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Greetings!!!. Hello everybody! I am Ms. Signorello and in today’s lesson we will work on some math skills, vocabulary, sentence completions, and writing exercises. Lesson # 2. Today’s Math Skills. More on Fractions Reciprocals Factors and Multiples. More on Fractions.

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Greetings!!!

Hello everybody! I am Ms. Signorello and in today’s lesson we will work on some math skills, vocabulary, sentence completions, and writing exercises.

Lesson # 2

Today’s Math Skills

More on Fractions

Reciprocals

Factors and Multiples

More on Fractions

Alternating between a decimal and a fraction is an important skill.

To change a fraction into a decimal you simply divide the top number by the bottom number.

Examples

Let’s say you want to change 4/5 to a decimal. You will divide 5 into 4.

= =

Or you can use a calculator

Online Calculator

Let’s try the online calculator to convert 7/5 to a decimal.

Changing from a decimal to a fraction

Let’s change .275 to a fraction.

.275 = 275/1000 = 11/40

Using the online calculator

Online Calculator

Let’s change .125 to a fraction.

On the calculator there’s a key that has

We’ll use that key and then enter in our decimal.

d f

Reciprocals

Using reciprocals is an important skill for solving algebraic equations.

If you multiply a number by it’s reciprocal, it will always equal 1.

Scientific Notation

Suppose you need to change 345 to scientific notation. The number 345 is the same as

300 + 40 + 5. It can also be written as 3 x 100 + 4 x 10 + 5 x 1 =

Factors

Factors are the positive integers that divide evenly into a number. For example the factors of 36 are:

36, 18, 12, 9, 6, 4, 3, 2, 1

I can divide 36 by any of these numbers and there will not be a remainder.

Multiples

Multiples are numbers that can be divided by the given number evenly. That means there is no remainder.

For example, the numbers 9, 18, 36, 45, and 54 are multiples of 9. 9 divides evenly into each of those numbers.

Examples

5A is divisible by both 2 and 3. If A is a digit, what is the value of A?

1

2

3

4

5

Example

If a - b is a multiple of 5, then which of the following must also be a multiple of 5?

b - a

a + b

ab

b - a 2

a + b 2

Solution

If a - b is a multiple of 5, we can pick a number for a and a number for b that makes this true. Let a = 13 and b = 8. So, 13 - 8 = 5, which is divisible by 5. We will substitute a = 13 and b = 8 in the answer choices.

Substituting

8 - 13 = -5

• b - a
• a + b
• ab
• b - a 2
• a + b 2

13 + 8 = 21

(13)(8) = 104

8 - 13

2

= -5 2

13 + 8 2

= 21 2

Example

Which of the following could be remainders when 3 consecutive positive integers are each divided by 4?

1, 2, 3

0, 3, 2

3, 0, 1

3, 2, 1

0, 1, 2

Solution

Pick any 3 consecutive integers, say 7, 8, and 9. Now divide each of those by 4 and record the remainder for each division.

7/4 has a remainder of 3.

8/4 has a remainder of 0.

9/4 has a remainder of 1.

Therefore, answer c is the correct answer!

Practice

Math Practice

Vocabulary List 2

arid- a dry, rainless climate

conflagration – a fire that is widespread

derived- adapted or copied from a source

discourse- conversation; verbal exchange

genre- category or type of artistic work

Vocab continued

impression- a belief or understanding of something; a feeling about something or somebody

obsolete- no longer in use

opulent- showing a display of great wealth

rational- logical; evidence of clear and sensible thinking

vilify- to make malicious, vicious, or abusive statements about

arid- a dry, rainless climate

The desert is an arid place.

conflagration – a fire that is widespread

The news reporter suggested that tsunami caused the destructive conflagration.

derived- adapted or copied from a source

The professor derived the quadratic formula by completing the square using

.

discourse- conversation; verbal exchange

The lawyer and his client were in deep discourse before entering the court room.

genre- category or type of artistic work

Music is categorized by it’s genre.

impression- a belief or understanding of something; a feeling about something or somebody

The motivational speaker had a great impression on me.

obsolete- no longer in use

The dial telephone is obsolete; most people use a cell phone now.

opulent- showing a display of great wealth

The once opulent Spanish-style houses have large carved wooden doors opening on to outdoor patios.

rational- logical; evidence of clear and sensible thinking

Please provide me with a rational explanation why you support their position.

The Republicans attempted to vilify President Obama, claiming he is a Muslim.

Practice and Quiz

Practice Quiz

Sentence Completions

Hoping to the conflict, negotiators propose a compromise that they felt would be to both policies and legislation.

