Greetings!!!

1. 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.

2. SAT Prep Lesson 1

3. Lesson 1 Mathematics Number and Operations Review Properties of Integers Arithmetic Word Problems Number Lines Squares and SquareRoots

4. 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, -1 Zero (0) is neither negative nor positive

5. 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

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

7. 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

8. Solution 5 treats x 30 bags = 150 treats total 150 treats/15 treats per bag = 10 bags

9. Example 2 Jorge 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

10. - .75change Solution $9.25 + .25 returned $10.00 $9.50 $9.50/10 = $0.95 for EACH pencil

11. 0 1 2 3 4 5 6 7 Number Lines On the number line above, the ratio of AC to AG is equal to the ratio of CD to which of the following? AD BD CG DF EG Solution A B C D E F G

12. A B C D E F G 0 1 2 3 4 5 6 7 Solution First, determine the lengths for each segment. AC = 2 AG = 6 CD = 1

13. COMPARE RATIOS: AC to AG is 2 to 6 First, set up a proportion

14. Solving the proportion CD x AC AG Cross multiply: so 2x = 6, divide both sides by 2, x = 3

15. Answer • AD measure is 3 • BD measure is 2 • CG measure is 4 • DF measure is 1 • EG measure is 2

16. 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.

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

18. Squares and Square Roots

19. 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.

20. 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.

21. 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.

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

23. Getting a common denominator For 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.

24. Step by step 9 times 3 is 27 and 2 times 7 is 14. add 27 and 14. 27 +14 = 41 is the answer. Reduce fraction if possible.

25. Subtracting Fractions Subtracting fractions works exactly the same as adding them.

26. Squaring Fractions Remember - 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. One way:

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

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

29. 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.

30. 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.

31. Vocabulary List 1 ambiguous- vague, more than one interpretation assertion- a statement or declaration disdain– contempt; scorn excerpt- a selected portion of a passage frank- to the point, candid, straightforward frenetic- very active or wildly excited

32. 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

33. ambiguous- vague, more than one interpretation The concluding paragraph in the student’s essay was quite ambiguous; it left the reader confused.

34. assertion- a statement or declaration The politician made his final assertion regarding the city’s budget proposal.

35. disdain– contempt; scorn Mark had a look of disdain on his face as he was being reprimanded.

36. excerpt- a selected portion of a passage The teacher instructed her students to read an excerpt from Anne Frank’s Diary.

37. frank- to the point, candid, straightforward To be perfectly frank, your performance on the job has been below average.

38. frenetic- very active or wildly excited Carla and Jose celebrated raised the 1st place trophy at a frenetic pace.

39. 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.

40. medieval- old-fashioned, belonging to the Middle Ages The costumes for the show, “The Knight’s Rise”, were medieval.

41. nocturnal- occurring at night; describes animals that are active at night Raccoons are considered to be nocturnal.

42. 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.

43. 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.

44. Sentence Completions Sentence completions are at the beginning of every critical reading section. You can expect between 5 and 8 questions of this type.

45. 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.

46. Sentence Completions continued… There are 2 types of sentence completions. They are: vocabulary in context and logic based

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

48. Logic-based Vocabulary To 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?

49. Sentence Completions continued… We will explore those key words as we work through example questions.

50. 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.