Resources
ELA TIPS TO BECOME A GOOD WRITER
PREWRITE
Plan your work. Select a topic and brainstorm what you will say about it. Organize your thoughts and the facts that support them. Keep in mind your audience and your reason for writing.
Draft
Write your work. Use sentences and paragraphs to communicate the idea from your prewriting
REVISE
Rethink your work. Correct any mistakes in your first draft, and look for ways to make your writing stronger. Work alone or with other people to edit your composition.
ppppeopp
PROOFREAD
Polish your work. Look one more time for errors in spelling or grammar. Check that punctuation and capitalization are correct. Make final changes.
PUBLISH
Share your work. Give it to a friend, read it aloud to an audience, turn it into a book, or post it on a website.
REMEMBER
· If you use someone else‟s work or words, you must cite the source.
· All citations must adhere to APA reference citing. Google APA for additional information.
70
The Parts of Speech
Part of Speech |
Definition |
Examples |
Usage(italics) |
|
thing, person, place, or idea |
park, cat, house, Joan, Canada, teacher, |
This is my mother. She drives a small car.
We go to church in Canada. |
|
replaces a noun |
I, you, he, she, some, his, hers, him |
They told him it was very expensive.
She left her coat at school. |
|
action or state |
(to) be, have, do, like, walk, run, talk, sing |
English is the primary language of Americans.
I like to walk. |
|
describes/modifies a noun |
some, good, big, red, well, interesting, beautiful |
I have three cars. My red car is a Camaro.
The book is interesting. |
|
describes a verb, adjective or adverb and specifies in what manner, when, where or how much |
hurriedly, rowdy, well, badly, very, really |
She was really sick. He treats her badly. He quickly jumped to Tara’s defense. |
Article |
introduces nouns and sometimes are classified as adjectives |
a, an, the |
There are only three articles in the English language: a, an, and the. |
|
links a noun to another word |
to, at, after, on, but |
My mother took Polly to the doctor before she went to work. |
|
joins clauses, phrases, sentences or words |
and, but, when, because |
I like oreo and coconut cookies. I eat oreo cookies but I don’t eat coconut cookies. |
|
short exclamation, sometimes inserted into a sentence |
ah!, oh!, ouch!, hey!, well! |
Ouch! That really hurt! Hey, watch where you are going! |
71
PUNCTUATION NUGGETS
1. Apostrophes
· The apostrophe is used to form possessives (i.e., the church’s steeple, the school’s mascot, John’s car) and contractions (i.e., we’ve, what’s, he’s, they’re, can’t).
· Colons (:) are used in sentences to introduce that something follows like a quotation, example or a list.
· Semicolons (;) are used to join two independent clauses, to separate main clauses joined by a conjunctive adverb or to separate items in a list that already uses commas.
· The colon and the semicolon can both be used to connect two independent clauses. When the second clause expands on or explains the first, use a colon. When the clauses are merely related, but the second does not follow from the first, use a semicolon.
· Example-Colon: Barry wanted to know why I didn’t respond to his text: I hadn’t received it .
· Example-Colon: Please bring the following items: a flashlight, a comfortable pair of hiking boots, and a jacket
· Example-Semicolon: Ninety eight percent of southerners eat grits; the majority of northerners don’t eat grits.
· Example-Semicolon: Dad is going bald; his hair is getting thinner and thinner.
3. Commas
· Use commas to indicate nonessential information.
· If explanatory matter can be omitted without changing the general meaning of the sentence, it should be set off with commas. If the explanatory matter is essential to the meaning of the sentence, do not set it off with commas.
· Example-Comma: America’s first president, George Washington, served from 1789 to 1797.
· Example-Comma: He hit the ball, dropped the bat, and ran to first base.
4. Hyphen
· Use a hyphen for compound adjectivesà when two or more words collectively serve as an adjective before the word they are modifying, those words should normally be hyphenated. Exception is given when the first word is an adverb ending in (-ly).
· Example-Hyphen: A well-respected CEO gets a hyphen, whereas a CEO who is well respected does not.
· Example-Hyphen: A widely known author does not require hyphenation.
· Example–Hyphen: Compound numbers and fractions use hyphens all the time: three-fifths and twenty- five should contain hyphens.
· Example-Hyphen: Some nouns, such as attorney-at-law, require hyphens in order to make the noun look complete.
5. Parentheses
· Parentheses should be used to clarify, for set asides, or for something that could be left out of the sentence that would not take away the meaning.
a) I.e. The hotel’s head chef (Susan’s cousin) will be preparing the food.
b) I.e. John (and his crazy dog) was always there.
72
PUNCTUATION NUGGETS
6. Quotation Marks
· They are used to set off and represent exact language that has come from somebody else.
· Capitalize the first letter of a direct quote when the quoted material is a complete sentence. I.e. Ms. Jones, who is our choreographer, said, “The students at this school dance better than those who took private dance lessons.”
· Do not use a capital letter when the quoted material is a fragment or only a piece of the original material’s complete sentence. I. e. Although Ms. Jones has seen some really good dancers at dance schools, she stated NDMS dancers “are better” than most.
· Quotation marks should be used with direct, not indirect quotes.
· Periods and commas go inside quotation marks, even if they aren’t part of the material being quoted. All other punctuation marks go outside the quotation marks, unless they are part of the material being quoted. I.e. “Any further delay,” she said, “would result in a lawsuit.” I.e. His latest story is titled “The Beginning of the End”; wouldn’t a better title be “The End of the Beginning”?
7. Exclamation Point
· The exclamation point expresses strong feeling and is a mark of terminal punctuation. As such, it should not be followed by a period or question mark.
a) I.e. What in the world are you doing outside!
· When a quotation ends with an exclamation point, a comma that would ordinarily be placed inside the closing quotation mark is omitted.
a) I.e. ““Get up!” Thomas yelled.
