The New SAT ® Important Information for High School Math Teachers

3The New SAT: Important Information for High School Math Teachers, June 2004 The New SAT Focuses on College Success ™ Skills Critical Reading Mathematics Writing The SAT ® tests students’ reasoning based on knowledge and skills developed through their course work. It measures their ability to analyze and solve problems by applying what they have learned in school.

4The New SAT: Important Information for High School Math Teachers, June 2004 Time Frame October 2004: New PSAT/NMSQT ® March 2005: New SAT

5The New SAT: Important Information for High School Math Teachers, June 2004 Time Frame Class of 2006 will take new SAT Class of 2005—current seniors Current SAT as seniors in fall 2004 New SAT as seniors in March 2005 (if necessary) Class of 2006—current juniors New PSAT/NMSQT as juniors in fall 2004 New SAT as juniors in March 2005 and later New SAT as seniors

6The New SAT: Important Information for High School Math Teachers, June 2004 Has the SAT Ever Changed Before? Yes, the SAT has changed several times since it was first administered in The SAT evolves to meet the changing needs of students, teachers, and colleges. The most recent changes were made in (Adding writing to the SAT was recommended but not possible in 1994 due to inadequate technology and lack of large number of readers needed.)

7The New SAT: Important Information for High School Math Teachers, June 2004 Why Is the SAT Changing? To better reflect today’s classroom practices and curriculum by replacing analogies with short reading passages and quantitative comparisons with more math problems, some including content from third-year college-preparatory math To reinforce the importance of writing skills To help colleges make better admissions and placement decisions

8The New SAT: Important Information for High School Math Teachers, June 2004 Will the New SAT Be Harder? No, the new SAT will be designed so that a student who could score a 500 on the math section (for example) of the current SAT could score a 500 on the math section of the new test. 97% of college-bound students complete 3 years of math so the test will more closely measure the math they are already studying. Extensive field trials confirmed that students are taking more upper level math, which is why the overall difficulty of the test is not affected. While the test is longer, field trials also confirmed that the increased length of the test has no impact on the students’ scores.

9The New SAT: Important Information for High School Math Teachers, June 2004 The Changes to the SAT and the PSAT/NMSQT ® Verbal Name will be changed to critical reading. Analogies will be eliminated. Short reading passages will replace analogies and will measure the kind of reasoning formerly measured by analogies.

10The New SAT: Important Information for High School Math Teachers, June 2004 The Changes to the SAT and the PSAT/NMSQT Math Quantitative comparisons will be eliminated The content is being expanded to reflect the mathematics that college-bound students typically learn during their first three years of high school. The reasoning aspects of the test together with the expanded content will more effectively assess the mathematics necessary for student success in college. Math content on the PSAT/NMSQT will also be enhanced, but it will not include Algebra II because most students will not be familiar with that level of math.

11The New SAT: Important Information for High School Math Teachers, June The Changes to the SAT and the PSAT/NMSQT Quantitative comparisons will be ELIMINATED Column AColumn B x=0 x+1 x–1 (A)The quantity in column A is greater (B)The quantity in column B is greater (C)The two quantities are equal (D)The relationship cannot be determined from the information given Correct Answer: B

12The New SAT: Important Information for High School Math Teachers, June 2004 The Changes to the SAT and the PSAT/NMSQT Writing Multiple-choice grammar and usage questions Will measure the student’s understanding of how to use language in a clear, consistent manner, how to revise and edit, and how to recognize an error in a sentence. Student-written essay (SAT only) Will measure the student’s use of language: logical presentation of ideas, development of a point of view, and clarity of expression under timed conditions. Essay practice tool provided AT NO COST to all schools administering the PSAT/NMSQT.

13The New SAT: Important Information for High School Math Teachers, June 2004 The Changes to the SAT and the PSAT/NMSQT Skills Feedback The PSAT/NMSQT provides individualized feedback to students through its Score Report Plus. The College Board is developing a similar tool for the SAT.

