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)

Kaplan Advantage: SAT Mathematics

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Warm-Up: MathIf 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. s2 – r is oddIII. 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

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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

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How do we bridge that gap?

Knowledge Performance

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Know the CONTENTKnow the CONTENT

Know the TESTKnow the TEST

Know the STRATEGIES

Know the STRATEGIES

instructionof conceptsand skills

applicationof content knowledge to the test

Foundations of Test Readiness

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AgendaI. Understanding the SATII. Program Structure

A. Student IntroductionB. AssessmentsC. AppendixD. Lesson Structure

III. Critical Thinking for Test ReadinessA. The 4-Step Method for Problem

SolvingB. Test-Taking Strategies

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SAT Format

http://www.collegeboard.com/newsat/

Sections TimingQuestion 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

Experimental

One 25-min. section

• Questions assess either Critical Reading, Math, or Writing

• Does not count toward score

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How the SAT is ScoredRaw 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 200-800. (Critical Reading,

Writing, Mathematics)• The maximum score is 2400.• The average score is 1500.

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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…

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The SAT is Standardizednorm-referenced vs. criterion-referenced

SAT Distribution Curve

200 300 400 500 600 700 800

Section Score

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The Bell Curve

500400 600200 800

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Sample SAT Problems

•Turn to page 3 in your session guide.

•Complete the sample SAT mathematics

problems.

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Program Organization: Mathematics

Each lesson can be delivered in 45-60 minutes.

Student Introductio

n

Provides a brief introduction to the SAT and to the Advantage SAT program

Unit 1 The 4-Step Method for Problem Solving

Unit 2 Number and Operations

MPT Number and Operations Mini Practice Test

Unit 3 Expressions and Functions

Unit 4 Equations and Inequalities

MPT Algebra Mini Practice Test

Unit 5 Geometry and Measurement

Unit 6 Probability, Statistics, and Data Analysis

MPT Geometry and Data Mini Practice Test

Appendix SAT Math in a Nutshell

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Student Introduction

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AssessmentsType Basics Timing

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.

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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

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Unit IntroductionObjectives identified for each lesson in the unit

Explanations of strategies students will learn

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Advantage SAT: Lesson Structure

PROGRAM COMPONEN

TDESCRIPTION

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 WrapStudents reflect on what they have learned in the lesson.

5 Min.

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Thinking KAP

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Instruction

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Student Supports

Provides helpful information about the SAT

Hints that support working with the content

Opportunity to apply strategies

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

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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.

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KAP Wrap

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

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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.

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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?

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Unit 2, Lesson 1

•Thinking KAP, session guide page 17

•Instruction, session guide pages 18-21

•Independent Practice, session guide pages 22-

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•KAP Wrap, session guide page 24

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Critical Thinking:Knowing what to do NEXTNEXT!

But how do we teach it?

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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

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Systematic Thinking: The 4-Step Method for Problem Solving

STEP 1: Understand the problem.STEP 2: Analyze important information.STEP 3: Plan and solve.

STEP 4: Check your work.

This method…• standardizes the language of problem

solving.• helps teachers model “expert” problem

solving.• provides students with a systematic

approach.

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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

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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?


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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.


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STEP 3: Plan and solve.

My work: V r2h

(3)2(10)

(9)(10)

90in2

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 r2h and substitute the correct values.

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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.

Formula Values

d 6

r 3

r2 9

h 10

V r2h V (9)(10) 90

Did you answer the right question?Yes, I figured out the volume of the cylinder.

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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

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STEP 1: Understand the problem.

STEP 2: Analyze important information.

STEP 3: Plan and solve.


4-Step Method for Problem Solving

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Activity: Strategy Synopsis

Using your assigned strategy:

•Model the strategy with the provided question in yoursession guide. (pp. 27-31)

•Present your strategy to the group in a 5-minutepresentation.

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Strategy:Knowing vs. Knowing

Know for Sure!

Don’tHave

a Clue

Don’tHave

a Clue

Sort of Know

Sort of Know

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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?

2007-2008 SAT Test Dates

• March 1, 2008• May 3, 2008• June 7, 2008

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Implementation Tips

SectionPage

Number

Thinking KAP

p. vi

Instruction p. vii

Independent Practice

p. viii

KAP Wrap p. ix

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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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Kaplan K12 Mission Statement

If you have questions, please contact us at:

[email protected]

We partner with schools to provide high-quality instructional programs that improve

results and help all students achieve.

Documents

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)