8. Avoid multiple punctuation at the end of a sentence.
· Never end a sentence with a question mark or exclamation point followed by a period. If a sentence ends with a period that is part of an abbreviation, do not add a second period.
9. Punctuation Questions
· Is it U.S.A. or USA? Co-worker or coworker? Lets or let’s? Teachers’ college or teachers college? Use a dictionary.
· If in doubt, rewrite it so you can avoid having convoluted, confusing, or inelegant sentences.
Spelling Rules
· I before E, except after C- or when sounded as A, as in neighbor or weigh
· Final consonants are not doubled when the word ends in more than one consonant
a) Example : transform à transformed or transforming
· When words end in soft ce or ge, keep the e before able and ous
a) Examples: advantageous, changeable, outrageous, likeable
· Change the ending of verbs that end in ie, to y before adding ing.
a) Examples: dieà dying lie à lying
· Change a final y to i before a suffix unless the suffix begins with i.
a) defy + ance àdefiance b) copy + ing à copying
· Double a final consonant before a suffix beginning with a vowel.
a) stop + ing à stopping b) admit + edà admitted
73
COMMON PREFIXES, SUFFIXES, AND ROOTS
Prefixes |
Suffixes |
Roots |
Definition |
Examples |
|
|
term |
end, limit |
determine, exterminate, terminal |
|
-s, -es |
|
plural, more than one |
hats, boxes, dishes, beliefs |
|
-ing |
|
action or process |
helping, skipping, seeing |
|
-ed |
|
past tense |
jumped, helped |
|
-er, -or |
|
person connected with, comparative degree, one who, that which |
teacher, bigger, colder, taller, conductor, survivor |
un- |
|
|
not, opposite of |
unlock, unsweetened |
re- |
|
|
again, back |
reread, rewrite, return, review |
|
-est |
|
superlative degree |
biggest, coldest, tallest |
|
-ful |
|
full of |
beautiful, painful, |
|
-less |
|
without |
careless, helpless, childless |
in-, im-, il-, ir- |
|
|
not |
inactive, impossible, improper |
dis- |
|
|
not, opposite of |
dislike, distrust, disagree |
pre- |
|
|
before |
pretest, preplan, preeminent |
tele- |
|
|
far, distant |
telegraph, |
|
-ies |
|
plural, more than one |
parties, babies, cities |
|
-ied |
|
past tense |
cried, pitied |
|
-ly |
|
characteristic of |
badly, friendly, quickly |
|
-y |
|
characterized by, like |
cloudy, fishy, sneaky |
|
|
bio |
life, living matter |
biography, biology, antibiotic |
|
|
graph/y |
Writing, recording |
seismograph, autograph,graphology |
|
|
phon/o/e/y |
sound |
phonograph, microphone, telephone |
|
|
per |
through, throughout |
permanent, permeate, persist |
non- |
|
|
not |
nonfat, nonsense, nonchalant |
over- |
|
|
too much, above |
overdone, overestimate, overhead |
mis- |
|
|
bad or badly, wrong or wrongly |
misbehave, misspell, mischievous |
de- |
|
|
reduce down, away from |
defeat, decrease, deform |
sub-, under- |
|
|
too little, below, under, beneath, secondary |
underfed, underground, subway, subsoil, substitute |
bi- |
|
|
two |
bicycle, binocular |
tri- |
|
|
three |
tricycle, triangle |
quad- |
|
|
four |
quadrilateral, quadrant |
oct- |
|
|
eight |
octagon, octopus |
|
-al, - ial |
|
related to, characterized by |
colonial, biennial, betrayal |
|
|
tort |
twist |
distort, contortion, retort |
|
-ation,ion, -ition,tion |
|
act of, state of , result of |
attention, invitation, restriction, ignition, union, elevation |
|
-ness |
|
condition, state of |
darkness, fairness, emptiness |
|
-ment |
|
act, process |
employment, replacement |
|
-en |
|
made of, to make |
wooden, dampen, strengthen |
|
|
rupt |
break, burst |
bankrupt, rapture, disruptive |
|
|
terr/a/i |
land, earth |
terrain, territory, extraterrestrial |
|
|
geo |
earth, ground, soil |
geography, geology, geometry |
74
|
Prefixes |
Suffixes |
Roots |
Definition |
Examples |
|
||
|
|
|
phot/o |
light |
photograph, photogenic, photon |
|
||
|
|
|
tract |
pull, draw (drag) |
tractor, attract, subtract, distract |
|
||
|
|
|
meter, metr/y |
measure |
speedometer, metronome, thermometer, perimeter |
|
||
|
en-, em- |
|
|
to cause to be, to put into or onto, to go into or onto |
encounter, enable, employ, embark, encircle |
|
||
|
fore- |
|
|
before, earlier |
forearm, foreword, foresee |
|
||
|
semi- |
|
|
half |
semicircle, semicolon |
|
||
|
anti- |
|
|
opposite, against |
antibiotic, antifreeze |
|
||
|
auto- |
|
|
self |
autograph, autonomy, automatic |
|
||
|
multi- |
|
|
many, much |
multicolor, multifamily |
|
||
|
poly- |
|
|
many, much |
polygon, polygamy |
|
||
|
deca-, deci- |
|
|
ten |
decathlon, decade, decimal |
|
||
|
kilo- |
|
|
one thousand, (1000) |
kilogram, kilowatt, kilometer |
|
||
|
milli-, mille- |
|
|
one thousand, (1000) |
millennium, millimeter |
|
||
|
centi- |
|
|
one hundred, (100) |
centimeter, centipede, centigram |
|
||
|
|
-able, - ible |
|
can be done |
enjoyable, sensible, likable |
|
||
|
|
-ive, - ative, - tive |
|
inclined/tending toward an action |
festive, talkative, sensitive |
|
||
|
|
-logy, - ology, - ologist |
|
science of, study of, one who studies |
biology, chronology, anthropolgist |
|
||
|
|
-ence, - ance |
|
act or condition of |
persistence, excellence, assistance |
|
||
|
|
-an, -ian |
|
