DEVELOPMENT Module 5 The Redesigned SAT Math that Matters Most Passport to Advanced Math Additional Topics in Math Professional Development Modules for the Redesigned SAT Module 1 Key ID: 201674
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PROFESSIONAL DEVELOPMENT Module
5
The Redesigned SAT
Math that Matters Most: Passport to Advanced Math Additional Topics in MathSlide2
Professional Development
Modules for the Redesigned SAT
Module 1 Key Changes
Module 2 Words in Context and Command of EvidenceModule 3 Expression of Ideas and Standard English ConventionsModule 4 Math
that Matters Most: Heart of AlgebraProblem
Solving and Data Analysis
Module 5
Math that Matters Most:Passport to Advanced MathAdditional Topics in MathModule 6 Using Assessment Data to Inform Instruction
2Slide3
CHAPTER
1
What is the Purpose ofModule 5?
Review the content assessed for two math domains
:
Passport to Advanced Math
Subscore
Additional Topics in Math
Connect
Passport to Advanced Math and Additional Topics in Math with classroom instruction in math and other subjectsSlide4
Score Reporting on the
Redesigned SAT
4Slide5
Scores and Score Ranges
Across the SAT Suite of Assessments
5Slide6
CHAPTER
2Overview of the SAT Math TestSlide7
SAT Math Test Domains
Four Math Domains:
Heart of AlgebraLinear equations
FluencyProblem Solving and Data AnalysisRatios, rates, proportions
Interpreting and synthesizing dataPassport to Advanced Math
Quadratic, exponential functions
Procedural skill and fluency
Additional Topics in Math (Questions under Additional Topics in Math contributeto the total Math Test score but do not
contribute
to
a
Subscore within the
Math Test)Essential geometric and trigonometric conceptsModule 57Slide8
SAT Math Test Specifications
The overall aim of the SAT Math Test is to assess fluency with, understanding of, and ability to apply the mathematical concepts that are most strongly prerequisite for and useful across a wide range of college majors and careers
.The Math Test has two portions:
Calculator Portion (38 questions) 55 minutesNo-Calculator Portion (20 questions) 25 minutes
Total Questions on the Math Test: 58 questionsMultiple Choice (45 questions)Student-Produced Response (13 questions)
8Slide9
Calculator and No-Calculator
PortionsThe
Calculator portion:gives
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 redesigned SAT to assess fluencies valued by postsecondary instructors and includes conceptual questions for which a calculator will not be helpful.
9Slide10
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
here.Students may also enter a fraction line or a decimal point.
10Slide11
SAT Math Test Specifications
SAT Math Test Question Types
Total Questions
58 questions
Multiple Choice (four answer choices)
45 questions
Student-Produced Responses (Student Produced Response or grid-ins)
13 questions
Contribution of Questions to Total Scores
Heart of Algebra
19 questions
Problem Solving and Data Analysis
17 questions
Passport to Advanced Math
16 questions
Additional Topics in Math*
6 questions
Contribution of Questions to Cross-Test Scores
Analysis in Science
8 questions
Analysis in Social Studies
8 questions
*Questions
under Additional Topics in Math contribute to the total Math Test score but do not contribute to a
subscore
within the Math Test
.
11Slide12
SAT Math Test Domains Activity
What are the top 3-5 things everyone needs to know in the SAT Math Test Domains
?
12Slide13
How Does The Math Test Relate to Instruction in Science, Social Studies, and Career-Related Courses?
Math questions contribute to Cross-Test
Scores, which will include a score for Analysis in Science and Analysis in History/Social Studies. The Math Test will have eight questions that contribute to each of these Cross-Test Scores
.Question content, tables, graphs, and data on the Math Test will relate to topics in science, social studies, and career.On the Reading Test and Writing and Language Test, students will be asked to analyze data, graphs, and tables (no mathematical computation required.)
13Slide14
CHAPTER
3Connecting the SAT Math Test with Classroom InstructionSlide15
General InstructionalStrategies
for SAT Math TestEnsure that students practice solving multi-step 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 do not 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.
15Slide16
Skill-Building Strategies
Brainstorming ExerciseUse the
Skill-Building Strategies Brainstorming Activity to brainstorm ways to instruct and assess Passport to Advanced Math and Additional Topics in Math.
16Slide17
Passport to Advanced Math
17Slide18
What is ‘Passport to Advanced Math?’
Problems in Passport to Advanced Math will cover topics that have great relevance and utility for college and career work.