Skills Feedback Score Report Plus 14

15The New SAT: Important Information for High School Math Teachers, June 2004 PSAT/NMSQT Score Report Plus Tells students how their scores compare with those of other sophomores or juniors Tells students what SAT score ranges they can expect Includes a question-by-question breakdown Helps students identify strengths and weaknesses and provides tips on how to improve specific skills

16The New SAT: Important Information for High School Math Teachers, June 2004 PSAT/NMSQT Score Report Plus New in 2004 Students will use their Score Report Plus code to access free enhancements online at Complete explanations for all answers, including why some answers were wrong. Full explanations of answers for additional higher-level math practice SAT questions on the back of the PSAT/NMSQT score report. Entire SAT essay scoring guide, plus actual sample essay papers at every score point for the practice essay on the back of the PSAT/NMSQT score report.

17The New SAT: Important Information for High School Math Teachers, June 2004 Skills Feedback Score Report Plus Improve Your Skills—Examples Being precise and clear How to improve: Learn to recognize sentence elements that are ambiguous and confusing. In your writing, choose words carefully and connect them for clear meaning. See questions 4, 6, 8. Understanding geometry and coordinate geometry How to improve: Review geometry units in your textbook involving perimeter, area, volume, circumference, angles, lines, slope. Familiarize yourself with the formulas given at the beginning of math sections of the set. See questions 7, 13, 19.

18The New SAT: Important Information for High School Math Teachers, June 2004 Time Specifications PSAT/NMSQT Current PSAT/NMSQTNew PSAT/NMSQT 2 hours 10 minutes Critical Reading 50 minutes Two 25-minute sections 50 minutes Two 25-minute sections Math 50 minutes Two 25-minute sections 50 minutes Two 25-minute sections Writing 30 minutes One 30-minute multiple-choice section 30 minutes One 30-minute multiple-choice section

19The New SAT: Important Information for High School Math Teachers, June 2004 Current SATNew SAT 3 hours3 hours 45 minutes Critical Reading 75 minutes Two 30-minute sections and one 15-minute section 70 minutes Two 25-minute sections and one 20-minute section Math 75 minutes Two 30-minute sections and one 15-minute section 70 minutes Two 25-minute sections and one 20-minute section Writing 60 minutes Two multiple-choice sections (one 25-minute section and one 10-minute section) and one 25-minute essay Variable Section30 minutes25 minutes Time Specifications SAT

20The New SAT: Important Information for High School Math Teachers, June 2004 Test Content and Question Types Current SATNew SAT Critical Reading Sentence Completion Critical Reading: Long reading passages Analogies Sentence Completion Critical Reading: short and long reading passages Math Multiple-choice items, student-produced responses, and quantitative comparisons measuring: Number and Operations; Algebra I and Functions; Geometry; and Statistics, Probability, and Data Analysis. Multiple-choice items and student-produced responses measuring: Number and Operations; Algebra I, II, and Functions; Geometry; and Statistics, Probability, and Data Analysis. Writing Multiple-choice items: Improving sentences and paragraphs, and identifying sentence errors. Student-written essay: Effectively communicate a point of view on an issue, supporting a position with reasoning and examples.

21The New SAT: Important Information for High School Math Teachers, June 2004 Current SATNew SAT Critical ReadingV 200–800CR 200–800 MathM 200–800 Writing (Subscores) W 200–800 Will include 2 subscores: Essay 2–12 (1/3 of writing score) Multiple-choice 20–80 (2/3 of writing score) Test Scores

22The New SAT: Important Information for High School Math Teachers, June 2004 The New SAT Field Trial Field trial was conducted in March 2003 to determine the impact of changes to the SAT and PSAT/NMSQT. More than 45,000 students from 680 high schools participated. Students were representative of SAT-takers and PSAT/NMSQT-takers. Students from underrepresented populations were oversampled.

23The New SAT: Important Information for High School Math Teachers, June 2004 The New SAT Field Trial Based on field trial results, the College Board expects that: Changes to the math and verbal sections will not affect the difficulty or reliability of the test. Performance differences by subgroups (by race/ethnicity and gender) on the new SAT will not be exacerbated. The relative differences in scores for underrepresented students will not increase due to any of the changes implemented with the new SAT. The score scales for math and critical reading on the new SAT will be comparable to the score scales on the math and verbal sections of the current SAT. The longitudinal data will be maintained. For example, a 600 on the new critical reading section will be equivalent to a 600 on the current verbal section, and a 580 on the new math section will be equivalent to a 580 on the current math section.