one having a certain skill, relating to, belonging to |
electrician, magician, American, suburban |
|
||
|
|
|
ject |
to throw |
inject, objection, project, eject |
|
||
|
|
|
struct |
to build |
construct, instructor |
|
||
|
|
|
vor, vour |
eat |
carnivorous, voracious, devour |
|
||
|
|
|
spir |
breathe |
inspire, transpire, spirit |
|
||
|
|
|
vid, vis |
to see |
vision, envision, evidence |
|
||
|
|
|
jud |
law |
judgment, judiciary, judicial |
|
||
|
|
|
log/o |
word or study |
prologue, apology, eulogy, monologue, logic, dialogue |
|
||
|
|
|
path |
feeling, emotion |
apathetic, empathy, sympathy |
|
||
|
|
|
astro, aster |
star |
astronaut, astronomy, asterisk |
|
||
|
|
|
mit, miss |
to send, let go |
emit, transmit, admit, missile, admission, dismissed, commit |
|
||
|
|
|
aud/i/io |
hear |
audience, audiovisual, audition |
|
||
|
|
|
dict |
to speak |
dictator, predict, verdict |
|
||
|
inter- |
|
|
between, among |
intercept, interstate,international |
|
||
|
trans- |
|
|
across/change/through/beyond |
transformation, transfer, transportation |
|
||
|
super- |
|
|
above/on top of/ beyond |
superfine, superhuman, supersonic |
|
||
|
2017 |
|
“Change Is Inevitable, Progress Is Intentional” North District Middle School Handbook |
2018 |
75 |
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Prefixes |
Suffixes |
Roots |
Definition |
Examples |
|
||
|
micro- |
|
|
small/minute |
microbiology, microscope |
|
||
|
|
-ent, -ant |
|
an action, condition |
student, contestant, immigrant |
|
||
|
|
-ent, -ant |
|
causing a specific action |
obedient, absorbent, abundant |
|
||
|
|
-ity, -ty |
|
state of/quality of |
prosperity, equality |
|
||
|
|
-ic |
|
relating to/ characterized by |
energetic, historic, stoic |
|
||
|
|
-ize |
|
to make/ to cause to become |
fertilize, criticize, apologize |
|
||
|
|
-age |
|
result of an action/ collection |
manage, drainage, acreage |
|
||
|
|
-ous,eous, -ious |
|
full of/ characterized by |
adventurous, nervous, mysterious, courteous |
|
||
|
|
|
port |
to carry |
portable, transport, export, portfolio |
|
||
|
|
|
scribe(scrib), script |
to write |
describe, manuscript, inscribe |
|
||
|
|
|
spectro, spect, spec |
to see, watch, observe |
prospect, respect, specimen |
|
||
|
|
|
vac |
empty |
vacate, evacuate, vacancy |
|
||
|
|
|
vocare (voc- vok) |
to call or summon |
vocal, vocabulary, vocation, voice |
|
||
|
|
|
hydr/o |
water, liquid |
hydrogen, hydrant, hydraulic |
|
||
|
|
|
chron/o |
time |
chronological, synchronize, chronic |
|
||
|
|
|
therm/o |
heat |
thermometer, thermostat, thermos |
|
||
|
|
|
bene |
good, well |
benefit, benign |
|
||
|
com-, con- |
|
|
with, together |
community, conjunction, conspire |
|
||
|
ex-, exo- |
|
|
out of, from |
exterior, external, exoskeleton |
|
||
|
pro- |
|
|
forward |
progress, proceed, produce |
|
||
|
se- |
|
|
apart |
separate, select |
|
||
|
retro- |
|
|
back, backwards |
retroactive, retrograde, retrospective |
|
||
|
|
-fy |
|
to make, to form into |
fortify, solidify, liquify |
|
||
|
|
-hood |
|
state, quality, condition of |
neighborhood, childhood, brotherhood |
|
||
|
|
-ice |
|
state or quality of |
justice, service, accomplice, apprentice, injustice |
|
||
|
|
-some |
|
characterized by a thing, quality, state, or action |
awesome, burdensome, winsome, quarrelsome |
|
||
|
|
-ward |
|
in the direction of |
forward, westward, toward |
|
||
|
|
-ish |
|
like, having the characteristics of, inclined or tending to |
childish, girlish, impish, freakish, bookish, oldish |
|
||
|
|
|
ad |
to, toward |
adequate, adhere, adjective, advertise |
|
||
|
|
|
amo, amatum |
love |
amateur, amiable, amorous, enamored |
|
||
|
|
|
aqua |
water |
aquatic, aquarium, aquamarine |
|
||
|
|
|
arbor, arboris |
tree |
arboretum, arborvitae |
|
||
|
|
|
cum |
with, together |
cumbersome,accumulate,document |
|
||
|
|
|
dendron |
tree |
dendrophile, dendrometer |
|
||
|
|
|
dia |
across, through |
diadem, diameter, diabolical |
|
||
|
|
|
facio, factum |
make, do |
factory, manufacture, deface |
|
||
|
2017 |
|
“Change Is Inevitable, Progress Is Intentional” North District Middle School Handbook |
2018 |
76 |
|
||
|
Prefixes |
Suffixes |
Roots |
Definition |
Examples |
|
||
|
|
|
figo, fixum |
attach |
fixture, crucifix, affix, prefix, suffix |
|
||
|
|
|
helios |
sun |
helium, heliotrope |
|
||
|
|
|
ignis |
fire |
igneous, ignite, ignition |
|
||
|
|
|
inter |
between |
international, interject, interlude |
|
||
|
|
|
jungo, junctum |
join |
conjunction, junction |
|
||
|
|
|
kinesis, cinema |
movement |
kinetic, kinesiology, cinematographer |
|
||
|
|
|
luna |
moon |
lunar, lunatic, lunancy, lunambulist |
|
||
|
|
|
cede, ceed, cess |
go, yield |
exceed, recede, success |
|
||
|
|
|
magnus |
large, big |
magnify, magnitude, magnificent, magnanimous |
|
||
|
|
|
phil |
love |
philosopher, Phildaelphia, |
|
||
|
Prefixes |
Suffixes |
Roots |
Definition |
Examples |
|
||
|
|
|
phobia |
fear |
, claustrophobia, hydrophobia |
|
||
|
|
|
pon |
put, place |
opponent, ponder, postpone |
|
||
|
|
|
pyr |
fire |
pyrotechnics, pyretic, pyrometer |
|
||
|
|
|
sci |
know |
science, conscience, ,omniscience |
|
||
|
|
|
sol |
