Order of operations within math problems gives students a set of rules to follow in order to get the same answer. In the standard order of operations, expressions within parentheses are worked first, then exponents, then multiplication, division, addition, and subtraction.

Suppose the problem is as simple as 85 +9 X 2. Without an order of operations, one person might calculate the problem as (85 +9) X 2 or 94 X 2 = 188, while another might calculate it as 85 + (9 X 2) or 85 + 18 =103. Similarly, does 2 X 3^{4} mean 6^{4}, or 1296, or does it mean to work the 3^{4 }and then multiply by 2, or 81 X 2 = 162?

By convention, exponents are solved first, then multiplications or divisions, from left to right, then additions or subtractions, from left to right. Therefore, the correct answer to 85 + 9 X 2 is not 188, but 103. There are no exponents in the problem, but there is a multiplication, 9 X 2, equaling 18. Working from left to right, the last step is adding 85 + 18, to equal 103. Similarly, in 2 X 3^{4}, the exponent is worked first, then the multiplication.

Parentheses in mathematical sentences take priority over all other operations, so they are solved first, from left to right. Suppose the problem really were (85 +9) X 2. In that case, the correct answer would be to solve within the parentheses first, then the multiplication. Similarly, (4x)^{3} does not mean the same as 4x^{3}. Within the order of operations, if x equals 2, (4x)^{3 }would equal 8^{3} or 512. If x equals 2, 4x^{3} would equal 4 X 2^{3} or 32.

When they are buying school supplies, students may wonder why their teachers specify certain types of calculators. That is because scientific calculators follow the algebraic order of operations, while other calculators do not. A scientific calculator will calculate the problem 85 +9 X 2 by doing the multiplication first, coming up with the answer 103, while a regular calculator will do the operations from left to right only, answering 188.

Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Oak Hill, WV: visit: Tutoring in Oak Hill, WV

]]>Volcanoes on Earth are usually caused when hot lava, volcanic ash, and gases escape from chambers below the crust. Although many volcanic mountains have cones with craters, other types of volcanoes exist. Volcanic activity occurs on land, under the sea, and elsewhere in the Solar System and beyond.

Temperatures are hot enough in the upper mantle that rock melts and becomes liquid under high pressure. In areas that are near the boundaries of tectonic plates, called subduction zones, friction and increased pressure combine to form large amounts of magma. Under the ocean, water forms steam that melts tock even further. Liquid magma is lighter than solid rock, so it tends to rise and find its way to the surface through volcanic vents.

Many volcanoes have cones and deep craters at the summit, but they are not the only type. Some volcano vents form deep fissures, creating places from which lava oozes. Fissure vents can also belch steam. Shield volcanoes, such as Mauna Loa in Hawaii, have sides that slope gently and cover a large area. Lava domes often form in mounds during larger eruptions, such as the 1980 eruption of Mt. St. Helens in Washington State. Lassen Peak is also a lava dome. Composite volcanoes form in steep layers from periodic eruptions, so that layers of hardened ash and lava alternate with layers of basalt and other types of igneous rock. They are very common, found in the Cascade Range and the central Andes; the Aleutian Islands and Japan.

The most destructive volcanic eruptions have been explosive. For example, the 1991 eruption of Mt. Pinatubo in the Philippines produced a cloud of ash hundreds of miles across, massive earthquakes, and avalanches of gases and mud. It was one of the largest volcanic eruptions of the 20^{th} century. The Mt. St. Helens eruption, Washington State, on May 18, 1980, produced a huge landslide and violent pyroclastic flows of superheated ash, pumice, and hot volcanic gases. The pyroclastic flow, a current of volcanic gases, rock, and ash, can reach speeds of 700 km per hour. The direct blast of Mt. St. Helens reached a force of 24 Megatons of TNT.

Lava flows are non-explosive eruptions, such as occur through vents in Iceland and in Hawaii. In contrast to more explosive eruptions, the lava contains more basalt and flows very slowly. Molten lava floods build up fields of lava. In Hawaii, types of lava are called by different names depending on their texture. Mount Kilauea, in Hawai’i Volcanoes National Park, has erupted in slow-moving lava flows since 1983.

