Kaplan Advantage: SAT Mathematics

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• Kaplan Advantage SAT Mathematics

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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. s2 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
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Its not what students knowits what they show!
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What causes the gap?Pieces of the Puzzle
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How do we bridge that gap?
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Foundations of Test Readiness
Know the STRATEGIES
Know the TEST
Know the CONTENT
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Agenda

• Understanding the SAT
• Program Structure
• Student Introduction
• Assessments
• Appendix
• Lesson Structure
• Critical Thinking for Test Readiness
• The 4-Step Method for Problem Solving
• Test-Taking Strategies

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SAT Format
Sections Timing Question Type and ()
Critical Reading Two 25-min. sections Sentence Completions (19) Reading Comprehension (48)
Critical Reading One 20-min. section Sentence Completions (19) Reading Comprehension (48)
Mathematics Two 25-min. sections Multiple-Choice (44) Grid-ins (10)
Mathematics One 20-min. section Multiple-Choice (44) Grid-ins (10)
Writing One 25-min. section Identifying Sentence Errors (18) Improving Sentences (25) Improving Paragraphs (6)
Writing One 10-min. section Identifying Sentence Errors (18) Improving Sentences (25) Improving Paragraphs (6)
Writing One 25-min. essay Identifying Sentence Errors (18) Improving Sentences (25) Improving Paragraphs (6)
Experimental One 25-min. section Questions assess either Critical Reading, Math, or Writing Does not count toward score
http//www.collegeboard.com/newsat/
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Test Order
SAT Section Time Content
1 25 min. Essay
2-7 25 min. Critical Reading, Writing, Mathematics, and Experimental
8-9 20 min. Critical Reading, Mathematics
10 10 min. Writing
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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 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?
But if we could eliminate a few answers each time
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The SAT is Standardized

• norm-referenced vs. criterion-referenced

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The Bell Curve
500
400
600
200
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
Student Introduction 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
Each lesson can be delivered in 45-60 minutes.
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Student Introduction
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Assessments
Type 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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• This slide is intentionally hidden to allow for
  presenters notes.

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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 Introduction

• Objectives identified for each lesson in the unit

Explanations of strategies students will learn
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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.
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Thinking KAP
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Instruction
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Student Supports
Hints that support working with the content
Provides helpful information about the SAT
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
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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 22-23
• KAP Wrap, session guide page 24

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Critical ThinkingKnowing what to do NEXT!
But how do we teach it?
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Meeting the Challenges
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Systematic Thinking The 4-Step Method for
Problem Solving

• 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.

• 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?

• 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.

• 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?

• Underline the clues.
• Rewrite the important information in a helpful
  way.
• I can draw it.

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STEP 3 Plan and solve.

What do youKNOW?
What do youNEED?
How can you use what you KNOW to find what you NEED?
My work V ??r2h ? ? (3)2(10) ? ? (9)(10) ?
90??in2
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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STEP 4 Check your work.

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

• Is your answer reasonable?
• Yes. 90? is about 270. Thats a reasonable volume.

Formula Values
? ?
d 6
r 3
r2 9
h 10
V ??r2h V ? ? (9)(10) ? 90 ?

• Can you solve the problem another way?
• Yes, I can use a chart instead.

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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?

1. 40
2. 120
3. 150
4. 240
5. 600

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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
  your
• session guide. (pp. 27-31)
• Present your strategy to the group in a 5-minute
• presentation.

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StrategyKnowing vs. Knowing
Know for Sure!
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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
Section Page 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 Teachers
  Introduction.
• Use the guiding questions on your lesson planning
  guide.

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Kaplan K12 Mission Statement
We partner with schools to provide high-quality
instructional programs that improve results and
help all students achieve.
If you have questions, please contact us
atadvantage_at_kaplan.com