sun |
solar, solarium, parasol, solstice |
|
||
|
|
|
son |
sound |
unison, sonnet, consonant |
|
||
|
|
|
stella |
star |
stellar, constellation, interstellar |
|
||
|
|
|
syn, sym |
with, together, same |
synchronize, synthesis, symmetry, sympathy, synonym |
|
||
|
|
|
temp |
time |
temporal, temporary, tempo, extemporaneous, contemporary |
|
||
|
|
|
thesis |
put, place |
thesis, theme parenthesis, synthesize |
|
||
|
|
|
trans |
across |
transcend, transcript, transaction |
|
||
|
|
|
tropos |
turning |
tropics, tropical, phototropic |
|
||
|
|
|
verbum |
word |
verb, proverb, verbatim, verbalize, verbose, verbiage |
|
||
|
|
|
verto, versum |
turn |
reverse, controversial, diversity |
|
||
|
|
|
vince, vic |
conquer |
convince, invincible, victory |
|
||
|
hom-, homo- |
|
|
same |
homonym, homophone, homogeneous, homeostasis |
|
||
|
hype- |
|
|
over, too much |
hypertension, hyperactive, hyperbole |
|
||
|
mid- |
|
|
middle |
midsummer, midnight, midsection |
|
||
|
neo- |
|
|
new, recent, revived |
Neolithic, neonatal, neoplasm, neon |
|
||
|
|
-ide |
|
chemical |
pesticide, sulfide, oxide |
|
||
|
|
-ways |
|
in what manner |
always, sideways, alleyways |
|
||
|
|
|
auto |
self, same, one |
autocrat, autograph, automatic |
|
||
|
|
|
annus |
year |
annual, annals |
|
||
|
|
|
bibli |
book |
bibliography, Bible, bibliomania |
|
||
|
|
|
capt, ceive |
take, hold |
perceive, captivate |
|
||
|
|
|
centum |
hundred |
century centimeter, percent |
|
||
|
|
|
corpus |
body |
corporation, corpse, corpulence |
|
||
|
2017 |
|
“Change Is Inevitable, Progress Is Intentional” North District Middle School Handbook |
2018 |
77 |
|
||
|
Prefixes |
Suffixes |
Roots |
Definition |
Examples |
|
||
|
|
|
decem |
ten |
decimeter, decimal |
|
||
|
|
|
demos |
the people, the citizens |
democracy, demography, epidemic |
|
||
|
|
|
dens, dentis |
tooth |
dentist, orthodontist, indent, dental |
|
||
|
Prefixes |
Suffixes |
Roots |
Definition |
Examples |
|
||
|
|
|
digitus |
finger, toe, inch |
digit, prestidigitation |
|
||
|
|
|
dormio |
sleep |
dormitory, dormant, dormouse |
|
||
|
|
|
duo |
two |
duet, duel, duplicate |
|
||
|
|
|
frater, fratris |
brother |
fraternity, fraternize, fraternal |
|
||
|
|
|
liber, libri |
book, free |
library, librarian, liberty, liberal |
|
||
|
|
|
lithos |
stone |
lithograph, monolith |
|
||
|
|
|
manus |
hand |
manufacture, manuscript |
|
||
|
|
|
mater, matris |
mother |
matriarch, maternal, matrimony |
|
||
|
|
|
mille |
thousand |
mile, millimeter, millenium |
|
||
|
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nomen, nominis |
name |
nominate, denominator, nomenclature |
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novem |
nine |
novennial, novemdigitate |
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octo |
eight |
octopus, octagon, octogenarian |
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pater, patris |
father |
patriarch, patron, patriotism |
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pes, pedis |
foot |
pedestrian, pedicure, pedometer |
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petros |
stone, rock |
petrified, petroleum, petroglyph |
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polis |
city |
metropolis, political, policy |
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pop |
people |
population, |
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pre |
before, in front of |
predict, preamble, precursor |
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pro |
for, before, forward, in place of |
profess, pronoun, proclaim, problem, proliferate |
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pneum/o |
breathing, lung, air, spirit |
pneumonia, pneumatic |
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ambi |
both, on both sides |
ambidextrous, ambiguous |
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anthrop/o |
human |
anthropology, philanthropy |
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cert |
sure |
ascertain, certain, certify |
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circum |
around, about |
circumvent, circumscribe, circumspect |
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claim, clam |
shout, speak out |
clamor, exclaim, proclamation |
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cerebr/o |
brain |
cerebral, cerebrate |
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fract, frag |
break |
fracture, fragile, fragment,fraction |
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loqu, locu |
speak |
eloquent, loquacious, elocution |
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merge, mers |
dip, dive |
,submerge, immerge, immerse |
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mega |
great, large, million |
megaphone, megastructure |
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purg |
clean |
purge, purgatory, expurgate |
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2017 |
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“Change Is Inevitable, Progress Is Intentional” North District Middle School Handbook |
2018 |
78 |
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MATH FACTS
I.
