Praxis Elementary Education Multiple Subjects
Terms in this set (442)
connection between spoken words and printed words
language and conventions of print
how to hold a book, where to begin to read, left to right tracking and how to go from one line to another
functions of print
print used for a variety of purposes including entertainment and information
pairing reading workshops and writing workshops with same book to enhance literacy
generic information stored in the mind
one's knowledge of word meanings
knowledge of spelling patterns and pronunciations
syntax and contextual information
background knowledge children use when encountering an unfamiliar word to choose a word that makes sense
background knowledge of a topic
knowledge of text to build expectations and to construct a framework of ideas to build meaning
the acknowledgement of sounds and words
the smallest unit of language capable of conveying distinction in meaning
the ability of the reader to recognize the sounds of spoken language
everything before the vowel and rime
the vowel and everything after it
Five basic types of phonemic awareness tasks
1)Ability to hear rhymes and alliteration
2)Ability to do oddity tasks
3) The ability to orally blend words and split syllables
4) The ability to orally segment words
5)the ability to do phonics manipulation tasks
process readers use to figure out unfamiliar words based on written patterns
process of automatically determining the pronunciation and some degree of the meaning of an unknown word
changing communication signals into messages
changing messages into symbols
method of teaching reading and spelling based on a phonetic interpretation of ordinary spelling
the words most often used in the English language
words that readers learn to read spontaneously, either because of frequency or lack of conformity to orthographic rules
words and illustrations that highlight salient features of meaning. Drawing or visualizing a picture of the word to enhance understanding.
letters stand for a message but do not know the relationship between spelling and pronunciation
early phonemic spelling
usually write first letter correctly, with the rest of the word compromising of consonants or long vowels
spell some words consistently and correctly
late elementary school-master short vowel sounds and know some spelling rules.
reaches this stage between high school and adulthood-spelling rules are being mastered.
developed new standards and assessments for English language proficiency K-12
the ability to recognize sounds, letters, and words by hearing
automatic word recognition which helps achieve comprehension of material
allows fast and accurate identification of whole words made up of specific letter patterns
involves intonation and rhythm through syllable accent and punctuation
four basic word types of English orthography
1)Regular, for reading and spelling
2)Regular, for reading but not spelling
Three cueing methods for reading fluency and comprehension
works that are made up by the author or are not true
written accounts of real people, places, objects, or events
plot, characters, setting, and themes
may find plot, characters, settings, and themes but also interpretations, opinions, theories, research, and other elements
Types of Nonfiction
right wins over wrong, hard work and perseverance are rewarded, and helpless victims find vindication
adventures of animals or humans and the supernatural typically characterize these stories
preschool-books tell a story with the illustrations as well as text
animals act like humans usually to teach a lesson
events from the earliest times, such as the origin of the world
similar to myths but tell events that more recently occurred
purposely exaggerate accounts of individuals with superhuman strength ex:Paul Bunyan
Modern Realistic Fiction
stories about real problems that real children face
introduces children to history in a beneficial way
reading about inventors, explorers, scientists, political and religious leaders, ect so children can see one person can make a difference
ways for children to learn more about something they are interested in or something they know little about
reader making a reasonable judgment based on the information given
helps students align their inferences with evidence form the text they are reading
represents humans, animals, ect- "who" the story is about
"where" the story takes place
introduction, rising action, climax of story, falling action, and conclusion "why"
Structure of Poetry
1)The pattern of sound and rhythm
2)The visible shape it takes
3)Thyme and free verse
rhythmic pattern of a single verse
group of certain number of verses with a rhyme scheme
when the initial sounds of a word are repeated in close succession ex Nate never knows
when a rhyme is not exact ex ill and shell
when the vowel sound in a word matches the sound of a nearby word. ex-tune and food
words used to evoke meaning by their sounds. ex-buzz, zap, zonk
the recurrences of stresses at equal intervals
bits of critical information found alongside a larger passage
title, often found at the top of a page
helps find information quickly by bringing reader to images, data points, charts, or graphs located within the document.
cause and effect
strategy used to organize information in a way that demonstrates an outcome.
problem and solution
information is laid out sequentially-problem, intervention that eradicated problem
first person point of view pronouns
second person point of view pronoun
third person point of view pronouns
rhyming is the manipulation of sounds indicative of:
print concepts, phonological awareness, phonics and word recognition, and fluency
phoneme deletion activity
deleted sound in word to assist with phonological awareness. ex. What is spoke without the /s/?