Sentence Completions

Artists often claim to create what they see, yet so many of them depart from strict ___ and opt to take ___ with their painting subjects.

knavery…freedoms

jargon…integrity

definition…vagaries

observation…care

imitation…liberties

Sentence Completions

Cactuses which grow in the Nevada desert can survive long periods of _ because they retain water in their leaves, stems and root systems.

aridity

monotony

dormancy

heat

substance

Sentence Completions

Mrs. Smith was a ____ manager she was always mean and would often force her employees to work overtime without pay in order to save money.

ludicrous

mawkish

miserly

friendly

ample

Sentence Completions

Johnson waged a personal against those who opposed his nomination for the office

harmony

agreement

expectation

bet

vendetta

Practice

Sentence Completion Practice

The Writing Section

The writing section on the SAT consists of:

• The Essay
• Improving Sentences
• Identifying Sentence Errors
• Improving Paragraphs
Writing Exercises

Be sure to vary the usage of verbs in the essay! Do not overuse the verb “to be” or any of its forms. They are:

am, is, are, was, were, be, being, been

More about writing the essay

Use variety of vocabulary words when you write. If you continue to use the same words over and over, the graders will get bored and move on to the next essay. DO NOT use big words if you don’t know their meaning!!

Grammar Review

Parts of Speech:

Noun is a person, place, thing, or idea.

A pronoun takes the place of a noun.

As the subject: he, she, they

As the object: him, her, them

As possessive: his, hers, theirs

As reflexive: myself, herself, himself

Verbs & Grammar

Verbs express action or a state of being. Types of verbs:

Linking verbs: often in the form of the verb to be. There is no action. Example - Math teachers are smart.

Helping verbs: work with other words to express mood and time. Example - Mary can run faster than anyone I know.

Verbs & Grammar

Transitive verbs: require the use of an object. Example: Joe sent a package in the mail. Sent cannot be used alone. It must have an object.

Verbs & Grammar

Intransitive Verbs: do not need an object. Example - The motor overheated.

Adjectives describe nouns. Examples:

The girl wore red shoes.

The dog had a curly tail.

The queen lived in a huge castle.

Adverbs describe a verb. The tell us more about the verb being used and can also describe other adverbs. Examples:

Debbie wanted to strategically place the plants in her flowerbed.

Prepositions and Grammar

Prepositions describe time or place relationships between words.

List of Prepositions

after against along

among around at

before behind below

beneath beside between

By down during

except for from

List of Prepositions

in front of in inside

instead of into like

near of off

on onto on top of

out of outside over

past since through

List of Prepositions

to toward under

underneath until

up upon with

within without

Conjunctions and Grammar

Conjunctions connect two nouns, two verbs, two adjectives, two adverbs, etc.

Examples: and, but, or, yet, for, nor, so

A little out of the ordinary

Abstract nouns - are general and lack specificity.

Examples: assignments, countries, decision

A little out of the ordinary

Infinitives: verbs that use the word “to”.

Examples:

To run, to jump, to swim, etc.

Juan couldn’t wait to see his friends.

A little out of the ordinary

Gerunds - special verb forms that end in -ing. It takes the place of a noun and indicates an action. Examples: Dancing makes me happy.

A little out of the ordinary

Present participles - also end in -ing but describes a noun. Example: The dancing bears at the circus are exciting to watch.

Practicing Grammar

The members of our class have more school spirit than _____

a) They

b) Them

Practicing Grammar

Matt and Martha didn’t understand why anyone should keep his feelings inside about grades when it’s so much more fun to compete with a classmate over them.

What’s wrong with this sentence?

Practicing Grammar

I’m convinced, though, that Emily will always be a better bassist than ____

a) me

b) I

Practicing Grammar

Few of the aquatic animals lived through the oil spill with _______ health intact.

a) Their

b) His or her

Practicing Grammar

Everyone in the debate group ____ experienced problems with using online databases.

a) has

b) have

Practicing Grammar

Brandon was focused the rest of the class was distracted.

a) Brandon was focused, the rest of the class was distracted.

b) Brandon was focused; the rest of the class was distracted.

c) No change

Use concrete language

When you are writing on the SAT, you’ll want to use concrete language to describe abstract ideas. Think of the word victory. By itself, it is abstract.

Concrete Language Continued

However if you were to write:

The Women’s Soccer team from the United States fell just shy of a victory in the World Cup.

It becomes concrete!!!

Identifying language that is abstract

By using the following endings on nouns you know, you can recognize abstract words:

-ness -age -tion

-ance -ty -ment

Let’s make up some of those abstract words

happiness

courage

concentration

clearance

fidgety

agreement

Practice

Using the words from the previous slide, find 3 sentences that use those words and make those sentences concrete. Provide definite examples in each sentence.

Writing Practice

Essay prompt

Resources

www.majortests.com

www.learning-centered.com