The Number System
II. Operations
a) Absolute Value is the distance away from zero. It will always be positive and it is symbolized by | |.
i.e |2| = 2 because 2 is 2 units from zero i.e. |-2| = 2 because -2 is 2 units from zero
b) Integer Addition Rules c) Integer Subtraction Rules
· Same signs, add and keep sign Change subtraction sign to addition,
i.e. (+3 + +4= +7) & (-3 + -4 = -7) change sign following to opposite,
· Different signs, subtract and take sign and follow addition rules.
of number with highest absolute value. i.e. {(-8 - +3) à -8 + -3 = -11}
{i.e. -5 + +8= +3} & {+5 + -8= -3} i.e. {(-8 - -3) à -8 + +3= -5}
d) Multiplication of Integers e) Division of Integers
· Same signs, answer is positive Same signs, answer is positive
· Different signs, answer is negative Different signs, answer is negative
III. Exponents and Powers
f) an =52 àa is the base and n is the exponent or power; the power tells you how many times to multiply the base by itself; 5 is the base and 2 is the exponent à 5·5 = 25
g) a-1= 1/a and 1/a-1 = a; 2-1= 1/21 and ½-1= 2
h) an·amàsince the bases are the same, you add the exponents together. {i.e. 32 ·33à35 = 243}
Proof: 32 = 9 and 33= 27 à 9 · 27 = 243 ; bases must be the same
i) an/ am à since the bases are the same, you subtract the exponents: an – mà 34/33à 34 – 3à 31à 3
Proof: 34= 81 and 33= 27 à 81 ÷ 27 = 3; bases must be the same
Examples to consider: 1) 25/23à 2 5-3à 22=4 2) 23/25à23-5à 2-2à ¼ (see “g” above)
j) (am)n = am·nà amnà (23)2 =23·2=26 =2·2·2·2·2·2= 64 Proof: 23= 8 and 82=64
79
MATH FACTS
IV. Order of Operations-Hierarchy of Math Operations
· Do the operation within the parentheses (or any enclosure symbol) first
· Powers/exponents are next
· Multiplication and division should be done from left to right next
· Addition and subtraction from left to right is last
Example 1: Evaluate {3 + 6 · (5 + 4) ÷ 3 – 7} à{ 3 + 6 · (9) ÷ 3 – 7}à{ 3 + 54 ÷ 3 – 7}à{3 +18 – 7}à{14}
Example 2: Evaluate {9 - 5 ÷ (8 - 3) · 2 + 6} à{9 -5÷5·2+6}à {9 -1·2+6} à{9 -2 + 6}à {13}
Example 3: Evaluate {3 · ( 5 + 8 ) - 22 ÷4 + 3}à{3 · 13 - 22÷4 + 3}à{3 · 13 - 4 ÷ 4 + 3à{3 · 13 – 1+3}
è {39 - 1 + 3}à {41}
V. Basics of Algebra
· What is algebra? Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols (today written as Latin and Greek letters) represent quantities without fixed values, known as variables.
· An algebraic expression is a collection of letters and numbers combined by the four basic arithmetic operations. Here are some examples of algebraic ... 7 + 2x, 8x, 3x+y, 3x-4y, x/(x+y), x2, (x+y)2
1) The numbers in these expressions that are not attached to a letter are called a constant such as the “7” in the expression {7 + 2x}
2) The numbers in these expressions that are attached to a letter are called coefficients such as the “2” in 7 + 2x, the “8” in 8x, the “3” and the “1” in 3x + y
3) When you don’t see a number attached to a variable such as “y” in the expression 3x+y, then the coefficient is 1.
4) A term is a mathematical expression involving multiplication or division. Terms are separated by an addition or subtraction sign. Example: 5a is one term, 5a -8 is two terms, and 3a2 -4a + 5 is three terms.
5) Like/similar terms are terms that have the same variables and exponents, written in any order. The coefficients do not have to be the same. Examples 5a and 8a are like terms, -2a2 and 5a2 are like terms, 8a2 and 9a3 are not like terms because their exponents are different, 2x2 and 2y2 are not the same because they don’t have the same variable.
· Operating with algebra
1) The expression (7 + 2x) should be interpreted/read as “7 plus 2 times the value of x”
2) Given (7 + 2x) and told to evaluate the expression when x=3 you should substitute 3 in for x and you would then have the expression (7 + 2·3) à (7 + 6) = 13. (Order of Operations)
3) Addition and Subtraction: Only like terms can be added or subtracted, that is the coefficient values of the like terms. I.e. {2x + 3y – 5 + 6y + 4x + 9= (2x+4x) +(3y + 6y) + (-5 + 9)à6x + 9y +4}
4) Any terms can be multiplied and you can use the rules for exponents when the bases are the same; Example: (5x3y8)(2x4y6) à (5·2)( x3· x4)(y· y6) = 10x7y14
5) Any terms can be divided and you can use the rules for exponents when the bases are the same; Example: (35x3y8)(7x4y6) à (35÷7)( x3-4)(y8-6) = 5x-1y2 à 5y2 (See III-Exponents and Powers- g)
x
· Properties of Numbers
1) Commutative: {a + b = b + a} and {a – b = a + (-b)}
2) Associative: {(a + b) + c = a + (b + c)} and {(a – b) – c = a +(-b + -c)}
3) Distributive: {a(b + c) = ab + ac} and {a(b –c) = ab – ac}
4) Double Negative: -(-a) = a
5) Addition and Subtraction Properties of Equality: {If a=b, then a+c=b+c} and {a-c=b-c}
80
· Properties of Numbers (continued)
6) Multiplication and Division Properties of Equality: {If a=b, then ac=bc} and {a/c = b/c when c≠0}
7) Symmetric: {If a=b, then b=a}
· Symbolic Representation
1) The symbol “=” means is equal to
2) The symbol “ ≠ ” means is not equal to
3) The symbol “ > ” means is greater or more than; can be interpreted as not less than
4) The symbol “ ≥ ” means is greater than or equal to
5) The symbol “ < “ means is less than or not more than; can be interpreted as not more than
6) The symbol “≤ ” means is less than or equal to
· Ratio, Proportion, and Percent
1) Ratios compare two values or quantities and can be written as such: 5 to 8, 5:8, 5/8, or 5
2) Percents compare numerical values to 100.
