© 2015 the college board professional development module 5 the redesigned sat math that matters...

© 2015 The College Board

PROFESSIONAL DEVELOPMENT

MODULE

5The Redesigned SATMath that Matters Most: Passport to Advanced Math Additional Topics in Math


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Professional DevelopmentModules for the Redesigned SAT

Module 1 Key Changes

Module 2 Words in Context and Command of Evidence

Module 3 Expression of Ideas and Standard English Conventions

Module 4 Math that Matters Most:

Heart of Algebra

Problem Solving and Data Analysis

Module 5 Math that Matters Most:

Passport to Advanced Math

Additional Topics in Math

Module 6 Using Assessment Data to Inform Instruction


CHAPTER

1What 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 subjects


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Score Reporting on theRedesigned SAT


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Scores and Score RangesAcross the SAT Suite of Assessments


CHAPTER

2Overview of the SAT Math Test


SAT Math Test DomainsFour 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

b. Procedural skill and fluency

4. Additional Topics in Math (Questions under Additional Topics in Math contributeto the total Math Test score but do not contributeto a Subscore within the Math Test)

a. Essential geometric and trigonometric concepts

Module 5

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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 minutes

- No-Calculator Portion (20 questions) 25 minutes

► Total Questions on the Math Test: 58 questions

- Multiple Choice (45 questions)

- Student-Produced Response (13 questions)

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Calculator and No-Calculator Portions► The 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.

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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.


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SAT Math Test SpecificationsSAT 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.


SAT Math Test Domains ActivityWhat are the top 3-5 things everyone needs to know in the SAT Math Test Domains?

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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.)


CHAPTER

3Connecting the SAT Math Test with Classroom Instruction


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General InstructionalStrategies for SAT Math Test► Ensure 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.


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Skill-Building StrategiesBrainstorming Exercise► Use the Skill-Building Strategies Brainstorming Activity to brainstorm ways to

instruct and assess Passport to Advanced Math and Additional Topics in Math.


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Passport to Advanced Math


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 expressions

- Reasoning with more complex equations

- Interpret and build functions

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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


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Passport to Advanced Math:Sample Question7. 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) –18

B) –2

C) 2

D) 10


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Passport to Advanced Math:Answer ExplanationChoice 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 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

(− )(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.


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Additional Topics in Math


What is ‘Additional Topics in Math?’The SAT will require the geometric and trigonometric knowledge most relevant to postsecondary education and careers.

► Geometry

- Analysis

- Problem solving

► Trigonometry

- Sine

- Cosine

- Tangent

► Pythagorean Theorem

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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


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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.


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Additional Topics in Math:Answer ExplanationWhat 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 = .


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Skill-Building StrategiesBrainstorming Exercise► Use the Skill-Building Strategies Brainstorming Activity to brainstorm ways to

instruct and assess Passport to Advanced Math and Additional Topics in Math.


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.

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Incorporating Strategies intoLesson PlansLesson Planning Guide


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 Instruction


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 question

Comparison to parent organization(s) performance

Access question details for disclosed form (question stem, stimulus, answer choices and explanations)

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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 Subscore

Access question details for each question on disclosed form (question stem, stimulus, answer choices and explanation)

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Follow Up Activity: Tips for Professional Learning Communities and Vertical TeamsThe “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:


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?

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Redesigned SAT Teacher Implementation GuideSee the whole guide at collegereadiness.collegeboard.org


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What’s in the SAT Teacher Implementation Guide?► Information and strategies for teachers in all subject areas

► Overview of SAT content and structure

► Test highlights

► General Instructional Strategies

► Sample test questions and annotations

- Skill-Building Strategies for the classroom

- Keys to the SAT (information pertaining to the redesigned SAT structure and format)

- Rubrics and sample essays

► Scores and reporting

► Advice to share with students


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Questions or comments about this presentation or the SAT redesign?Email: [email protected]

mailto:[email protected]


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Exit Surveyhttps://www.surveymonkey.com/s/PD_Module_5

https://www.surveymonkey.com/s/PD_Module_5

© 2015 the college board professional development module 5 the redesigned sat math that matters...

Documents

total math test score

math section score

math domains

reading test

language test

crosstest scores

writing section score

section scores