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® The SAT Suite of Assessments Self-guided Course 5 Math That Matters Most: Passport to Advanced Math Additional Topics in Math Self-guided Courses for the SAT Suite of Assessments Course 1 Key Features Course 2 Words in Context and Command of Evidence Course 3 Expression of Ideas and Standard English Conventions Course 4 Math that Matters Most Heart of Algebra Problem Solving and Data Analysis Course 5 Math that Matters Most Passport to Advanced Math Additional Topics in Math Course 6 The SAT Suite of Assessments: Using Scores and Reporting to Inform Instruction Course 7 Connecting History/Social Studies Instruction with the SAT Suite of Assessments Course 8 Connecting Science Instruction with the SAT Suite of Assessments Course 9 The SAT Essay Course 10 Supporting Students with Official SAT Practice on Khan Academy 4 What Is the Purpose of Course 5? Chapter 1 Score Reporting on the SAT Suite of Assessments Longitudinal Progress Monitoring Section Scores are placed on a vertical scale. SAT (200–800) PSAT 10 & PSAT/NMSQT (160–760) PSAT 8/9 (120–720) 100 200 300 400 500 600 700 800 The same concept holds true for the Test, Cross-Test Scores, and Total Score. SAT (10–40) SAT (400–1600) PSAT 10 & PSAT/NMSQT (320–1520) PSAT 10 & PSAT/NMSQT (8–38) PSAT 8/9 (6–36) 6 10 15 20 25 PSAT 8/9 (240–1440) 30 35 40 200 400 600 800 1000 1200 1400 1600 9 Overview of the SAT Math Test Chapter 2 Math Test Information • The overall aim of the SAT Math Test is to assess fluency with, understanding of, and ability to apply the mathematical concepts that are the prerequisites for, and are useful across, a wide range of college majors and careers. • The SAT Math Test has two portions: - Calculator Portion (38 questions) -55 minutes - No-Calculator Portion (20 questions) - 25 minutes • Total Questions on the SAT Math Test: 58 questions - Multiple Choice (45 questions) - Student-Produced Response (13 questions) 11 Calculator and No-Calculator Portions • The Calculator portion: - Provides insight into students’ capacity to use appropriate tools strategically. - Includes more complex modeling and reasoning questions to allow students to make computations more efficiently. - Includes questions in which the calculator could be a deterrent to expedience. • Students who make use of structure or their ability to reason will reach the solution more rapidly than students who get bogged down using a calculator. • The No-Calculator portion: - Allows the SAT Suite to assess fluencies valued by postsecondary instructors and includes conceptual questions for which a calculator won’t be helpful. Student-Produced Response Questions Student-produced response questions or grid-ins: • The answer to each student-produced response question is a number (fraction, decimal, or positive integer) that will be entered on the answer sheet into a grid such as the one shown at the left. • Students may also enter a fraction line or a decimal point. 13 Math Test Specifications Question Types Total Questions Multiple Choice Student-Produced Response SAT 58 45 13 PSAT/NMSQT and PSAT 10 48 40 8 PSAT 8/9 38 31 7 16 16 14 2 16 16 6 0 7 7 6 6 Contribution of Questions to Subscores Heart of Algebra Problem Solving and Data Analysis Passport to Advanced Math Additional Topics in Math* 19 17 16 6 Contribution of Questions to Cross-Test Scores Analysis in Science 8 Analysis in History/Social Studies 8 *Questions under Additional Topics in Math contribute to the total Math Test score but don’t contribute to a subscore within the Math Test. 14 Math Test Domains Four Math Domains: 1. Heart of Algebra a. Linear equations b. Fluency 2. Problem Solving and Data Analysis a. Ratios, rates, proportions b. Interpreting and synthesizing data 3. Passport to Advanced Math a. Quadratic, exponential functions Module 5 b. Procedural skill and fluency 4. Additional Topics in Math a. Essential geometric and trigonometric concepts 15 Math Test Domains Activity 1.Which domains are included in the current curriculum and pacing guides? In which course(s)? 2.Which domains need to be added to the curriculum? 3.In which areas will students be well-prepared? 4.In which areas will students struggle? 18 How Does the SAT Suite Relate to Instruction in Science and History/Social Studies Courses? • Cross-test scores include scores for Analysis in Science and Analysis in History/Social Studies, derived from questions on all three tests. - Some passages used for analysis on the Reading Test and the Writing and Language Test have foundations in science and history/social studies. - One passage used on the Reading Test will be a U.S. founding document or from the Great Global Conversation. - Tables, graphs, and data accompanying some passages relate to topics in science and/or history/social studies. - Some math questions will have science or social science contexts. 19 Passport to Advanced Math Chapter 3 What is “Passport to Advanced Math”? • Problems in Passport to Advanced Math cover topics that have great relevance and utility for college and career work. - Understand the structure of expressions - Analyze, manipulate, and rewrite expressions - Be able to reason with more complex equations - Interpret and build functions 21 Passport to Advanced Math: Assessed Skills • Create and solve quadratic and exponential problems • Create and solve radical and rational equations • Solve systems of equations • Understand the relationship between zeros and factors of polynomials 22 Passport to Advanced Math: Sample Question The function f is defined by f (x) = 2x³ + 3x² + cx + 8, where c is a constant. In the xy-plane, the graph of f intersects the x-axis at the 1 three points (−4, 0), ( , 0 ), and (p, 0). What is the value of c? 2 A) –18 B) –2 C) 2 D) 10 23 Passport to Advanced Math : Answer Explanation Choice A is correct. The given zeros can be used to set up an equation to solve for c. Substituting –4 for x and 0 for y yields –4c = 72, or c = –18. 