Greetings!!!

Hello everybody! I am Ms. Signorello and in today’s lesson we will work on some math skills, vocabulary, sentence completions, and take a brief look at the essay.

SAT Prep

Lesson 1

Lesson 1 Mathematics

Number and Operations Review

Properties of Integers Arithmetic Word ProblemsNumber Lines

Squares and Square Roots

Properties of Integers

Integers - the set of numbers that consists of positive and negative whole numbers.

Positive integers: 1, 2, 3, ….Negative integers: …-3, -2, -1Zero (0) is neither negative nor positive

Odd and Even Integers, Consecutive Integers, and

Adding Integers

Odd integers: {…, -5, -3, -1, 1, 3, 5, …}

Even integers: {…, -6, -4, -2, 2, 4, 6,…}

Consecutive integers: -3, -2, -1, 0, 1, 2

Adding integers: even + even = even,

odd + odd = even,

odd + even = odd

Multiplying Integers

Multiplying integers: even x even = even, odd x odd = oddEven x odd = evenMultiplying or dividing by 1 doesn’t change the value of a number.

Arithmetic Word Problems

Ms. Foster is making bags of party treats. If she puts 5 treats in each bag, she will make 30 bags of treats and have none left over. If instead she puts 15 treats in each bag, how many bags of treats can she make?solution

Solution

5 treats x 30 bags = 150 treats total

150 treats/15 treats per bag = 10 bags

Example 2Jorge bought 10 pencils from the store. He gave the cashier a ten-dollar bill and got back $0.75 in change. Jorge saw that he had gotten too much change, and he gave $0.25 back to the cashier. What was the price of each pencil?Solution

Solution

$10.00

$9.50/10 = $0.95 for EACH pencil

+ .25returned

$9.25

- .75 change

$9.50

Number Lines A B C D E F G

On the number line above, the ratio of AC to AG is equal to the ratio of CD to which of the following?

(A) AD

(B)BD

(C)CG

(D)DF

(E) EG Solution

0 1 2 3 4 5 67

Solution

First, determine the lengths for each segment.AC = 2AG = 6CD = 1

2

6

1

x

A B C D E F G

0 1 2 3 4 5 67

COMPARE RATIOS:

AC to AG is 2 to 6

First, set up a proportion

Solving the proportion

Cross multiply:so 2x = 6,

divide both sides by 2, x = 3

2

6

1

x

2x 1 6

2x

2

6

2

AC

AG

CD

x

Answer

(A)AD measure is 3

(B)BD measure is 2

(C)CG measure is 4

(D)DF measure is 1

(E)EG measure is 2

Working with perfect squares

It is very important to know all the perfect squares for all integers from -12 through 12. Knowing these will help you solve problems involving factoring, simplifying expressions, solving equations, using the Pythagorean Theorem, and applications involving area.

More…

Knowing these will help you solve problems involving factoring, simplifying expressions, solving equations, using the Pythagorean Theorem, and applications involving area

Squares and Square Rootsx 1 2 3 4 5 6 7 8 9 10 11 12

x2 1 4 9 16 25 36 49 64 81 100

121

144

x -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 -11 -12

x2 1 4 9 16 25 36 49 64 81 100

121

144

Fractions and Rational Numbers

It is necessary to know the basic operations with fractions. You must be able to add, subtract, multiply and divide fractions.

More……..

Also, knowing how to reduce fractions to lowest terms, find a common denominator, be able to alternate between mixed numbers and improper fractions and work with a complex fraction is very important.

Adding and Subtracting Fractions

You MUST find a common denominator first, then carry out the addition or subtraction using only the numerator. The denominator remains the same.

Adding Fractions

3

7

2

9

To add fractions you need to find a common denominator. In this problem the common denominator is 63.

Getting a common denominatorFor the denominator to equal 63, the first fraction needs to be multiplied, top and bottom by 9. In the second fraction you will multiply top and bottom by 7.

3 9

7 9

2 7

9 7

Step by step

9 times 3 is 27 and 2 times 7 is 14.

27

63

14

63

27 14

63 add 27 and 14.

27 +14 = 41

41

63 is the answer. Reduce fraction if possible.

Subtracting Fractions

3

4

2

3

9

12

8

12

9 8

12

1

12

Subtracting fractions works exactly the same as adding them.

Squaring Fractions

One way:

2

5

2

2

5

2

5

4

25Remember - when you are “squaring numbers” it means you are multiplying the number by itself! To multiply fractions, remember, top times top and bottom times bottom.

Another way

2

5

2

22

52 4

25

You can also think of squaring each number in the fraction separately.

Math Wrap Up

Today we explored some basic concepts in mathematics. There will be many more topics in future lessons.

Next…..Vocabulary

To do well on the critical reading portion of the SAT, it is vital for students to have a broad vocabulary. 10 new vocabulary words will be in each lesson during this course.

Word - Definition Using it in a Sentence

For each vocabulary word, we will explore the word’s meaning and how it is used in a sentence.

Vocabulary List 1

ambiguous- vague, more than one interpretation

assertion- a statement or declarationdisdain – contempt; scornexcerpt- a selected portion of a passagefrank- to the point, candid,

straightforwardfrenetic- very active or wildly excited

Vocabulary continued….

incumbent- obligatory; necessary as a result of duty

medieval- old-fashioned, belonging to the Middle Ages

nocturnal- occurring at night; describes animals that are active at night

phenomenon- an observable event that is unusual; out of the ordinary and excites people’s interest

ambiguous- vague, more than one interpretation

The concluding paragraph in the student’s essay was quite ambiguous; it left the reader confused.

assertion- a statement or declaration

The politician made his final assertion regarding the city’s budget proposal.

disdain – contempt; scorn

Mark had a look of disdain on his face as he was being reprimanded.