Interested in science tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Hilo, HI: visit Tutoring in Hilo, HI

]]>Earthquakes are caused when energy is suddenly released in the earth’s crust, so that it shakes and trembles. Most are mild, but some are violent, resulting in massive devastation, injury, and loss of life, such as the recent earthquakes in Nepal in April and May, 2015

The tectonic plates that make up the Earth’s crust move and slide past one another, so that the rocks on the boundaries constantly store elastic energy. When the energy is released, movement fractures the rock, resulting in an earthquake. Some types occur because the tectonic plates collide with one another, while others happen because the plates either slide past each other or slide apart and form a rift. The plates do not slide smoothly, but stick and jerk as they move.

Waves are created by the energy from an earthquake as it is transmitted past its focus. Seismic waves called body waves flow outward from a point below the surface of the earth. Primary waves are caused by the compression of rock and are the first to reach an observer, while secondary waves are transmitted more slowly, and only move through solids. Surface waves travel from the epicenter of the earthquake. Some are long waves that travel up and down, while others travel from side to side.

The Richter, or moment magnitude scale, is used to measure the strength of seismic waves as measured by a seismograph. It is a logarithmic scale for measuring the amplitude of those waves. The taller the wave, the more energy is released. Each magnitude is 10 times greater than the one before it. Millions of micro-earthquakes occur every year, at the lowest reaches of the scale. They cause little to no damage, and most people cannot even feel them. In contrast, the Nepal earthquake April 25 measured 7.8 on the Richter scale, while one of its largest aftershocks measured 7.3. The most recent pictures from space showed movement of large areas on the surface of the earth, at distances of 7-10 meters.

Nearly 90% of the world’s earthquakes occur around the Ring of Fire, an area that stretches along the western United States, Canada, Mexico, Central, and South America, through western Alaska and the Aleutian Islands, to eastern Russia, Japan, Indonesia, the Philippines, all bordering the Pacific Ocean. Another active area extends from Java to Sumatra through the Himalayas, the Mediterranean, and out into the Atlantic. Collision between the India and the Eurasia tectonic plates caused the formation of the Himalayan mountain ranges and numerous earthquakes in the region.

Interested in science tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Washington, DC: visit Tutoring in Washington, DC

]]>Writing an outline is an important step to ensure structure in a finished essay. Some writers choose to form a firm thesis statement before they write the first draft, and then write a draft outline. Others choose to write a rough thesis statement, write a very rough draft of the essay, and then write an outline afterwards to make sure all the points are there. Either strategy will help writers in the early stages of composing essays.

The thesis statement covers the topic of your essay in one or two sentences. Suppose while brainstorming ideas for possible essay topics, Jean decided to write about the future of space exploration. That is a very broad topic, so she will need to narrow it down and create a focus. Perhaps she decides to discuss the contributions that other nations, such as the European Union, Japan, China, and India, have made. Perhaps she decides to write about proposed explorations in different parts of the Solar System, using the existing framework of the planets. Most often, the thesis statement develops as the essay is written.

Some writers begin with a scratch outline of their proposed essay, from a working thesis statement and a list of their main points. That can be enough to start the writing process. Others prefer to write a first paragraph and then develop and outline as part of the process. Most writers do not have a complete outline when they begin writing their essays. Outlines often gain depth and definition as the essay is rewritten and the topic is refined.

An outline map is another way to develop an outline of ideas without becoming bogged down in a formal structure. Start with a rough working thesis statement, list main ideas so that each point can be developed within its own paragraph, and list supporting details for each idea. Then, a very rough draft can be written from the outline map. When main ideas and supporting details are listed in an outline map, it is easier to add details that pertain to each main point, as well as discard those details that do not fit with the argument.

Another way to develop an outline is to write a rough draft as quickly as possible, then base the outline upon the working thesis and main points written in the rough draft. The advantage to writing the outline after a rough draft is that sometimes the framework of the essay becomes clearer during the process of writing. For many writers, it is easier to revise once some words are on paper rather than try to make ideas fit into an outline beforehand.