Substitute phonemes in words
The word is tub. Change the /b/ to /n/. What's the new word?
composed of the sounds represented by the letters of the alphabet
gives information pertaining to the meaning of the word
-ology or -logy
suffix meaning 'the study of'
WIDA entering level
student identifies language that indicates the narrative points of view
Bloom's Taxonomy when student's offer one-word responses
most common rimes
-ash, -ell, -ug
cvcc, cvc, ccvc, ccvcc
What is fluency as known as?
the rhythm and intonation of language
last paragraph of story
where the moral of a story is typically located
minor and irrelevant details
what does an effective summary delete?
technique used to encourage word recognition
metered poetry technique- help set the rhythmic paces of literary piece
example of literary element
syntax and diction
word choices the author makes characterizing the style of a passage
assesses similarities and differences
qualitative evaluation of text
levels of meaning, structure, language conventionality, and clarity
text leveling used to identify a student's reading level in grades K-8
Lexile Framework for Reading NC
The label NC means it is nonconforming and does not fit the normal pattern for grade level. Ex:Contains vocabulary and sentence length that are complex compared to the subject matter.
Opinionated and argumentative
styles of opinion writing
what do informative and explanatory genres of writing always contain?
intent of a speech
1)convey a message
2)be concise and effective
3)target an audience
pertain to the surface mistakes that may occur in a paper-address problems with spelling, grammar, punctuation, or word choice
Zaner Bloser writing development from ages 2 to 6
Dr. Mel Levine's six stages of writing
material that comes form the "horse's mouth"
ex. census data, artifact, letters, interviews, photograph, diaries
any research material that is not primary. Ex-magazine article, critical analysis of a subject, encyclopedias
when you read text and write it in your own words
when you copy text word for word as your own
criteria for credible website sources
always end in /s/ or /es/
my, mine, you, yours, hers, his
direct comparison between two unlike things
comparison using like or as
the use of one term that is closely associated with another to mean the other. ex. referring to the "crown" when talking about the monarchy
giving human characteristics to a non-human thing or idea
invalid arguments against the person - attacks character or behavior of person taking a stand on the issue rather than issue itself
using particulars to draw a general conclusion
using general facts or premises to reach a specific conclusion
link two parts of a sentence together- and, but or
has two independent clauses and is linked by the word "and"
a word formed from another word
an expression used in the English language. ex "Singing at the top of her lungs"
abstract use of language
two words that are spelled differently, even though they sound very much alike
possession without the use of an apostrophe
second-tier vocabulary words in the Common Core State Standards
What is another term for diction?
the ability to understand or comprehend language heard or read
essential to getting a point across without using words. Ex. gesture, wink, wave
conveying ideas and expressing themselves to others
main ideas that an author conveys in literary text
main ideas of the story, although not stated explicitly.
Three components of Text Complexity
3)reader and task
text cohesion, word length, readability, sentence length, word frequency, total word count
levels of meaning, levels of purpose, clarity of language, predictability, structure, familiarity with topic, appropriate age/maturity level
reader and task
student motivation, interest level, background knowledge, purpose of task, level of rigor in questions being asked
author takes a stance on an issue or subject and supports that stance through rational written arguments that intend to influence the reader to agree with the author
tells a story about an event or experience that happened to the author
factual and specific with the objective of informing the reader of information pertaining to the specific topic of the writing
looks to explain concepts, ideas, or subjects in as much detail as possible
first step in the writing process where the author identifies the purpose or goal of the writing
"rough draft" -initial thoughts are written down by the author in rough form
final step in writing process checking for potential spelling or grammatical errors
author's presumption of what the reasonable answer tot he research question is
rules or patterned relationships that correctly create phrases and sentences from words
a deliberate exaggeration for effect
a contradiction in terms for effect-"jumbo shrimp"
the expression of something other than the literal meaning-such as words of praise when blame is intended
the artful adaption of language to meet various purposes
attitude the author takes towards the subject
Which colonists were most willing to work with the Native Americans?
involved the territorial and westward expansion within the United States
New England Colonies
Connecticut, Massachusetts, Rhode Island, and New Hampshire
Middle Atlantic Colonies
New York, New Jersey, Pennsylvania, Delaware, and Maryland
"Breadbasket" of the New World
What was the Middle Atlantic Colonies known as?
