Professional Development MODULE 4
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Professional Development Modules for the SAT Suite of Assessments Module 1 Key Features 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 Module 7 Connecting History/Social Studies Instruction with the SAT Suite of Assessments Module 8 Connecting Science Instruction with the SAT Suite of Assessments Module 9 The SAT Essay What is the Purpose of Module 4? CHAPTER 1  Review the content assessed for two math Subscores:
 Heart of Algebra
 Problem Solving and Data Analysis
 Connect Heart of Algebra and Problem Solving and Data Analysis skills with classroom instruction in math and other subjects
Score Reporting on the SAT Suite of Assessments
Score ranges on this table are for the SAT.
Scores and Score Ranges Across the SAT Suite of Assessments Overview of the 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 most strongly prerequisite for and useful across a wide range of college majors and careers.
 The SAT Math Test has two portions:
 Calculator Portion (38 questions) 55 minutes
 NoCalculator Portion (20 questions) 25 minutes
 Total Questions on the SAT Math Test: 58 questions
 Multiple Choice (45 questions)
 StudentProduced Response (13 questions)
 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 NoCalculator portion:
 allows the SAT Suite to assess fluencies valued by postsecondary instructors and includes conceptual questions for which a calculator will not be helpful.
StudentProduced Response Questions Studentproduced response questions, or gridins:  The answer to each studentproduced 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 below.
 Students may also enter a fraction line or a decimal point.
Math Test Specifications
Question Types

SAT

PSAT/NMSQT and PSAT 10

PSAT 8/9

Total Questions

58

48

38

MultipleChoice

45

40

31

StudentProduced Response

13

8

7

Contribution of Questions to Subscores
 


Heart of Algebra

19

16

16

Problem Solving and Data Analysis

17

16

16

Passport to Advanced Math

16

14

6

Additional Topics in Math*

6

2

0

Contribution of Questions to CrossTest Scores
 


Analysis in Science

8

7

6

Analysis in History/Social Studies

8

7

6

*Questions under Additional Topics in Math contribute to the total Math Test score but do not contribute to a subscore within the Math Test.
Math Test Domains Four Math Domains:  Heart of Algebra
 Linear equations
 Fluency
 Problem Solving and Data Analysis
 Ratios, rates, proportions
 Interpreting and synthesizing data
 Passport to Advanced Math
 Quadratic, exponential functions
 Procedural skill and fluency
 Additional Topics in Math
 Essential geometric and trigonometric concepts
Module 4
Math Test Domains Activity What are the top 35 things everyone needs to know in the Math Test Domains? How Does The Math Test Relate to Instruction in Science, Social Studies, and CareerRelated Courses?  Math questions contribute to CrossTest Scores, which include a score for Analysis in Science and Analysis in History/Social Studies.
 The Math Test has eight questions that contribute to each of these CrossTest Scores on the SAT, seven on PSAT/NMSQTPSAT 10, and six on PSAT 8/9
 Question content, tables, graphs, and data on the Math Test relate to topics in science and history/social studies.
 On the Reading Test and the Writing and Language Test, students are asked to analyze data, graphs, and tables (no mathematical computation required).
Heart of Algebra What is ‘Heart of Algebra?’  Algebra is the language of high school mathematics; students must be proficient in order to do most of the other math learned in high school
 The ability to use linear equations to model scenarios and to represent unknown quantities is powerful across the curriculum in the classroom as well as in the workplace
 Algebra is a prerequisite for advanced mathematics
Heart of Algebra: Assessed Skills  Analyzing and fluently solving equations and systems of equations
 Creating expressions, equations, and inequalities to represent relationships between quantities and to solve problems
 Rearranging and interpreting formulas
Heart of Algebra (Calculator) When a scientist dives in salt water to a depth of 9 feet below the surface, the pressure due to the atmosphere and surrounding water is 18.7 pounds per square inch. As the scientist descends, the pressure increases linearly. At a depth of 14 feet, the pressure is 20.9 pounds per square inch. If the pressure increases at a constant rate as the scientist’s depth below the surface increases, which of the following linear models best describes the pressure p in pounds per square inch at a depth of d feet below the surface? A) p = 0.44d + 0.77 B) p = 0.44d + 14.74 C) p = 2.2d – 1.1 D) p = 2.2d – 9.9 Heart of Algebra: Answer Explanation Choice B is correct. To determine the linear model, one can first determine the rate at which the pressure due to the atmosphere and surrounding water is increasing as the depth of the diver increases. Calculating this gives [fraction numerator 20.9 −18.7 over denominator 14 − 9 end fraction] equals [fraction numerator 2.2 over denominator 5 end fraction] comma or 0.44. Then one needs to determine the pressure due to the atmosphere or, in other words, the pressure when the diver is at a depth of 0. Solving the equation 18.7 = 0.44 ( 9 ) + b gives b = 14.74. Therefore, the model that can be used to relate the pressure and the depth is p = 0.44 d + 14.74. Problem Solving and Data Analysis What Is ‘Problem Solving and Data Analysis?’  Quantitative Reasoning
 Analysis of Data
 Ratios
 Percentages
 Proportional reasoning
 In Problem Solving and Data Analysis, students will encounter an important feature of the SAT Suite of Assessments: multipart questions
 Asking more than one question about a given scenario allows students to do more sustained thinking and explore situations in greater depth
 Students will generally see longer problems in their postsecondary work
Problem Solving and Data Analysis: Assessed Skills  Creating and analyzing relationships using ratios, proportions, percentages, and units
 Describing relationships shown graphically
 Summarizing qualitative and quantitative data
Problem Solving and Data Analysis: Sample Question (Calculator) A typical image taken of the surface of Mars by a camera is 11.2 gigabits in size. A tracking station on Earth can receive data from the spacecraft at a data rate of 3 megabits per second for a maximum of 11 hours each day. If 1 gigabit equals 1,024 megabits, what is the maximum number of typical images that the tracking station could receive from the camera each day? A) 3 B) 10 C) 56 D) 144 Problem Solving and Data Analysis: Answer Explanation Choice B is correct. The tracking station can receive 118,800 megabits each day which is about 116 gigabits each day If each image is 11.2 gigabits, then the number of images that can be received each day is Since the question asks for the maximum number of typical images, rounding the answer down to 10 is appropriate because the tracking station will not receive a complete 11th image in one day. CHAPTER 3 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 classroombased 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.
Heart of Algebra Sample Question (No Calculator) Problem Solving and Data Analysis Sample Question (Calculator) A survey was conducted among a randomly chosen sample of U.S. citizens about U.S. voter participation in the November 2012 presidential election. The table below displays a summary of the survey results. Reported Voting by Age (in thousands) Move to the next slide for the question prompt and answer choices: 
VOTED

