Kaplan Advantage: SAT Mathematics 1

2 Warm-Up: Math If r is an even integer and s is an odd integer, which of the following must be true? I. r(r + s) is even II.s 2 – r is odd III.3r + 2s is odd (A) None (B) I and II only (C) I and III only (D) II and III only (E) I, II, and III

3 It’s not what students know— it’s what they show! Knowledge Performance

What causes the gap? Pieces of the Puzzle A broad range of content High stakes No partial credit on multiple choice Rigidly timed 4

5 How do we bridge that gap? Knowledge Performance

6 Know the CONTENT Know the TEST Know the STRATEGIES instruction of concepts and skills application of content knowledge to the test Foundations of Test Readiness

7 Agenda I.Understanding the SAT II.Program Structure A.Student Introduction B.Assessments C.Appendix D.Lesson Structure III.Critical Thinking for Test Readiness A.The 4-Step Method for Problem Solving B.Test-Taking Strategies

8 SAT Format SectionsTimingQuestion Type and (#) Critical Reading Two 25-min. sections Sentence Completions (19) Reading Comprehension (48) One 20-min. section Mathematics Two 25-min. sections Multiple-Choice (44) Grid-ins (10) One 20-min. section Writing One 25-min. section Identifying Sentence Errors (18) Improving Sentences (25) Improving Paragraphs (6) One 10-min. section One 25-min. essay ExperimentalOne 25-min. section Questions assess either Critical Reading, Math, or Writing Does not count toward score

9 Test Order SAT Section #TimeContent 125 min.Essay min. Critical Reading, Writing, Mathematics, and Experimental min. Critical Reading, Mathematics 1010 min.Writing

10 How the SAT is Scored Raw Score Students receive 1 point for every correct answer. For every incorrect answer to a MC question, they lose 1/4 point. There is no guessing penalty for grid-in questions. Scaled Score Each section is scored (Critical Reading, Writing, Mathematics) The maximum score is The average score is 1500.

11 Guessing: Can it work? What happens if a student guesses on five questions? Result: no gain, no loss. But if we could eliminate a few answers each time…

12 The SAT is Standardized norm-referenced vs. criterion-referenced

13 The Bell Curve

14 Sample SAT Problems Turn to page 3 in your session guide. Complete the sample SAT mathematics problems.

15 Program Organization: Mathematics Each lesson can be delivered in minutes. Student Introduction Provides a brief introduction to the SAT and to the Advantage SAT program Unit 1The 4-Step Method for Problem Solving Unit 2Number and Operations MPTNumber and Operations Mini Practice Test Unit 3Expressions and Functions Unit 4Equations and Inequalities MPTAlgebra Mini Practice Test Unit 5Geometry and Measurement Unit 6Probability, Statistics, and Data Analysis MPTGeometry and Data Mini Practice Test AppendixSAT Math in a Nutshell

16 Student Introduction

17 Assessments TypeBasicsTiming Mini Practice Test 3 tests Allows students to apply strategies they have just learned to SAT-like questions 25 min. each Full- Length Practice Test Provides students with a test-like experience in terms of content and length 70 min.

18 This slide is intentionally hidden to allow for presenter’s notes.

19 Appendix: SAT Math in a Nutshell Overview p. A1 Appendix teaching suggestions SmartPoints p. A3 Ranks most frequently tested skills Content pp. A4-A19 Content summarizing sections

20 Unit Introduction Objectives identified for each lesson in the unit Explanations of strategies students will learn

21 Advantage SAT: Lesson Structure PROGRAM COMPONENT DESCRIPTION APPROX. TIME Thinking KAP Each lesson begins with a brief warm-up activity. 4 Min. Instruction Students learn new strategies and practice them with feedback from the teacher. 24 Min. Independent Practice Students practice applying the strategies on their own and then review their work. 12 Min. KAP Wrap Students reflect on what they have learned in the lesson. 5 Min.

22 Thinking KAP

23 Instruction

24 Student Supports Provides helpful information about the SAT Hints that support working with the content Opportunity to apply strategies

25 Independent Practice 6-8 questions in each section Hints provided for each question

26 Reviewing Independent Practice As Students Work: Redirect students as needed by asking effective questions. To Review: Focus on students’ solutions, not their answers. Look out for classic traps.