Interested in English tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Pullman, WA: visit: Tutoring in Pullman, WA

]]>Sometimes, the most difficult part of writing an essay is getting past the first few sentences or even the first few words. The blank page or the blinking cursor on the blank computer screen mocks the writer who doesn’t know what to write. There is hope, with some strategies for prewriting the essay to get past that first step.

Many students from elementary school on have written freely for 10, 15, 20, or 30 minutes as a discipline every day or every few days. Some people journal to write about thoughts and feelings. It can also be a strategy for prewriting, because eventually a topic that is close to thoughts and feelings will emerge. Jan is a basketball player on the varsity team. During freewriting, she writes about the struggle of balancing conditioning workouts, team practices, and games with getting algebra, history, and English homework done.

Another way to generate the essay topic is by clustering ideas. Write a main topic in the middle of a page, and when write down all the ideas that occur to you about the topic. Suppose that Jim is thinking about choosing a career. Some of the topics include interests, abilities, strengths and weaknesses, and education needed to be successful. Once the ideas are written on the page, they can be connected in a web. If the web doesn’t work immediately, try writing ideas in a list and cross out those that do not fit with the others.

Another way to narrow down a broad topic is to look at it from different perspectives. How can it be described? How can it be compared and contrasted? What does the topic suggest? For example, the broad topic of prejudice might suggest segregation to one person and riots and marches to another. How can the subject be analyzed and broken down into smaller parts? Similarly, how can it be used and why is it useful? What are its benefits? What are the reasons for and against it? That strategy is useful when writing an essay about current events.

Once there are a number of ideas and relationships on the screen, it is possible to develop a working topic and a draft outline. Students who are writing on the computer may be able to start with their list of ideas, copying and pasting those that work together, and deleting those that do not, or at least moving them to another place on the computer screen. At this point, a draft first paragraph might come out of the idea clusters and examinations. The essay probably won’t write itself at this point, but at least there might be something on the page.

Interested in English tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Charlottesville, VA: visit: Tutoring in Charlottesville, VA

]]>Operations with real numbers are the most familiar types in mathematics. Those numerical expressions with constants and operations include such actions as addition, subtraction, multiplication, and division. Many algebraic expressions are usually operations with real numbers.

The set of real numbers include the entire set of rational numbers, such as positive and negative integers, whole numbers, and natural numbers. Positive and negative fractions are rational numbers, because the numerator and denominator of the fraction represents a ratio. Whole numbers are rational numbers, because they are ratios in simplified form. For example, the fraction 4/1 is usually represented as 4. Irrational numbers, such as pi π, the constant e, √7, or √2 are also real numbers, but imaginary numbers and the infinities are not.

Addition of real numbers can be represented on the number line by moving right on the number line. For example, 4 +3 =7 can be modeled on the number line by starting at 4 spaces from 0 and then moving right 3 more spaces. Fractions can be added by finding their common denominator, then adding the numerators. For example, ½ +1/3 = 3/6 +2/6 = 5/6.

Real numbers can be subtracted on the number line by moving to the left. Subtraction is the same as adding the additive inverse, so that 7-5 means the same thing as adding 7 + (-5). The additive inverse of a number is the opposite of that number, so that the additive inverse of 3 is -3, the additive inverse of 1/5 is -1/5, and the additive inverse of -12 is 12. Fractions can also be subtracted by adding the additive inverse, as long as the common denominators are found.

In the most common model of multiplication and division, multiplication is repeated addition and division is repeated subtraction. When multiplying two positive or two negative numbers, the product is positive, but if one number is positive and the other is negative, the product will be negative. Division by zero is undefined, the product of any number and 0 is zero, and the quotient of 0 and any nonzero number is 0.

Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Barre, VT: visit: Tutoring in Barre, VT

]]>The language of algebra is written in symbols, numerals, variables, constants, and expressions. In order to be successful in math, students should be able to translate its language into words and words into math language. Numerals and many symbols should already be familiar, as well as many operations with real numbers.

Several mathematical symbols should already be familiar, such as + for addition, – for subtraction, x or ·for multiplication, and ÷ for division. Similarly, most students are familiar with = for equals, < for less than, and > for greater than. The integers 0, 1, 2, 3 … are common, as are fractions such as ½, 1/3, ¼, 2/3, and so on. By the time students begin studying algebra, they are familiar with working problems that involve basic operations, as well as some that aren’t so basic.