a. They can be written using the % signà 30%
b. They can be written as a fractionà 30% = 30/100 = 3/10
{the percent value is your numerator and 100 is your denominator}
c. They can be written as a decimalà 30% = .30
{move the decimal point two places to the left and drop the percent sign}
3) Change a decimal number to a percent: Ex. .56= 56%, à
a. {move the decimal point two places to the right and add the percent sign after the number}
4) Proportions are equivalent ratios or fractions: Ex. {4 to 5 as 8 is to 10; 4:5::8:10 and 4/5=8/10}
5) Solving proportions: Ex . 4 = n 1) Cross multiplyà 5·n = 4·40 à 5n=160
5 40 2) Divide-à n = 160 ÷ 5 à n = 32
6) Percent Problems can be solved using proportion:
a) What percent of 180 is 40?
“is” number = % à 40 = n à 180·n = 40·100à 180n = 4000 à n= 4000÷180=22.2% “of” number 100 180 100
· Commonly Used Formulas
a) Simple Interest: i= prt à i= interest, p= principal, r= rate or percentage rate, t= time expressed in the same period as the rate
b) Compound Interest: A= p(1 + r/n)nt : A=total amount, p = principal, r = rate of interest, t= time expressed in years, n= number of periods per year
c) % of Decrease à amount of decrease = % decrease à solve as a proportion original value 100
d) % of Increase à amount of increase = % increase à solve as a proportion original value 100
e) % of Discountà amount of discount = % discountà solve as a proportion original value 100
f) % of Markupà amount of markup = % markup à solve as a proportion original price 100
g) % of Profità amount of profit = % profità solve as a proportion total income 100
h) % of Commissionà amount of commission = % commissionà solve as a proportion sales 100
· Coordinate Plane
· Basic Geometry
1) Perimeter is the distance around any polygon and is found by adding the lengths of all sides.
2) Area is the amount of space inside a flat figure.
3) Four sided figures are:
a) rectangle b) parallelogram c) square d) rhombus e) trapezoid
4) Parallel lines are two lines on a plane that never meet. They are always the same distance apart.
5) Perpendicular lines are lines that are at right angles (90 ) to each other.
6) The Pythagorean Theorem: Each right triangle has two legs and a hypotenuse, respectively a and b are the legs and c is the hypotenuse. The length of the hypotenuse of the triangle is the longest side.
SCIENCE FACTS
Scientific Equations
I. Electricity
a) P = V · I ; Power = Voltage · Current
b) V = I · R ; V=potential (volt,v) I =current (ampere, a) R=resistance (ohm,Ω)
c) Q = I ·T; Charge = Current · Time
d) E = V ·Q; Energy = Voltage · Charge
e) E= V ·I · T; Energy = Voltage · Current ·Time
II. Energy
a) Efficiciency (%) = (useful energy out ÷ total energy in) ·100
b) GPE = mgh; GPE= Mass · Gravity · Height
c) KE = ½ MV2; Kinetic Energy = 0.5 ·mass · velocity2
d) W = F · d; W= work Done(joule, j) F=force (newton, N) d= distance (meter, m)
e) W = E ; Work done = Energy transferred
f) P = E ÷ t ; Power = Energy ÷ time
g) E = c · m · Ɵ; Energy = Specific heat capacity · mass ·change in temperature
III. Forces and Motion
a) S = d ÷ t ; speed = distance ÷ times
b) A= (v-u) ÷ t; acceleration = change in velocity ÷ time
c) F= m · a ; F= force(newton, N) m =mass(kilogram, kg) a= acceleration (m/s2)
d) W= m · g; Weight = mass ·gravity
e) P= m · v ; Momentum = mass ·velocity
f) (mv – mu)= F · t ; Change in momentum = Force · time
g) d= m ÷ v; density= mass ÷ volume
h) p=F ÷ a; Pressure= force ÷ area
i) m=F · d; moment=force · perpendicular distance from pivot
IV. Waves
a) v = f · λ.; velocity = frequency · wavelength.
SCIENCE FACTS
THE SOLAR SYSTEM
Planet |
Distance from Sun |
Length of a Solar Orbit |
Interesting Facts |
Mercury |
36 million miles |
88 earth days |
· Smallest planet · Diameter at equator is 3,032 miles |
Venus |
67 million miles |
225 earth days |
· Spins in opposite direction of earth · Diameter at equator is 7,521 miles |
Earth |
93 million miles |
365 earth days |
· Only planet known to have life · Diameter at equator is 7,926 miles |
Mars |
142 million miles |
687 earth days |
· Has polar ice caps and frozen water · Diameter at equator is 4,222 miles |
Jupiter |
484 million miles |
12 earth years |
· Has at least 62 known moods · Diameter at equator is 88,846 miles |
Saturn |
886 million miles |
29 earth years |
· Could float in water due to low density · Diameter at equator is 74,898 miles |
Uranus |
1.8 billion miles |
84 earth years |
· Tilts sideways;poles face sun ½ the time · Diameter at equator is 3,032 miles |
Neptune |
2.8 billion miles |
165 earth years |
· Neptune’s moon orbits in the opposite direction of the planet’s orbit · Diameter at equator is 30,777 miles |
Pluto |
No longer considered a planet |
||
A mnemonic device for remembering order of planets from moon
~My Very Educated Mother Just Served Us Noodles~ |
CLASSIFICATION OF ANIMALS
(Vertebrates vs. Invertebrates)
Vertebrates Invertebrates
1) Have a backbone 1) Don’t have a backbone
2) Five specific vertebrates 2) Eleven specific vertebrates
a) reptiles a) protozoa
b) fish b) flatworms
c) amphibians c) annelid worms
d) birds d) echinoderms
e) mammals e) coelenterates
f) arthropods
g) molluscs
h) arachnids
i) crustaceans
j) insects
k) myriapods
SCIENCE FACTS
Did You Know?
