®
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: SATinstructionalsupport@collegeboard.org
41
Exit Survey
https://www.surveymonkey.com/s/PD_Module_5
42