A Closer Look at the Math Section of the New SAT

25The New SAT: Important Information for High School Math Teachers, June 2004 Math Section Measures problem-solving skills Emphasis on math reasoning: SAT math measures the ability to apply math content to real-life problems. The SAT is unique in having some “grid-in” questions requiring student-produced responses—as recommended by NCTM (National Council of Teachers of Mathematics). Approximately 15–20% of math questions on the new SAT and 15% of math questions on the new PSAT/NMSQT will either cover new topics or will cover existing topics in greater depth.

26The New SAT: Important Information for High School Math Teachers, June 2004 Most Four-Year Colleges Require 3 Years of Math for Admission 70% of all high school students finish Algebra II 97% of college-bound students complete 3 years of math and 69% complete 4 or more years of math 92% of minority college-bound students complete 3 years of math

27The New SAT: Important Information for High School Math Teachers, June 2004 Calculator Policy A scientific or graphing calculator will be recommended for the new tests. Though every question can still be answered without a calculator, calculators are definitely encouraged. Previously, a basic 4-function calculator was recommended, but now scientific is the base level recommendation. Students should bring a calculator with which they are comfortable and familiar.

28The New SAT: Important Information for High School Math Teachers, June 2004 Calculator Policy The following are not permitted: Powerbooks and portable/handheld computers Electronic writing pads or pen-input/stylus-driven (e.g., Palm, PDAs, Casio ClassPad 300) Pocket organizers Models with QWERTY (i.e., typewriter) keyboards (e.g., TI-92 Plus, Voyage 200) Models with paper tapes Models that make noise or “talk” Models that require an electrical outlet Cell phone calculators

Enhanced Math Section Number and Operations

30The New SAT: Important Information for High School Math Teachers, June 2004 t 8 The Enhanced Math Section Number and Operations Sequences involving exponential growth Questions that require knowledge of exponential growth or geometric sequences. Example: 7, 21, 63, 189, … is a geometric sequence that has constant ratio 3 and begins with the term 7. The term obtained after multiplying n times by 3 is 7 x 3 n Since these sequences have real-life applications, questions might be presented in contexts such as population growth. Example: a population that initially numbers 100 and grows by doubling every eight years. The expression 100 x 2 would give the population t years after it begins to grow.

31The New SAT: Important Information for High School Math Teachers, June 2004 The Enhanced Math Section Number and Operations Sets (union, intersection, elements) Questions might ask about the union of two sets (i.e., the set consisting of elements that are in either set or both sets) or the intersection of two sets (i.e., the set of common elements). Example: If set X is the set of positive even integers and set Y is the set of positive odd integers, a question might ask students to recognize that the union of the two sets is the set of all positive integers.

Enhanced Math Section Algebra and Functions

33The New SAT: Important Information for High School Math Teachers, June 2004 Absolute Value Students should be familiar with both the concept and notation of absolute value and be able to work with expressions, equations, and functions that involve absolute value. Rational Equations and Inequalities Example:. Equations or inequalities involving such expressions will be included on the new SAT Radical Equations Example: Enhanced Math Section Algebra and Functions

34The New SAT: Important Information for High School Math Teachers, June 2004 Integer and Rational Exponents On the current SAT, exponents are restricted to positive integers. The new SAT will have expressions such as z -3 involving negative exponents. There will also be expressions such as m where the exponent is a rational number. 3 4 Enhanced Math Section Algebra and Functions

35The New SAT: Important Information for High School Math Teachers, June 2004 Integer and Rational Exponents–Sample Problem If x -3 =64, what is the value of x ? (A) (B) (C)4 (D)8 (E)16 Correct Answer: B What’s new about this question? The current SAT has questions involving positive integer exponents. The new SAT will have expressions involving negative exponents, such as x -3, and fractional exponents, such as x Enhanced Math Section Algebra and Functions

36The New SAT: Important Information for High School Math Teachers, June 2004 Direct and Inverse Variation Questions involving quantities that are directly proportional to each other. The quantities x and y are directly proportional if y= kx, for some constant k. They are said to be inversely proportional if y= for some constant k k x Enhanced Math Section Algebra and Functions

37The New SAT: Important Information for High School Math Teachers, June 2004 Enhanced Math Section Algebra and Functions Function Notation Students should be familiar with both the concept of a function and with function notation. Example: If the function f is defined by f(x) = x + 2 x, students should know that f(5) = = 37.