DID NOT VOTE

NO RESPONSE

TOTAL

18 to 34yearolds

30,329

23,211

9,468

63,008

35 to 54yearolds

47,085

17,721

9,476

74,282

55 to 74yearolds

43,075

10,092

6,831

59,998

People 75 years old and over

12,459

3,508

1,827

17,794

Total

132,948

54,532

27,602

215,082
 Problem Solving and Data Analysis Sample Question (Calculator) Of the 18 to 34yearolds who reported voting, 500 people were selected at random to do a followup survey where they were asked which candidate they voted for. There were 287 people in this followup survey sample who said they voted for Candidate A, and the other 213 people voted for someone else. Using the data from both the followup survey and the initial survey, which of the following is most likely to be an accurate statement?
A) About 123 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.
B) About 76 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.
C) About 36 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.
D) About 17 million people 18 to 34 years old would report voting for Candidate A in the November 2012 presidential election.
SkillBuilding Strategies Brainstorming Exercise  Review the Sample SAT Math Questions – Answer Explanations
 Use the SkillBuilding Strategies Brainstorming Guide to brainstorm ways to instruct and assess Heart of Algebra and Problem Solving and Data Analysis.
Additional SkillBuilding Strategies – SAT Suite of Assessments  Provide students with equations and/or explanations that incorrectly describe a graph.
 Ask students to identify the errors and provide corrections.
 As students work in small groups to solve problems, facilitate discussions in which they communicate their own thinking and critique the reasoning of others.
 Organize information to present data and answer a question or show a problem solution.
 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.
 Use “Guess and Check” to explore different ways to solve a problem when other strategies for solving are not obvious.
 Students first guess the solution to a problem;
 Check that the guess fits the information in the problem and is an accurate solution;
 Work backward to identify proper steps to arrive at the solution.
Scores and Reporting CHAPTER 4
For more information about SAT Suite of Assessments scores and reports:
Professional Development Module 6 – Using Assessment Data to Guide Instruction
SAT Suite of Assessments: Using Scores and Reporting to Inform Instruction
Sample Reports  Score Report (Statistics for state/district/school)
 Mean scores and score band distribution
 Participation rates when available
 Highlevel 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 subscore and crosstest score mapped to each question
 Comparison to parent organization(s) performance
 Access question details for disclosed form (question stem, stimulus, answer choices and explanations)
Sample Reports (continued)  Instructional Planning Report
 Aggregate performance on subscores
 Mean scores for subscore and related test score(s)
 Display applicable state standards for each subscore
 Drills through to the questions linked to subscores and crosstest scores
FollowUp 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:
 Self Assessment/Reflection  How well do I teach students skills related to Heart of Algebra?
 How well do I teach students skills related to Problem Solving and Data Analysis?
 What can I do in my classroom immediately to help students understand what they’ll see on the SAT?
 How can I adjust my assessments to reflect the structure of questions on the 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?
See the whole guide at collegereadiness.collegeboard.org
What’s in the Redesigned 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
 SkillBuilding Strategies for your classroom
 Keys to the SAT (information pertaining to the SAT structure and format)
 Rubrics and sample essays
 Scores and reporting
 Advice to share with students
Questions or comments about this presentation or the SAT Suite? Email: SATinstructionalsupport@collegeboard.org Exit Survey https://www.surveymonkey.com/s/PD_Module_4 