1. Water is an excellent conductor of electricity.
2. Do not mix ammonia and bleach together.
3. Acid into water, never water into acid.
4. What goes up, must come down.
5. An object at rest stays at rest… : …because of Newton’s First Law of Motion.
6. An object in motion stays in motion… : …also due to Newton’s First Law of Motion.
7. Matter is neither created nor destroyed.
8. Energy is neither created nor destroyed.
9. What constitutes a chemical change. : Chemical changes – such as burning, cooking, decomposition, and others – permanently alter the composition of an object.
10. What constitutes a physical change. : Unlike chemical changes, those of the physical variety (cutting, carving, breaking, etc.) only alter the shape or form of an object and leave their core compositions intact.
11. Red and yellow, kill a fellow… : …red and black, friend of Jack. This mantra helps amateur and professional naturalists alike tell the difference between the deadly coral snake and the entirely harmless scarlet king snake.
12. Spiders are not insects- many people lump spiders in with the insects, but their eight legs, simplistic eye structure, and lack of wings do not place them in that classification. Rather, biologists consider them arachnids, related more to scorpions and ticks than wasps and ants.
13. Dolphins and whales are not fish- because of their shape and aquatic habitat, people continuously mistake dolphins, whales, and porpoises as fish. As endothermic creatures with hair, mammary glands, and the ability to give birth to live young, they fully qualify as mammals – specifically, cetaceans.
14. Bats are not birds-due to the fact that they actually fly rather than glide, many people still adhere to the belief that bats are birds. In reality, their hair, endothermic body heating, milk production, and giving birth to live young land them squarely in the mammalian classification.
15. Never put a magnet near electronics-magnets and their accompany fields can negatively interfere with or outright damage most electronics.
16. Frozen water is capable of cracking metal containers-even though cold contracts, the act of freezing water creates a solid with the dangerous ability to split open even metal confines.
17. A light year is not a unit of time-although the term “year” factors into the nomenclature, a light year actually measures extremely long distances and is used in mapping galaxies, planets, stars, and other astronomical phenomena.
18. Heat expands-heat causes the atoms and molecules of a substance to vibrate more, and subsequently expand as a result.
19. Lightning is electricity-Many people find lightning dramatic and frightening, but few pause to remember that it is, in fact, a massive discharge of electricity resulting from an imbalance of positive and negative particles.
20. Thunder is the sound of lightning heating up atmospheric gas-because sound travels significantly slower than light (the fastest known element in the universe), thunder will always lag behind a lightning strike.
21. Computers cannot do anything without a human command at some point-although computer technology
is capable of calculations and processes far faster than that of a human brain, at some point in a person had to give the commands that needed execution.
22. Space is not a complete vacuum.
23. Rats do not carry the plague-rats in and of themselves are never actually to blame for the onset of bubonic plague
– in spite of their abundance, they did not inherently cause the Black Death and other instances
24. Humans are not the only animals who use tools.- humanity oftentimes arrogantly points to its use of tools as one reason it stands as superior to other species. However, a diverse number of animals possess the intelligence and resourcefulness to creatively use elements of their environments to make their lives easier.
25. Hair and nails do not continue to grow after death. : Vampire mythos and other tales of the dead often declare that hair and nails keep growing long after an individual has been buried. While the concept makes for intriguing speculative fiction, it fully remains just that – untrue! As the human body decomposes, the skin begins shrinking back and creates the illusion that the subcutaneous bits of hair and nails that begin peeking out are actually actively growing. Keratin – the substance that comprises both nails and hair – dies along with the body.
85
SCIENCE FACTS
The Human Skeleton
86
SCIENCE FACTS
THE PERIODIC TABLE
87
I. United States of America- The fifty states and their capitals
State |
Capital |
|
State |
Capital |
|
|
|
|
|
Alabama |
Montgomery |
|
Montana |
Helena |
Alaska |
Juneau |
|
Nebraska |
Lincoln |
Arizona |
Phoenix |
|
Nevada |
Carson City |
Arkansas |
Little Rock |
|
New Hampshire |
Concord |
California |
Sacramento |
|
New Jersey |
Trenton |
Colorado |
Denver |
|
New Mexico |
Santa Fe |
Connecticut |
Hartford |
|
New York |
Albany |
Delaware |
Dover |
|
North Carolina |
Raleigh |
Florida |
Tallahassee |
|
North Dakota |
Bismarck |
Georgia |
Atlanta |
|
Ohio |
Columbus |
Hawaii |
Honolulu |
|
Oklahoma |
Oklahoma City |
Idaho |
Boise |
|
Oregon |
Salem |
Illinois |
Springfield |
|
Pennsylvania |
Harrisburg |
Indiana |
Indianapolis |
|
Rhode Island |
Providence |
Iowa |
Des Moines |
|
South Carolina |
Columbia |
Kansas |
Topeka |
|
South Dakota |
Pierre |
Kentucky |
Frankfort |
|
Tennessee |
Nashville |
Louisiana |
Baton Rouge |
|
Texas |
Austin |
Maine |
Augusta |
|
Utah |
Salt Lake City |
Maryland |
Anapolis |
|
Vermont |
Montpelier |
Massachusetts |
Boston |
|
Virginia |
Richmond |
Michigan |
Lansing |
|
Washington |
Olympia |
Minnesota |
Saint Paul |
|
West Virginia |
Charleston |
Missippi |
Jackson |
|
Wisconsin |
Madison |
Missouri |
Jefferson City |
|
Wyoming |
Cheyenne |
II. US MAP
88
III. The Preamble To The Constitution of The United States
We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.
IV. Bill of Rights (First Ten Amendments of Constitution)
The first 10 amendments to the Constitution make up the Bill of Rights. Written by James Madison in response to calls from several states for greater constitutional protection for individual liberties, the Bill of Rights lists specific prohibitions on governmental power.