1 Alternatively, since –4, 2, and p are zeros of the polynomial function f (x) = 2x³ + 3x² + cx + 8, it follows that f (x) = (2x − 1)(x + 4)(x − p). Were this polynomial multiplied out, the constant term would be (−1)(4)(− p) = 4 p. (We can see this without performing the full expansion.) Since it is given that this value is 8, it goes that 4p = 8 or rather, p = 2. Substituting 2 for p in the polynomial function yields f (x) = (2x − 1)(x + 4)(x − 2), And, after multiplying the factors, one finds that the coefficient of the x term, or the value of c, is –18. 24 Additional Topics in Math Chapter 4 What Is “Additional Topics in Math”? The SAT requires the geometric and trigonometric knowledge that’s the most relevant to postsecondary education and careers. • Geometry - Analysis - Problem Solving • Trigonometry - Sine - Cosine - Tangent • Pythagorean Theorem 26 Additional Topics in Math: Assessed Skills • Solve problems using volume formulas • Solve problems involving right triangles • Apply theorems about circles • Solve problems about lines, angles, and triangles 27 Additional Topics in Math: Sample Question (Calculator) An architect drew the sketch below while designing a house roof. The dimensions shown are for the interior of the triangle. What is the value of cos x? NOTE: This is a “student-produced response question,” which asks the students to write in the correct answer rather than selecting one of the given answers. About 20% of the Math Test will be student-produced response questions. 28 Additional Topics in Math: Answer Explanation What is the value of cos x? This problem requires students to make use of properties of triangles to solve a problem. Because the triangle is isosceles, constructing a perpendicular from the top vertex to the opposite side will bisect the base and create two smaller right triangles. In a right triangle, the cosine of an acute angle is equal to the length of the side adjacent to the angle divided by the length of the hypotenuse. 16 This gives cos x = 24, which can be simplified to 2 cos x = 3. 29 Connecting the Math Test with Classroom Instruction Chapter 5 General Instructional Strategies for the Math Test • Ensure that students practice solving multistep problems. • Organize students into small working groups. Ask them to discuss how to arrive at solutions. • Assign students math problems or create classroom-based assessments that don’t allow the use of a calculator. • Encourage students to express quantitative relationships in meaningful words and sentences to support their arguments and conjectures. • Instead of choosing a correct answer from a list of options, ask students to solve problems and enter their answers in grids provided on an answer sheet on your classroom and common assessments. 31 Brainstorming Instructional Strategies Activity What strategies do you currently use to support the development of skills related to Passport to Advanced Math and Additional Topics in Math? 32 Additional Skill-Building Strategies • Provide students with explanations and/or equations that incorrectly describe a graph and ask them to correct the errors. • Ask students to create pictures, tables, graphs, lists, models, and/or verbal expressions to interpret text and/or data to help them arrive at a solution. • Organize students in small groups and have them work together to solve problems. • Use “Guess and Check” to explore different ways to solve a problem when other strategies for solving aren’t obvious. 33 Scores and Reporting Chapter 6 34 K-12 Assessment Reporting Tool • Accesses a wide array of standard reports. • Provides benchmarks and consistent feedback to help teachers encourage and accelerate students over time. • Allows educators to drill down to the student level. • Can be configured to create personalized reports Filter by student-provided information Create reporting groups based on user criteria 35 K-12 Score Reporting Portal Access through College Board Account 37 Valuable Data in Linked Reports Deliver complementary reports together Institutional Reports: • Scores by Institution • Benchmarks by Institution • Essay Scores by Institution (where applicable) Three Tab Design Instructional Planning: Focus Improvement Efforts Note: All data is illustrative 38 Question Analysis Report Understand Student Achievement at a Detailed Level Note: All data is illustrative 39 Self-Assessment/ Reflection • How well do you teach students skills related to Passport to Advanced Math? • How well do you teach students skills related to Additional Topics in Math? • What can you do in your classroom immediately to help students understand what they’ll see on the assessments in the SAT Suite? • Which long-term adjustments can you make to support students in developing their mastery of Passport to Advanced Math and Additional Topics in Math? • Which additional resources do you need to gather in order to support students in becoming college and career ready? • How can you help students keep track of their own progress toward meeting the college and career ready benchmark? 40 Questions or Comments About This Presentation or the SAT Suite of Assessments? • Email: [email protected] 41 Exit Survey https://www.surveymonkey.com/s/PD_Module_5 42