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are needed to see this picture.

excerpt- a selected portion of a passage

The teacher instructed her students to read an excerpt from Anne Frank’s Diary.

frank- to the point, candid, straightforward

To be perfectly frank, your performance on the job has been below average.

frenetic- very active or wildly excited

Carla and Jose celebrated raised the 1st place trophy at a frenetic pace.

QuickTime™ and a decompressor

are needed to see this picture.

incumbent- obligatory; necessary as a result of duty

It is therefore incumbent upon us to do all we can to educate the world on the importance of recycling.

medieval- old-fashioned, belonging to the Middle Ages

The costumes for the show, “The Knight’s Rise”, were medieval.

QuickTime™ and a decompressor

are needed to see this picture.

nocturnal- occurring at night; describes animals that are active at night

Raccoons are considered to be nocturnal.

QuickTime™ and a decompressor

are needed to see this picture.

phenomenon- an observable event that is unusual; out of the ordinary and

excites people’s interest

The creation of lightning during a storm is a phenomenon that is still not completely understood.

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are needed to see this picture.QuickTime™ and a

decompressorare needed to see this picture.

Using vocabulary to get the right answer on Sentence

Completions As your vocabulary is strengthened, you will utilize that knowledge to find the correct answer in the Sentence Completion portion of the Critical Reading Sections.

Sentence Completions

Sentence completions are at the beginning of every critical reading section.

You can expect between 5 and 8 questions of this type.

Sentence Completions continued…

The level of difficulty is in order from easiest to most difficult.

You can expect the first 1/3 of the questions to be easy, the middle 1/3 to be medium, and the last 1/3 to be the hardest questions.

Sentence Completions continued…

There are 2 types of sentence completions. They are:

vocabulary in context and

logic based

Vocabulary in Context

A vocabulary in context question is testing you on your knowledge of a words definition.

Logic-based VocabularyTo answer these questions you

will need to use clues in the sentence to determine the correct answer. You will look for key words which indicate the direction a sentence is going in. Will the end of the sentence change direction or will it remain the same?

Sentence Completions continued…

We will explore those key words as we work through example questions.

The Technique

Sentence completions may have one or two blanks that need to be filled in with the correct word or words. The basic strategy is the same for both types.

- Sentence Completions - One Blank

The most important part to finding success on sentence completions is NOT to be mislead by the answer choices. So we don’t look at them!!! Cover them with a sheet of paper or your hand.

Sentence Completions - One Blank

Carefully read the sentence provided, then using your own vocabulary, pick a word that makes sense in the blank. Compare your word to those in the answer choices. When you find a match, you’ve found the correct answer.

ExampleWhen the earthquake began, the

ground shook violently causing people to scream in terror. .

a.slowlyb.graduallyc.violentlyd.quietlye.mildly

ExampleThe store clerk has a personality; her smile and herkindness was evident immediately.

a.boringb.unfriendlyc.austered.magnificente.ample

Example

The new student wasin 3 different languages.a.adamantb.fluentc.vocald.pallide.vivacious

Example

Many-layered mapmaking is helping scholars recreate vanished landscapes and envision history.

a.alienatedb.brittlec.triviald.tenuouse.vanished

2 Blanks are just as easy!

Always start by covering the answer choices. You don’t want them to influence you!

Read the sentence and pick 1 of the blanks to start with.

Pick your OWN word for that blank and begin eliminating answer choices.

Two blanks continued

Eliminate (cross out) any answer choice that doesn’t have the word that matches yours.

Now pick your own word for the second blank

Two blanks continued

From the remaining answer choices (the ones you haven’t crossed out), match your word to the ones that are left.

Example

After all her effort, the artist was ________ to learn that her drawing had been ________ for publication.

a) elated...disallowedb) dismayed...approvedc) troubled...recommendedd) enthralled...refusede) distraught...rejected

ExampleBy using public records and

databases, investigators found evidence to arrest the criminal.

a) journalists...huntersb) abolitionists...protestorsc) activists...offenderd) researchers...incumbente) investigators... criminal

Example

The coach praised and ------- her athletes.

a) reprimanded...cheeredb) praised...applaudedc) worked...denouncedd) encouraged...chastisede) lectured...rejected

Wrap-up

Sentence completions are easy IF you have a strong vocabulary. Work on your vocabulary every day!!!

We will do more examples in the lessons ahead.

The Essay - A Brief Introduction

The very first section on the SAT is always the essay. Students are required to write an original, first draft piece of work under a time constraint.

As long as you know how to approach the essay, you will find it easy to write.

Structure

Your essay MUST include the following:

•An introductory paragraph

•2-3 paragraphs that make up the body

•A concluding paragraph

Time Allotment

Students are allowed 25 minutes to write their essay.

The first 3 minutes are spent thinking of the examples you will use to support your position.

The next 16-20 minutes are spent writing the essay. The final minutes are spent on the conclusion.

More to Come

In future lessons we will discuss reading the prompt, choosing a side, and how you determine what you will write.

Practice

Using the following link, practice, practice, practice!

Sentence Completions PracticeInteger Practice

Don’t forget to study your 10 vocabulary words!

The End of Lesson 1

This is the end of lesson 1. Remember to do the practice problems that I’ve assigned!

Until next time, have a fabulous day!

References

http://www.centurynovelty.com detail_356_146-414.ht

ml?reasonAdded=Item_List

http://www.nytimes.com/pages/technology/index.html

http://www.majortests.com/sat/sentence-completion-te

st01

http://amby.com/educate/math/integ_x1.html

http://creativecommons.org/licenses/by-nc-sa/3.0/

Images are from Microsoft Office