38The New SAT: Important Information for High School Math Teachers, June 2004 Function Notation–Sample Problem If f is a linear function and if f(6)=7 and f(8)=12, what is the slope of the graph of f in the xy-plane. Correct Answer: or 2.5 What’s new about this question? The new element in this question is the use of the notation f(x) to refer to the function. 5 2 Enhanced Math Section Algebra and Functions

39The New SAT: Important Information for High School Math Teachers, June 2004 Enhanced Math Section Algebra and Functions Concepts of Domain and Range The new SAT will include questions that ask about values of x at which a particular function is not defined (outside the domain), or values that f(x) cannot equal (outside the range). Functions as Models The new SAT will include questions that involve mathematical models of real-life situations. A question might present information about the projected sales of a product at various prices and ask for a mathematical model in the form of a graph or equation that represents projected sales as a function of price.

40The New SAT: Important Information for High School Math Teachers, June 2004 Enhanced Math Section Algebra and Functions Linear Functions–Equations and Graphs The new SAT will include questions involving linear equations, such as y=mx+b, where m and b are constants. Some questions may involve graphs of linear functions

41The New SAT: Important Information for High School Math Teachers, June 2004 Linear Functions–Equations and Graphs– Sample Problem In the figure above, if line k has a slope of -1, what is the y-intercept of k? (A)6 (B)7 (C)8 (D)9 (E)10 Correct Answer: B What’s new about this question? The use of the term “y-intercept.” Enhanced Math Section Algebra and Functions Note: Figure not drawn to scale

42The New SAT: Important Information for High School Math Teachers, June 2004 Enhanced Math Section Algebra and Functions Quadratic Functions– Equations and Graphs Questions involving quadratic equations and/or their graphs may appear on the new SAT. For example, a question might involve comparing the graphs of y=2x 2 and y=2(x-1) 2.

Enhanced Math Section Geometry and Measurement

44The New SAT: Important Information for High School Math Teachers, June 2004 Geometric Notation for Length, Segments, Lines, Rays, and Congruence Geometric notation such as and will be used. The term “congruent” and the congruence symbol will be used. Enhanced Math Section Geometry and Measurement

45The New SAT: Important Information for High School Math Teachers, June 2004 Problems in which trigonometry may be used as an alternative method of solution The new SAT will include more questions that rely on the special properties of triangles or triangles. Example: In the triangle below, the value of x can be found by using trigonometry (sin 30 o =. But the value of x can also be determined with the knowledge that in a triangle, the leg opposite the 30-degree angle is half as long as the hypotenuse. x 12 Enhanced Math Section Geometry and Measurement

46The New SAT: Important Information for High School Math Teachers, June 2004 Properties of Tangent Lines Questions on the new SAT may require knowledge of the property that a line tangent to a circle is perpendicular to a radius drawn to the point of tangency, as illustrated below. Enhanced Math Section Geometry and Measurement

47The New SAT: Important Information for High School Math Teachers, June 2004 Enhanced Math Section Geometry and Measurement Coordinate Geometry Some questions on the new SAT may require knowledge of the properties of the slopes of parallel or perpendicular lines. Some questions may require students to find the equations of lines, midpoints of line segments, or distance between two points in the coordinate plane.

48The New SAT: Important Information for High School Math Teachers, June 2004 Qualitative Behavior of Graphs and Functions A question on the new SAT might show the graph of a function in the xy-coordinate plane and ask students to give (for portion of graph shown) the number of values of x for which f(x)=3. Correct Answer: 4 Enhanced Math Section Geometry and Measurement

49The New SAT: Important Information for High School Math Teachers, June 2004 Enhanced Math Section Geometry and Measurement Transformations and Their Effect on Graphs of Functions The new SAT will include questions that ask students to determine the effect of simple transformation on graphs of functions. Example: Graph of function f(x) could be given and students would be asked questions about the graph of function f(x+2).

Enhanced Math Section Data Analysis, Statistics, and Probability

51The New SAT: Important Information for High School Math Teachers, June 2004 Enhanced Math Section Data Analysis, Statistics, and Probability Data Interpretation, Scatterplots, and Matrices A question on the new SAT might ask about the line of best fit for a scatterplot. Students would be expected to identify the general characteristics of the line of best fit by looking at the scatterplot. Students would not be expected to use formal methods of finding the equation of the line of best fit. Students will be expected to interpret data displayed in tables, charts, and graphs.