Virginia, North and South Carolina, and Georgia
First permanent successful English colony
prohibited English settlement beyond the Appalachian Mountains to appease the Native Americans
imposed tax on foreign molasses, sugar, and other goods imported into the colonies
prohibited colonial government from issuing paper money
placed tax on newspapers, legal documents, licenses, almanacs, and playing cards. First "internal" tax on the colonies.
Sons of Liberty
secret group that staged riots against the agents who collected the taxes and marked items with a special stamp (Stamp Act)
Townshend Acts of 1767
taxes placed on lead, glass, paint, paper and tea in attempt to generate revenue and regain control of the colonists by England.
Boston Tea Party
response by colonists to The Tea Act of 1773 which gave British East India Company a monopoly on sales of tea.
Declaration of Rights and Grievances
issued by the First Continental Congress in 1774-pledged allegiance to the king but protested the right of Parliament to tax the colonies
Factions caused jealousies, false alarms, and could cause damage
Why did George Washington warn against the creation of factions?
Who spurred the formation of the first political parties in the newly created United States of America?
What year did the first political parties play a role in the election?
The political party that favored strong national growth and were untied behind President John Quincy Adams. Primarily supported by Northeast business people and wealthy southern planters.
Kansas-Nebraska Act of 1854
erased the imaginary line in the Louisiana Territory and provided that the people of those two territories could decide for themselves whether or not to permit slavery.
Missouri Compromise of 1820
drew an imaginary line across the Louisiana Territory to divide parts that would be free from parts that would be slave.
The state that directly affected the presidential election of 1860 in which Abraham Lincoln and Stephen Douglas were running for U.S. Senate.
The philosophy that was concerned with the common-sense needs of average people.
The era in which countries obtained colonies throughout the world to bolster the nation's economies.
The Sherman Antitrust Act
Passed by Congress in 1890 to curtail the trusts and the creation of monopolies
political movement that believes in the elimination of all government and the replacement of government by a cooperative community of individuals
another term for Dictatorship- rule may be by an individual or small group of individuals
state takes guiding role in national economy and provides extensive social services to it's population
the president is elected by direct or indirect election
rules by a nonelected, usually heredity leader.
Articles of Confederation
result of the first attempt of the newly independent states to reach a new understanding among themselves.
Albany Plan of Union
proposed as peaceful resolution with Great Britain by establishing a unified form of government within the colonies.
describes and defines the organization of government for the United States
The Declaration of Independence
based on Greek ideas of democracy, individual rights, the philosophy of John Locke and ideas of the Enlightenment and Renaissance
How many of the original 13 states were required to ratify the Constitution before it officially became the law of the land. the ratification was completed on June 21, 1788.
Guarantees freedom of religion
Provides that powers not mentioned in the Constitution shall be retained by the states or the people
guarantees the right to a trial by jury
protects people from unreasonable search and seizures
refers to the natural and artificial features of an area
a specific point ex. 123 Main Street
features such as rivers, mountains, and deserts
three main concepts:humans adapting to environment, modifying the environment , and depending upon the environment
area defined by actual boundaries
defined by a common function, such as telephone service
region formed by people's perception, such as the South
the smallest homogeneous division of land surface at a given scale or resolution
percentage of Earth's surface made up of land
What country are the Atlas Mountains located?
flat top of a hill or mountain, usually has steep sides, and is similar to a plateau but smaller
considered a nation's lifeblood because they begin as small streams, flow into larger bodies of water, serve as transportation systems, and have many tributaries
Atlantic and Pacific
Which oceans does the Panama Canal connect?
Lines of latitude
Lines of longitude
A civilization that lived in a region upstream from the first cataract of the Nile River in Egypt. They were hunters and fishers, herded cattle, and gathered grain. They lived a highly settled way of life and are thought to be the second oldest civilization in Africa.
ancient civilization known for it's city-states
How long did the ancient civilization of Rome last?
"Roman Peace"-it was a long period of peace that allowed free travel and trade, which spread people, culture, goods, and ideas all over a vast area of the known world
Unified Greece and introduced the culture throughout the eastern world.
the ancient civilization that served as a model for modern government, especially in federal systems such as that found in the United States.
the decade that marked the fall of the Soviet Union
Saddam Hussein was the former dictator of which country?
the mechanism that brings buyers and sellers in contact with each other so that they can buy and sell.
markets in which goods and services are sold
factors of production
land, labor, and capital
what sellers produce
what buyers will purchase
factor of production
a resource that is bought and sold
the market where factors of production are bought and sold
determined as the overlap of the buying decisions of buyers with the selling decisions of sellers
President that appointed Lewis and Clark to explore the Louisiana Territory
Corps of Discovery
expedition name of Lewis and Clark
Dred Scott decision
1857-ruling by Supreme Court stating, though Scott has lived in a state that was free, he was not a free man since slaves were not U.S.citizens.