27 KAP Wrap Purpose: To apply, review, and reflect on strategies Complete: For homework, for a journal entry, with a partner, or alone

28 Instructional Support Teacher’s Notes provide tips from mentor teachers. Hazard symbols alert you to common student errors. Content Background boxes provide content tips as needed.

29 Activity: Teacher and Student Roles In each section of the lesson, what does the teacher do? What does the student do? What would you do differently?

30 Unit 2, Lesson 1 Thinking KAP, session guide page 17 Instruction, session guide pages Independent Practice, session guide pages KAP Wrap, session guide page 24

31 NEXT Critical Thinking: Knowing what to do NEXT! But how do we teach it?

32 Kaplan’s programs meet the challenges with two key approaches: 2. A toolbox of strategies 1. An approach for every question type Step 1. Step 2. Step 3. Step 4. Meeting the Challenges

33 Systematic Thinking: The 4-Step Method for Problem Solving S TEP 1: Understand the problem. S TEP 2: Analyze important information. S TEP 3: Plan and solve. S TEP 4: Check your work. This method… standardizes the language of problem solving. helps teachers model “expert” problem solving. provides students with a systematic approach.

34 Using the 4-Step Method Mark buys a set of 3 tennis balls. The tennis balls are packaged in a cylindrical container. The container has a height of 10 inches and the top of the container has a diameter of 6 inches. How much space is inside the container? A 30 cubic inches B 60 cubic inches C 60  cubic inches D 90  cubic inches

35 STEP 1: Understand the problem.  Scan the problem; what is it basically about? This problem is about the volume of a cylinder.  Restate the question in your own words. What is the volume of a cylinder with a height of 10 inches and a diameter of 6 inches? Mark buys a set of 3 tennis balls. The tennis balls are packaged in a cylindrical container. The container has a height of 10 inches and the top of the container has a diameter of 6 inches. How much space is inside the container?

36 STEP 2: Analyze important information. Underline the clues. Rewrite the important information in a helpful way. I can draw it. 10 in. 6 in. 3 in. Mark buys a set of 3 tennis balls. The tennis balls are packaged in a cylindrical container. The container has a height of 10 inches and the top of the container has a diameter of 6 inches. How much space is inside the container?

37 STEP 3: Plan and solve. My work: V  r 2 h  (3) 2 (10)  (9)(10)  90  in 2 What do you KNOW? What do you NEED? How can you use what you KNOW to find what you NEED? I know the dimensions of the cylinder. I need to figure out the volume of the canister. I will use the formula V  r 2 h and substitute the correct values.

38 STEP 4: Check your work.  Is your answer reasonable? Yes. 90  is about 270. That’s a reasonable volume.  Can you solve the problem another way? Yes, I can use a chart instead. FormulaValues  d6 r3 r2r2 9 h10 V  r 2 hV   (9)(10)  90   Did you answer the right question? Yes, I figured out the volume of the cylinder.

39 Try It Out! The Environmental Club receives a certain amount of money from the school to host a teach-in. They budget 40% of the funds for a guest speaker, 25% for books, 20% for use of the auditorium, and the remainder for lunch. If the club plans to spend $90 on lunch for the participants, how much do they plan to spend on the guest speaker? (A)$40 (B)$120 (C)$150 (D)$240 (E)$600

40 STEP 1: Understand the problem. STEP 2: Analyze important information. STEP 3: Plan and solve. STEP 4: Check your work. 4-Step Method for Problem Solving

41 Activity: Strategy Synopsis Using your assigned strategy: Model the strategy with the provided question in your session guide. (pp ) Present your strategy to the group in a 5-minute presentation.

42 Strategy: Knowing vs. Knowing Know for Sure! Don’t Have a Clue Don’t Have a Clue Sort of Know

43 How will you implement Advantage? When will you start the program? When will you need to end the program? How many days a week will you devote? How many minutes of each day will you devote? SAT Test Dates March 1, 2008 May 3, 2008 June 7, 2008

44 Implementation Tips SectionPage Number Thinking KAPp. vi Instructionp. vii Independent Practice p. viii KAP Wrapp. ix

45 Planning a Lesson Activity: Using the planning guide on pages 34 and 35 in your session guide, plan a lesson that you will use with your class. Review the sample lesson on pages 32 and 33 in your session guide. Use the implementation tips from the Teacher’s Introduction. Use the guiding questions on your lesson planning guide.

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