52The New SAT: Important Information for High School Math Teachers, June 2004 A science class bought 20 different batteries of various brands and prices. They tested each battery’s duration by seeing how long it would keep a motor running before losing power. For each battery, the class plotted the duration against the price, as shown above. Of the 5 labeled points, which one corresponds to the battery that cost the least amount per hour of duration? (A)A (B)B (C)C (D)D (E)E Correct Answer: C What’s new about this question? The new SAT will have more questions involving scatterplots and proportional reasoning, of which this question is an example. Enhanced Math Section Data Analysis, Statistics, and Probability Data Interpretation, Scatterplots, and Matrices–Sample Problem A. B. C.C. D. E.

53The New SAT: Important Information for High School Math Teachers, June 2004 Enhanced Math Section Data Analysis, Statistics, and Probability Geometric Probability Example: If a point is to be chosen at random from the interior of a region, part of which is shaded, students might be asked to find the probability that the point chosen will be from the shaded portion.

54The New SAT: Important Information for High School Math Teachers, June 2004 Colleges Requiring a Standardized Writing Test Colleges that accept the SAT will continue to do so, and all will receive the writing score. Many colleges have announced that they will require or recommend that students taking any college admissions exam must submit a writing score (including an essay) beginning with those entering college in the fall of 2006.

55The New SAT: Important Information for High School Math Teachers, June 2004 Additional Research on the New SAT Survey of Admissions Directors A recent College Board sampling of 774 four-year colleges indicates that 59 percent of the institutions sampled will use the writing score for admissions and another 31 percent are still considering its use. The colleges varied by admissions selectivity and size, and represented a good cross-section of higher education institutions.

56The New SAT: Important Information for High School Math Teachers, June 2004 Additional Research on the New SAT Survey of Admissions Directors The findings: 74 percent of respondents say they will use the new SAT writing score in admissions decisions. 68 percent of respondents plan to download and print applicants’ essays. 35 percent of these respondents said they would read all essays and 19 percent said they would read most essays. 32 percent of respondents will use the essay for course placement.

57The New SAT: Important Information for High School Math Teachers, June 2004 Additional Research on the New SAT Survey of Admissions Directors The reasons most often cited by those respondents saying that they plan to read applicants’ essays were: To provide additional information about a candidate’s writing skills To compare and verify an application essay To use as an additional placement essay

58The New SAT: Important Information for High School Math Teachers, June 2004 Additional Information about the SAT Subject Tests January 2005: The SAT Subject Test in Writing will be administered for the last time All other SAT Subject Tests will continue, including Math I and Math II

59The New SAT: Important Information for High School Math Teachers, June 2004 How Students Can Prepare Students should: Challenge themselves throughout high school by taking rigorous courses, including at least three years of math Read and write as much as possible—both in and outside of school Familiarize themselves with the SAT so they know what to expect on test day Familiarize themselves with the different types of questions on the SAT, the directions for each type of question, and how the test is scored Take the new PSAT/NMSQT in October 2004–the new PSAT/NMSQT will be the best preparation for the new SAT

60The New SAT: Important Information for High School Math Teachers, June 2004 How Students Can Prepare Availability of Sample Questions The PSAT/NMSQT Student Bulletin, the free booklet that includes a full-length practice test, will be available early fall The 2004 PSAT/NMSQT Score Report Plus will be sent to schools in December 2004 and will include explanations for every question (available online to any student who takes the PSAT/NMSQT in 2004). The 2004 PSAT/NMSQT Score Report Plus mailing will include advanced math sample questions. The new SAT Preparation Booklet ™, (the successor to Taking the SAT), the free booklet that includes a full-length practice test, will be available in fall 2004.

61The New SAT: Important Information for High School Math Teachers, June 2004 How Students Can Prepare Availability of Sample Questions The Official SAT Study Guide: For the New SAT ™, will be available in fall The Official SAT Online Course ™, the successor to One-on-One with the SAT ®, will be available in fall The online SAT Learning Center ® at will include new SAT sample questions beginning in fall 2004.

62The New SAT: Important Information for High School Math Teachers, June

63The New SAT: Important Information for High School Math Teachers, June