioned into two halves, much like Korea, along the 17th parallel. Fighting between North and South eventually escalated into a regional war. the Gulf of Tonkin Resolution, passed in reaction to a supposed North Vietnamese attack upon American destroyers, brought the U.S. into the war as a belligerent. Saigon was captured on April 30, 1975, and Vietnam was unified under Communist rule a year later, effectively bringing an end to one of the most unpopular wars of all time.

The Cuban Missile Crisis (1961)

(JFK) An international crisis in October 1962, the closest approach to nuclear war at any time. When the U.S. discovered Soviet nuclear missiles on Cuba, President John F. Kennedy demanded their removal and announced a naval blockade of the island; the Soviet leader Khrushchev acceded to the U.S. demands a week later, on condition that US doesn't invade Cuba.

The space race

1957 with the Soviet launch of Sputnik.

the USSR reached several important milestones, such as the first craft on the Moon (Luna 2)

12 April 1961 the first human in space (Yuri Gagarin)

the U.S. Mercury, Gemini, and Apollo programs, which culminated in Apollo 11 astronauts landing on the moon on 20 July 1969.

Fall of the Berlin Wall East Germany and West Germany were reunified in 1990.


Women's right to vote

More than 18 million people passed through the Gulag, with a further 6 million being exiled to remote areas of the Soviet Union

independence and partition of India and Pakistan

Gandhi's nonviolence and Indian independence movement against the British Empire influenced many political movements around the world, including the civil rights movement in the U.S., and freedom movements in South Africa and Burma.

The Quit India Movement was a civil disobedience movement in India which commenced on 8 August 1942 in response to Gandhi's call for immediate self-rule by Indians and against sending Indians to World War II. He asked all teachers to leave their schools, and other Indians to leave their respective jobs and take part in this movement.

When Britain reached out to the US asking for help in the war, the US offered help contingent on Britain's decolonizing post-WWII.

On 3 June 1947, Viscount Louis Mountbatten, the last British Governor-General of India, announced the partitioning of British India into India and Pakistan. On 15 August 1947 India became a sovereign and democratic nation.

South Africa - After the creation of the apartheid system in 1948. In 1990, prominent ANC figures such as Nelson Mandela were released from prison. Apartheid legislation was repealed on 17 June 1991, pending multiracial elections held under a universal suffrage set for April 1994. In April 1994, Nelson Mandela was elected as South Africa's first black president.

Burma - In 1989, the ruling military government changed the name from Burma to Myanmar after thousands were killed in an uprising. The city of Rangoon also became Yangon... The name change was also a way to rid the country of British colonial influences. On 15 March 2016, Htin Kyaw was elected as the first non-military president since the military coup of 1962.[114] On 6 April 2016, Aung San Suu Kyi assumed the newly created role of State Counsellor, a role akin to a Prime Minister.

After a long period of civil wars and conflicts with western powers, China's last imperial dynasty ended in 1912. The resulting republic was replaced, after another civil war, by a communist People's Republic in 1949. At the end of the 20th century, though still ruled by a communist party, China's economic system had largely transformed to capitalism.

The Great Chinese Famine was a direct cause of the death of tens of millions of Chinese peasants between 1959 and 1962. It is thought to be the largest famine in human history.

The Soviet War in Afghanistan caused one million deaths and contributed to the downfall of the Soviet Union.

The Tiananmen Square protests of 1989, culminating in the deaths of hundreds of civilian protesters, were a series of demonstrations in and near Tiananmen Square in Beijing, China. Led mainly by students and intellectuals, the protests occurred in a year that saw the collapse of a number of communist governments around the world.

European integration began in earnest in the 1950s, and eventually led to the European Union, a political and economic union that comprised 15 countries at the end of the 20th century. The EU and European citizenship were established when the Maastricht Treaty came into force in 1993.

C. Understands the role of cross-cultural comparisons in world history instruction

D. Knows key terms and basic concepts of economics (e.g., supply and demand, scarcity and choice, money and resources)

  • economics the branch of knowledge concerned with the production, consumption, and transfer of wealth
  • supply and demand relationship between the amount of product and the desire for the product
  • scarcity and choice scarcity limits our options and necessitates that we make choices
  • The law of demand states that a higher price leads to a lower quantity demanded and that a lower price leads to a higher quantity demanded.
  • Demand curves and demand schedules are tools used to summarize the relationship between quantity demanded and price.
  • In economic terminology, demand is not the same as quantity demanded. When economists talk about demand, they mean the relationship between a range of prices and the quantities demanded at those prices
  • The law of supply states that a higher price leads to a higher quantity supplied and that a lower price leads to a lower quantity supplied.
  • Supply curves and supply schedules are tools used to summarize the relationship between supply and price.
  • When economists talk about supply, they mean the amount of some good or service a producer is willing to supply at each price.
  • When the price of gasoline rises, for example, it encourages profit-seeking firms to take several actions, e.g. build new oil refineries.
  • Supply curve shift: Changes in production cost and related factors can cause an entire supply curve to shift right or left. This causes a higher or lower quantity to be supplied at a given price.
  • The ceteris paribus assumption: Supply curves relate prices and quantities supplied assuming no other factors change. This is called the ceteris paribus assumption. Economists call this assumption ceteris paribus, a Latin phrase meaning “other things being equal”.
  • Supply and demand curves intersect at the equilibrium price. This is the price at which we would predict the market will operate.



E. Understands how economics affects population, resources, and technology


F. Understands the government’s role in economics and the impact of economics on government