Battle of Gettysburg
changed the direction of the Civil War
water, forests, coal, iron, silver, copper, petroleum
homes made of cardboard, scraps of wood, and tents during the Great Depression when people were evicted from their homes
year of the Great Depression
legislation intended to accomplish three goals:relief, recovery, and reform to end the Great Depression and get the nation back on track,
Social Security Act of 1935
established pensions for the aged and infirm as well as a system of unemployment insurance
aimed at preventing the spread of communism, involved economic aid that was sent to Europe in the aftermath of the Second World War
offered military aid to countries in danger of communism upheaval
North Atlantic Treaty Organization (NATO)
formed in 1949 for the purposes of opposing communist aggression
established income tax
World War II
atomic bomb was developed and used for the first time in this war
House of Representatives and Senate-initiates bills (House) and treaties (Senate)
2 year terms
term of House members
6 year terms
term of Senate members
president and vice-president. Has advisers to the president in the departments of State, Defense, Education, Treasury, and Commerce.
consists of a series of courts and decides whether the laws of the land are constitutional.
principle author of the Declaration of Independence
amendment that outlawed slavery
amendment that gave women the right to vote
original voting age in the Constitution. Was changed to 18 in the Twenty-Sixth Amendment.
concerned with the sustainability of the Earth-policy is the preservation of a region, habitat, or ecosystem.
invented the wheel, developed irrigation through the use of canals, dikes, and devices for raising water, devised the system of cuneiform writing, learned to divide time, built large boats for trade
devised the famous Code of Hammurabi, a code of laws
developed an alphabet, allowed conquered people to retain their own customs, laws, and religions
country that developed the alphabet, based on the Greek transformation of the Phoenician letters. This alphabet was adopted throughout it's empire and is still used today.
international assembly given the authority to arrange and enforce international resolutions
identification of individuals or groups as they are influenced by their belongings to a particular group or culture. Refers to a sense of who one is, what values are important, and what racial and ethnic characteristics are important in one's self-understanding and manner of interacting with the world and with others.
theory that explains not only the movement of the continents in the Earth's crust caused by internal forces
rigid blocks of the Earth's crust and upper mantle
broken into nine large sections made up of rigid solid blocks of the Earth's crust and upper mantle
currents of hot mantle rock rise and separate creating new oceanic crust at the rate of two to ten centimeters per year
when ocean crust collides with either another oceanic plate or a continental plate forming an enormous trench and generating volcanic activity.
the supercontinent that was broken up
natural mountain building
layer closest to the Earth's surface. All weather phenomena occur here.
layer that contains very little water, clouds are extremely rare, ozone layer is here.
layer that extends upward into space.
lower part of the thermosphere-charged particles and free electrons can be found here. Gases in this layer cause the aurora borealis (Northern Hemisphere) and aurora australis (Southern Hemisphere).
upper portion of the thermosphere. Van Allen belts.
folding and faulting
most major mountain ranges are formed by these processes
a volcano that is currently erupting or building to an eruption
a volcano that is between eruptions but still shows signs of internal activity that might lead to an eruption in the future
a volcano no longer capable of erupting
occurs when fluid sediments are transformed into solid rocks.
made from molten rock, or magma, as it cools
rocks formed by high temperatures and great pressures
natural, non-living solids with a definite chemical composition and crystalline structure
minerals or rock deposits that can be mined for a profit
a time period in which glaciers advance over a large portion of a continent
the remains or trace of an ancient organism that has been preserved naturally in the Earth's crust
rocks in which most fossils ar found
the inclusion and transportation of surface materials by another moveable material-usually water, wind or ice
the breaking down of rocks at or near the Earth's surface
era we are currently in- started 65 million years ago until present day
beginning of Earth to 570 million years ago
4 time eras
states that the physical, chemical, and biological laws that operated in the geologic past operate in the same way today
the concept that the Earth was shaped by catastrophic events of a short-term nature
the use of radioactivity to make accurate determinations of Earth's age
the number of established planets in our solar system
parts of the sun
produces solar flares disturbing radio reception and affects the magnetic field on Earth
area of the Sun that is only visible during a total eclipse
groups or patterns of stars
vast collections of stars
objects that have collapsed to such a degree that light cannot escape from the surface
masses of frozen gases, cosmic dust, and small rocky particles
composed of particles of rock and metal various sizes
a burning meteoroid falling through the Earth's atmosphere-also known as a shooting star
meteors that strike the Earth's surface
proposes that the solar system began with a near collision of the Sun and a large star.