Variables are letters or symbols used to represent any value that can change, depending on the needs in the expression. Constants do not change. They may be numerals or particular values. For example, the letter pi π is a constant that always means the same thing, 3.1416, give or take a few decimal places. Numerical expressions contain only constants and symbols for operations, such as 2 +2 = 4. Algebraic expressions are similar, but they also contain variables, constants and symbols for operations. While 2 + 2 =4 is a numerical expression, x +y = 4 is a simple algebraic expression. It contains two variables, x and y; one constant, 4; and two symbols for operations, + and =.

In order to translate from symbols to words, understand what the symbols mean and analyze them. For example, the expression “x +2” can mean the sum of x +2 or x increased by 2. The expression “5 –a” can mean the difference of 5 and a, or a less than 5. The expression “8z” can mean 8 times z or the product of 8 and z. The expression “y/5” can mean y divided by 5 or the quotient of y and 5.

In order to translate words into mathematical expressions, such as for a word problem or real-life application of math, analyze the statement in words and the relationships between them. Drawing a picture can be a useful strategy to translate a problem into an algebraic expression. Certain words and phrases mean particular operations. Are things to be put together? Addition might be the operation. Is one thing more or less than another? Subtraction might be needed. Are equal numbers of things to be grouped? Multiplication might be the key. If equal groups need to be separated, they are divided.

Interested in math tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Provo, UT: visit: Tutoring in Provo, UT

]]>Astronomers have observed planets orbiting other stars in the Milky Way galaxy and in other galaxies. Some of these objects are below the mass of Earth, while others are larger than the planet Jupiter. Over 1900 extrasolar planets are registered, many found by telescopes in space, such as the Kepler Space Mission.

Planets were officially defined in 2003 by the International Astronomical Union, partly because of the controversy around the status of Pluto, Eris, and other objects within the Solar System. Since astronomers were observing planetary bodies around other stars, they accommodated extrasolar planets in their definition. Planets orbit stars or stellar remnants; they are not large enough to start fusion reactions on their own; and they are not smaller than the smallest planet in the Solar System. This definition is controversial enough, as some objects that have been discovered are estimated larger than the upper limit of 13 times the size of Jupiter. It may take more than huge size within a gaseous body to ignite thermonuclear reactions and turn it into a star, according to scientists who disagree with the IAU’s definition.

Some very large planets have been observed directly as faint infrared images orbiting their parent star. Most are detected indirectly, by small variations in the parent star’s brightness or motion. In 1992, rocky planets were seen orbiting a pulsar, discovered by minute variations in the pulse rate of the pulsar. They are theorized to be remnants thrown out of the exploding supernova that created the pulsar, or rocky cores from gas giants destroyed in the explosion.

Some of the most surprising exoplanets are thought to have the mass of the planet Jupiter but orbit closer to their star than 1 AU, closer than the distance between the Earth and the Sun. They radiate huge amounts of infrared energy, showing that they have high surface temperatures. Other solid planets have been observed that are between 4 and 10 times the size of Earth, nicknamed “Super-Earths” by exoplanet searchers. Some exoplanets do not appear to orbit stars at all. These rogue planets are massive, and may have been ejected from planetary systems as they were formed.

The Kepler Space Telescope was launched in 2009, with a specific mission to search for planets that orbit other stars. It has discovered 1000 confirmed extrasolar planets, with about three times as many unconfirmed. It has a very large camera that is specifically designed to measure the small distances in brightness when planets transit stars. It orbits the Sun in an orbit that takes over 370 days, collecting telemetry as it goes, and transmitting it to scientists on Earth.

Interested in science tutoring services? Learn more about how we are assisting thousands of students each academic year.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Baltimore, MD: visit Tutoring in Baltimore, MD

]]>The magnetosphere around a planet is the area of space where charged particles are controlled by its magnetic field. In the Solar System, Jupiter and Earth have the strongest magnetospheres because of the strength of well-developed magnetic fields. Close to the surface of a planet, the lines of force of the magnetic field look like a dipole, but further away, lines of force are warped by electric currents from plasma in the solar wind.

