# SAT Advantage - Math 08-04-09

```Kaplan Advantage: SAT Mathematics
1
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
2
It’s not what students know—
it’s what they show!
Knowledge
Performance
3
What causes the gap?
Pieces of the Puzzle
range of
content
Rigidly
timed
High
stakes
No partial
credit on
multiple
choice
4
How do we bridge that gap?
Knowledge
Performance
5
Know the
STRATEGIES
Know the TEST
Know the CONTENT
application
of content
knowledge
to the test
instruction
of concepts
and skills
6
Agenda
I. Understanding the SAT
II. Program Structure
A. Student Introduction
B. Assessments
C. Appendix
D. Lesson Structure
A. The 4-Step Method for Problem
Solving
B. Test-Taking Strategies
7
SAT Format
Sections
Timing
Question Type and (#)
Two 25-min. sections Sentence Completions (19)
One 20-min. section Reading Comprehension (48)
Critical
Mathematics
Two 25-min. sections Multiple-Choice (44)
One 20-min. section Grid-ins (10)
One 25-min. section
Writing
One 10-min. section
One 25-min. essay
Experimental
One 25-min. section
Identifying Sentence Errors (18)
Improving Sentences (25)
Improving Paragraphs (6)
• Questions assess either Critical
• Does not count toward score
http://www.collegeboard.com/newsat/
8
How the SAT is Scored
Raw Score
• 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.
10
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…
11
The SAT is Standardized
norm-referenced vs. criterion-referenced
SAT Distribution Curve
200
300
400
500
Section Score
600
700
800
12
The Bell Curve
200
400
500
600
800
13
Sample SAT Problems
•Turn to page 3 in your session guide.
•Complete the sample SAT mathematics problems.
14
Program Organization: Mathematics
Student
Provides a brief introduction to the SAT and to the
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
Appendix
Geometry and Data Mini Practice Test
SAT Math in a Nutshell
Each lesson can be delivered in 45-60 minutes.
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Student Introduction
16
Assessments
Type
Mini
Practice
Test
FullLength
Practice
Test
Basics
• 3 tests
• Allows students to apply
strategies they have just
learned to SAT-like
questions
• Provides students with a
test-like experience in
terms of content and
length
Timing
25 min.
each
70 min.
17
Appendix: SAT Math in a Nutshell
Overview
SmartPoints
Content
• p. A1
• Appendix teaching suggestions
• p. A3
• Ranks most frequently tested skills
• pp. A4-A19
• Content summarizing sections
19
Unit Introduction
Objectives identified for
each lesson in the unit
Explanations of strategies students will
learn
20
PROGRAM
COMPONENT
Thinking KAP
Instruction
DESCRIPTION
APPROX.
TIME
Each lesson begins with a brief
warm-up activity.
4 Min.
Students learn new strategies
and practice them with feedback
from the teacher.
24 Min.
Students practice applying the
Independent
strategies on their own and then
Practice
review their work.
Students reflect on what they
KAP Wrap
have learned in the lesson.
12 Min.
5 Min.
21
Thinking KAP
22
Instruction
23
Student Supports
Hints that
support working
with the content
information
Opportunity to
apply strategies
24
Independent Practice
• 6-8 questions in each section
• Hints provided for each question
25
Reviewing Independent Practice
As Students Work:
Redirect students as needed
questions.
To Review:
Focus on students’
Look out for classic traps.
26
KAP Wrap
Purpose:
To apply, review, and
reflect on strategies
Complete:
For homework, for a journal
entry, with a partner, or
alone
27
Instructional Support
Content Background boxes
provide content tips as needed.
Teacher’s Notes provide tips
from mentor teachers.
common student errors.
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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 Thinking:
Knowing what to do NEXT!
But how do we teach it?
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Meeting the Challenges
Kaplan’s programs meet the
challenges with two key approaches:
2. A toolbox of
1. An approach
for every question strategies
type
Step 1.
Step 2.
Step 3.
Step 4.
32
Systematic Thinking: The 4-Step Method
for Problem Solving
STEP 1: Understand the problem.
STEP 2: Analyze important information.
STEP 3: Plan and solve.
This method…
• standardizes the language of problem solving.
• helps teachers model “expert” problem solving.
• provides students with a systematic approach.
33
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
34
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?
35
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?
10 in.
• Underline the clues.
• Rewrite the important information in a
I can draw it.
6 in.
3 in.
36
STEP 3: Plan and solve.
What do you
KNOW?
What do you
NEED?
I know the dimensions of
the cylinder.
I need to figure out the
volume of the canister.
How can you
use what you I will use the formula V
r2h and substitute the
KNOW to
find what you correct values.
NEED?
My work:
V r2h
  (3)2(10)
  (9)(10)
 90in2
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 Did you answer the right question?
Yes, I figured out the volume of the cylinder.
That’s a reasonable
volume.
 Can you solve the problem
another way?
Yes, I can use a chart
Formula
Values


d
r
r2
6
3
9
h
10
V r2h
V   (9)(10)  90 
38
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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4-Step Method for Problem Solving
STEP 1: Understand the problem.
STEP 2: Analyze important information.
STEP 3: Plan and solve.
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Activity: Strategy Synopsis
• 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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Strategy:
Knowing vs. Knowing
Sort of Know
Know for Sure!
Don’t
Have
a Clue
Sort of Know
Don’t
Have
a Clue
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How will you implement
• 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
44
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
• 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
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instructional programs that improve results and
help all students achieve.
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