proposes that the solar system began with the rotating clouds of dust and gas
Big Bang Theory
widely accepted by many astronomers, states that the universe originated from a magnificent explosion spreading mass, matter, and energy into space
Steady State Theory
least accepted theory, states that the universe is continuously being renewed
Earth's tilt on it's axis causes the Northern Hemisphere to lean towards the sun
Earth's tilt on it's axis causes the Southern Hemisphere to lean towards the sun
cyclic rise and fall of large bodies of water caused by the orientation and gravitational interaction between the Earth and the moon
moon is invisible or the first signs of the crescent appear
the right crescent of the moon is visible
the right quarter of the moon is visible
only the left crescent is not illuminated
the entire illuminated half of the moon is visible
only the right crescent of the moon is not illuminated
the left quarter of the moon is illuminated
only the left crescent of the moon is illuminated
make up cells
make up tissues
make up organs
groups of organs make up
basic unit of all living things
the common element of organic life
consist only of bacteria and blue-green algae. Have no defined nucleus or nuclear membrane.
found in protists, fungi, plants, and animals.
brain of the cell
DNA,RNA, and proteins tightly coiled to conserve space
loose structure of chromosomes
where ribosomes are made.
contains pores that let the RNA out of the nucleus.
the site of protein synthesis
"roadway" of a cell and allow for the transport of materials.
golgi complex or golgi apparatus
functions to sort, modify, and package molecules that are made in other parts of the cell.
found mainly in animal cells. Contain digestive enzymes that break down food.
large organelles that make ATP to supply energy to the cell. found only in animal cells.
found in photosynthetic organisms only. Similar to the mitochondria due to their double membrane structure and have their own DNA.
found in plants only-composed of cellulose and fibers.
hold stored food and pigments
composed of protein filaments attached to the plasma membrane and organelles
the production of sperm and egg cells
the division of somatic cells. Two cells result from each division. Chromosome number is identical. Division is for cell growth and repair.
the division of sex cells. Four cells result from each division. Chromosome number is half the number of parent cells. Recombination provide genetic diversity.
Mitosis stage in which chromatin is loose, chromosomes are replicated, and cell metabolism is occurring.
Mitosis stage in which the chromatin condenses to become visible chromosomes. Nucleolus disappears and nuclear membrane breaks apart.
Mitosis stage in which kinetechore fibers attach to the chromosomes, which cause the chromosomes to line up in the center of the cell (think middle for metaphase)
Mitosis stage in which centromeres split in half and homologous chromosomes separate.
Mitosis stage in which there are two nuclei with a full set of DNA identical to the parent cell.
inheritable changes in DNA
example of nondisjunction in which three of chromosome 21 are present
Mitochondria are on the ____________ scale in size while the animal cell that contains them is on the ________ scale in size.
2 cells; diploid
The mitotic division of one somatic cell results in what number of diploid/haploid cells?
a person having one dominant and one recessive allele for a gene
the change in population's heritable traits over time
all of these reproduce asexually
traits or characteristics that come in several forms
the stronger of two traits
the weaker of two traits
having two of the same genes present
some genes allow for better survival of an animal.
four types of organismal behavior
1) competitive (compete for scarce resources with other species)
2) instinctive (innate behavior is common to all members of a given species)
3) territorial (animals act aggressively to protect territory form other animals)
4) mating (important to interspecies interactions)
behavior that is inborn or instinctual
any behavior that is modified due to past experience
the science of classification
Five Kingdoms of Living Organisms
the study of organisms
group of same species in a specific area
group of populations residing in the same area
communities that are ecologically similar in relation to temperature, rainfall, and species that live there
levels of biomes in increasing complexity
moderates population growth within an environment and is fixed. As population growth increases and resources are depleted more, the carrying capacity limits the rate at which populations can continue to grow until populations can no longer grow.