Solar wind particles escape from the upper atmosphere of the Sun in a stream of plasma. Electrons, protons, and alpha particles with high energy flow outward constantly to a distance far beyond the orbit of Pluto. The electrical currents caused by these particles are strong enough to strip the atmosphere away from a planet unless it is protected by its own magnetic field. Solar wind particles have been found in many different locations in the Solar System, wherever cosmic rays strike.

The planets Mercury, Earth, Jupiter, Uranus, and Neptune all have strong enough magnetospheres to protect them against the destructive effects of the solar wind. Their magnetic fields are generated by the materials in the core of the planet and the speed of rotation. When an object rotates rapidly enough, as well as creating convection currents between its core and the surface of the planet, it generates its own magnetic field. By contrast, the planet Venus rotates too slowly to generate its own magnetic field. The solar wind wraps completely around the planet, and its electric currents have allowed most of the free hydrogen to escape from the Venusian atmosphere, leaving behind heavy carbon dioxide and other compounds.

The magnetosphere doesn’t have a spherical shape around Planet Earth. It extends from about 10 times the radius of the Earth on the sunward side to a tail in the shape of a parabola 200 times the radius of the Earth on the opposite side. It protects from the solar wind and cosmic rays. The magnetosphere expands and contracts in response to solar activity.

The magnetosphere of Jupiter is larger and stronger than that of Earth. It extends from 7 million km sunward and almost to the orbit of Saturn for its parabolic tail. Jupiter’s magnetic field is generated by powerful electric currents created in its liquid core. Volcanic eruptions of sulfur from its moon Io intensify thick radiation belts around the planetary system. The planet Jupiter is a very bright source of radio transmissions.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Houston, TX: visit Tutoring in Houston, TX

]]>More is known about the Sun than any other star, because the details of its structure, its features, and its effects can be observed at relatively close range. The magnetic field of the Sun leads to changes in solar activity, such as the number and timing of sunspots and solar flares. Telescopic observations and solar space missions have enhanced understanding and raised more questions about its composition, activity, and effects.

The Sun, like other stars, has a magnetic field created by the movement of plasma in currents between its core and its surface. It is not a solid body, so the heated plasma at different latitudes rotate at different speeds. Differential rotation and convection create huge dynamos that produce self-sustaining electric currents. Some electric currents are deep within the star and other chaotic systems are nearer the surface. The solar magnetic field may be partially responsible for heating of the corona.

The solar cycle of sunspots corresponds to the oscillation between magnetic fields, a cycle that takes about 11 years. Sunspots are the result of intense concentrations of magnetic activity that keep heat from reaching the surface. Their magnetic polarity reverses at alternate cycles. At the lowest point of the cycle, very few sunspots can be seen, but at the highest point, large groups of sunspots form at the solar equator. Although sunspots themselves are between 2700° C and 4200° C, the surrounding photosphere is about 5500° C, so they look dark by contrast. The most recent observations show that sunspots usually last from days to weeks, and underneath the spot itself a rotating downdraft concentrates and traps the magnetic field.

When sunspots link the solar interior with the surrounding solar atmosphere, huge flashes of energy called solar flares affect all layers, the photosphere, chromosphere, and corona. As much as 1/6 of the total energy output of the sun can be released in a few minutes. Sometimes, mass can be ejected through the corona. Some of the X-rays and UV radiation from solar flares can disrupt long-range radio and other types of communications on Earth.

Detailed observations of solar activity have been made from observatories on Earth, and some observatories have special instruments to study the Sun without damage. Some of the earliest space probes, the Pioneer series launched in the 1960s, measured the Sun’s magnetic field and the solar wind. The SOHO mission is joint between the United States and the European Space Agency and was extended to 2012. Its successor, the Solar Dynamics Observatory, has a series of instruments built to study the Sun at a number of wavelengths. Other probes are planned to launch, continuing observations from space without interference from the atmosphere of the Earth.

SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Mount Juliet, TN: visit Tutoring in Mount Juliet, TN

]]>