Understand the structure of expressions
Analyze, manipulate, and rewrite expressionsReasoning with more complex equationsInterpret and build functions
18Slide19
Passport to Advanced Math:
Assessed Skills
Create and solve quadratic and exponential problemsCreate and solve radical and rational equationsSolve systems of equationsUnderstand the relationship between zeros and factors of polynomials
19Slide20
Passport to Advanced Math:
Sample Question
7
. 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 three points (−4, 0), (
, 0 ),
and
( p, 0). What is the value of c?A) –18B
) –
2
C
) 2
D) 10 20Slide21
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.Alternatively
, since –4,
, and
p are zeros of the polynomial functionf (x) = 2x³ + 3x² + cx + 8, it follows that
f (x
) = (2
x
− 1)(
x + 4)(x − p).Were this polynomial multiplied out, the constant term would be (− )(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 yieldsf (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.
21Slide22
Additional Topics in Math
22Slide23
What is ‘Additional Topics in Math?’
The SAT will require the geometric and trigonometric knowledge most relevant to postsecondary education and careers.
Geometry
AnalysisProblem solving TrigonometrySine
CosineTangent
Pythagorean Theorem
23Slide24
Additional Topics in Math:
Assessed Skills
Solve problems using volume formulasSolve problems involving right triangles
Apply theorems about circlesSolve problems about lines, angles, and triangles24Slide25
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 question 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.
25Slide26
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. This gives cos
x
=
, which can be simplified to cos x
=
.
26Slide27
Skill-Building Strategies
Brainstorming Exercise
Use the Skill-Building Strategies Brainstorming Activity to brainstorm ways to instruct and assess Passport to Advanced Math and Additional Topics in Math.
27Slide28
Skill-Building Strategies for Math
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 are not obvious.
28Slide29
Incorporating Strategies
intoLesson Plans
Lesson Planning Guide
29Slide30
CHAPTER
4Scores and Reporting
For more information about SAT scores, reports, and using data (available in September, 2015):
Professional
Development Module
6 – Using Assessment Data to Inform
Instruction
SAT Suite of Assessments Scores and Reporting: Using Data to Inform InstructionSlide31
Sample SAT Reports
Score Report
(Statistics for state/district/school)
Mean scores and score band distribution
Participation rates when available
High-level benchmark information, with tie to detailed benchmark
reports
Question Analysis Report
Aggregate performance on each question (easy vs. medium vs. hard difficulty) in each test
Percent
of students who selected each answer for each question
Applicable Subscores and Cross-Test Score mapped to each questionComparison to parent organization(s) performanceAccess question details for disclosed form (question stem, stimulus, answer choices and explanations)
31Slide32
Sample SAT Reports (continued)
Subscore
Analysis Report
Aggregate performance on
Subscores
Mean scores for
Subscores
and related
Test Score(s
)
Aggregate student performance on questions (easy vs. medium vs. hard difficulty) related to each
Subscore
Display applicable state standards for each SubscoreAccess question details for each question on disclosed form (question stem, stimulus, answer choices and explanation)32Slide33
Follow Up Activity: Tips for Professional Learning Communities and Vertical Teams
The “Tips for Professional Learning Communities and Vertical Teams” is available to guide teams of colleagues in the review and analysis of SAT reports and data
.
Professional
Learning Community Data Analysis
Review the data and make observations.
Consider all of the observations of the group. Determine whether the group discussion should be focused on gaps, strengths, or both. Select one or two findings from the observations to analyze and discuss further.
Identify content skills associated with the areas of focus.
Review other sources of data for additional information.
Develop the action plan.
Goal:
Measure of Success:
Steps:
When you’ll measure:
33Slide34
Self Assessment/Reflection
How well do I teach students skills related to Passport to Advanced Math?
How well do I teach students skills related to Additional Topics in Math?
What can I do in my classroom immediately to help students understand what they’ll see on the redesigned SAT?
How can I adjust my assessments to reflect the structure of questions on the redesigned SAT?
What additional resources do I need to gather in order to support students in becoming college and career ready?
How can I help students keep track of their own progress toward meeting the college and career ready benchmark?
34Slide35
Redesigned SAT Teacher Implementation Guide
See the whole guide at collegereadiness.collegeboard.org
35Slide36
What’s in the SAT Teacher Implementation Guide?
Information and strategies for teachers in all subject areasOverview of SAT content and structure
Test highlightsGeneral Instructional Strategies
Sample test questions and annotationsSkill-Building Strategies for the classroomKeys to the SAT (information pertaining to the redesigned SAT structure and format)Rubrics and sample essays
Scores and reportingAdvice to share with students
36Slide37
Questions or comments about this presentation or the SAT redesign?
Email:
SATinstructionalsupport@collegeboard.org
37Slide38
Exit Survey
https://
www.surveymonkey.com/s/PD_Module_5
38