The Bill of Rights is a list of limits on government power. For example, what the Founders saw as the natural right of individuals to speak and worship freely was protected by the First Amendment’s prohibitions on Congress from making laws establishing a religion or abridging freedom of speech. For another example, the natural right to be free from unreasonable government intrusion in one’s home was safeguarded by the Fourth Amendment’s warrant requirements.
Other precursors to the Bill of Rights include English documents such as the Magna Carta, the Petition of Right, the English Bill of Rights, and the Massachusetts Body of Liberties.
Amendment I
a) Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.
· Amendment II
b) A well-regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed.
· Amendment III
c) No soldier shall, in time of peace be quartered in any house, without the consent of the owner, nor in time of war, but in a manner to be prescribed by law.
· Amendment IV
d) The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no warrants shall issue, but upon probable cause, supported by oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
· Amendment V
e) No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a grand jury, except in cases arising in the land or naval forces, or in the militia, when in actual service in time of war or public danger; nor shall any person be subject for the same offense to be twice put in jeopardy of life or limb; nor shall be compelled in any criminal case to be a witness against himself, nor be deprived of life, liberty, or property, without due process of law; nor shall private property be taken for public use, without just compensation.
89
· Amendment VI
f) In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the state and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the assistance of counsel for his defense.
· Amendment VII
g) In suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved, and no fact tried by a jury, shall be otherwise reexamined in any court of the United States, than according to the rules of the common law.
· Amendment VIII
h) Excessive bail shall not be required, nor excessive fines imposed, nor cruel and unusual punishments inflicted.
· Amendment IX
i) The enumeration in the Constitution, of certain rights, shall not be construed to deny or disparage others retained by the people.
· Amendment X
j) The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people.
V. United States of America Government
· The U.S. government has three branches: executive, judicial, and legislative. Each branch has its own responsibilities and also has the ability to check the powers of the other two branches. This ensures that the government is balanced and no branch or person has too much power.
· Legislative branch makes laws
· Executive branch carries out the laws
· Judicial branch interprets laws
VI. Hierarchy of U.S.A. Government
Constitution of USA
Legislative Executive Judicial
Congress President Supreme Court
Vice President
House of Representatives Senate
90
V. United States Presidents and Political Party Affiliation
1. George Washington (1789-1797)… ......................................................................................Independent
2. John Adams (1797-1801)...........................................................................................................Federalist
3. Thomas Jefferson (1801-1809). .......................................................................... Democratic-Republican
4. James Madison (1809-1817)............................................................................... Democratic-Republican
5. James Monroe (1817-1825). ............................................. Democratic-Republican/National Republican
6. John Quincy Adams (1825-1829)....................................................................... Democratic-Republican
7. Andrew Jackson (1829-1837). ................................................................................................ Democratic
8. Martin Van Buren (1837-1841)…. ..................………………………………………….......Democratic
9. William Henry Harrison (1841)…....................……………………………………………………Whig
10. John Tyler (1841-1845)………. ...................……………………………………….Whig/Independent
11. James K. Polk (1845-1849)………………………………….………..…...................…….Democratic
12. Zachary Taylor (1849-1850)……………………………………………..................…………….Whig
13. Millard Fillmore (1850-1853)………………………………………………….................………Whig
14. Franklin Pierce (1853-1857)………………………………….……...…….................……Democratic
15. James Buchanan (1857-1861)……………………………………….................…………..Democratic
16. Abraham Lincoln (1861-1865)…………………….......……… ................ National Union/Republican 17. Andrew Johnson (1865-1869)…………………………..……...................National Union/Democratic 18. Ulysses S. Grant (1869-1877)…………………………….…................. ………………….Republican
19. Rutherford B. Hayes (1877-1881)………………………… ................ ……………………Republican
20. James A. Garfield (1881)………………………………………................ ………………..Republican
21. Chester Arthur (1881-1885)…………………………………................ …………………. Republican
22. Grover Cleveland (1885-1889)………………………………................………………….Democratic 23. Benjamin Harrison (1889-1893)………………………………............... …………………Republican 24. Grover Cleveland (1893-1897)………………………………................………………….Democratic
25. William McKinley (1897-1901)……………………………… ............... …………………Republican 26. Theodore Roosevelt (1901-1909)…………………………… ............... …………………..Republican 27. William Howard Taft (1909-1913)……………………………................ ………………...Republican
28. Woodrow Wilson (1913-1921)…………………………………................…………….....Democratic
29. Warren G. Harding (1921-1923)…………………………………................. ……………..Republican
30. Calvin Coolidge (1923-1929)…………………………………… ................ ……………...Republican
31. Herbert Hoover (1929-1933)…………………………………… ................ ………………Republican 32. Franklin D. Roosevelt (1933-1945)…… .................…………………………….…………Democratic 33. Harry S Truman (1945-1953)…………… .................………………….………………….Democratic 34. Dwight D. Eisenhower (1953-1961)……................. ………………………………………Republican 35. John F. Kennedy (1961-1963) .................………………………………………………….Democratic
36. Lyndon B. Johnson (1963-1969) .................……………………………………………….Democratic
37. Richard Nixon (1969-1974)…................. ………………………………………………….Republican
38. Gerald Ford (1974-1977)… ................. …………………………………………………….Republican
39. Jimmy Carter (1977-1981)…..................……………………………..................................Democratic
40. Ronald Reagan (1981-1989)…… ................................................ ………………………….Republican
41. George Bush (1989-1993)……................................................ …………………………….Republican
42. Bill Clinton (1993-2001)……………….................................................…………………..Democratic
43. George W. Bush (2001-2009)…………................................................. …………………..Republican
44. Barack Obama (2009-2017)………....................................................……………………..Democratic
45. Donald Trump (2017-present). ............................................................................................ Republican