validated by extensive testing and review before accepted as fact
stage when the researcher incorporates mathematical operations and graphical representation to critically explain trends in the study.
measured in meter/second
measured in volts
measured in joule/second
describe how a substance's composition can be changed, resulting in a new substance.
conversion of gas to liquid
conversion of solid to liquid
conversion from solid to gas
conversion from liquid to gas
positively charged particle
negatively charged particle
particle with no charge
the number of protons and neutrons
average mass of an element's isotopes
number of protons
atomic mass unit
standard unit of measurement for atomic mass
when two elements are chemically bound
measurement of force
Newton's 3rd Law
states that for every action there is an equal and opposite reaction
Law of Gravity
two bodies in the universe attract each other with a force that is directly proportional to the product of their masses
Newton's 2nd Law
if a force acts on an object it will cause the object to accelerate
Newton's 1st Law
an object in motion will remain in motion unless acted upon by an external force
law of conservation of energy
energy is neither created nor destroyed; energy changes form; energy is conserved over time
units of measurement for work
atomic particles primarily responsible for electricity
do not change the structure, energy, or composition of atomic nuclei
rice, corn, and wheat
three majors crops that feed the world
function is support of the body. Determines body size and shape that is limited to the forces of gravity. bones
function of the body is movement. Three types: skeletal muscle, Smooth muscle, and cardiac muscle.
neuron is the basic unit of this system. Carries impulses away from and to the cell body.
function to break down food in the body and absorb it in the bloodstream.
functions in the gas exchange of oxygen and carbon dioxide in the body.
carries oxygenated blood and nutrients to all cells of the body and return carbon dioxide waste to be expelled form the lungs.
main source of energy in the human diet.
necessary for growth, development, and cellular function. Poultry, fish, legumes, eggs, ect.
a concentrated energy source and important component of the human body.
vitamins and minerals
organic substances that the body requires in small quantities for proper functioning.
makes up 55-75 % of the human body-essential for most bodily functions.
nature of science
1)the scientific world view
an explanation of a set of related observations based on a proven hypothesis
usually lasts longer than a scientific theory and has more experimental data to support it
how many phonemes are in the word "ball"?
an English-language learner who is capable of matching pictures with words and phrases from a story but cannot yet use those pictures to recreate the sequence of a story is functioning at which of the following language proficiency levels?
most commonly used in digital text to give reader access to additional information about a topic
stage of developmental writing in which writer shows an awareness of spacing, makes sporadic use of proper capitalization, and contains some inventive spelling
technology based tool that best facilitates both personal writing and written discussion about writing
mountain range that crosses through the state of Washington
type of map that shows the boundaries of countries, states, or municipalities
Brown v. Board of Education of Topeka
legal doctrine known as "separate but equal" was overturned by the Supreme Court's ruling
In the United States, the division of power between the national and state governments demonstrates this principle
percent of seats in the United States House of Representatives that are up for election every two years
India's hierarchical groups are organized by this
the value of what is forgone when the economic choice is made.
adds new rock to the surface of the Earth
the study of the relationship between motion and the forces affecting motion
resistance of force
force of friction of two surfaces that are in contact but do not have any motion relative to each other
force of friction of two surfaces in contact with each other when there is relative motion between the surfaces
when an object moves in a circular path, a force must be directed toward the center of the circle in order to keep the motion going
shows that like charges repel each other and unlike charges attract each other and that the size of the force varies inversely as a square of the distance between the 2 charged objects
allows fusion to happen when two or more nuclei come very close together and "glue" to each other
force of gravity
the force by which the Earth, moon, or other massively large object attracts another object towards itself
state of matter
depends on the speed of the molecules and the amount of kinetic energy the molecules possess
the measure of how much energy or heat is available for work
splitting of nuclei
chemical reactions that consumer energy
chemical reactions that release energy
any number that can be written as a ratio
you can change the order of the terms or factors for addition and multiplication a+b=b+a ab=ba
you can regroup terms as you like for addition and multiplication
a number that when added to a term gives the original term or that when multiplied by a term gives the original term. For addition: a + 0= a; for multiplication a X 1= a
a number that when added to another number results in 0 or that when multiplied be another number results in 1
addition: a+ (-a)=0
multiplication: a X (1/a)=1
allows us to operate on the terms inside parentheses without first performing operations within the parentheses
a(b + c)= ab +ac