The sat suite of Assessments Professional Development module 4 ® Math that Matters Most: Heart of Algebra Problem Solving and Data Analysis

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The SAT Suite of Assessments

Professional Development MODULE



Math that Matters Most: Heart of Algebra Problem Solving and Data Analysis

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?



  • 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



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
  • 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)

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 SAT Suite to assess fluencies valued by postsecondary instructors and includes conceptual questions for which a calculator will not 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 below.
  • Students may also enter a fraction line or a decimal point.

Math Test Specifications

Question Types



PSAT 8/9

Total Questions








Student-Produced Response




Contribution of Questions to Subscores



Heart of Algebra




Problem Solving and Data Analysis




Passport to Advanced Math




Additional Topics in Math*




Contribution of Questions to Cross-Test Scores



Analysis in Science




Analysis in History/Social Studies




*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 3-5 things everyone needs to know in the Math Test Domains?

How Does The Math Test Relate to Instruction in Science, Social Studies, and Career-Related Courses?

  • Math questions contribute to Cross-Test 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 Cross-Test Scores on the SAT, seven on PSAT/NMSQT-PSAT 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.

Connecting the Math Test with Classroom Instruction



General Instructional Strategies for the 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.

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:





18- to 34-year-olds





35- to 54-year-olds





55- to 74-year-olds





People 75 years old and over










Problem Solving and Data Analysis Sample Question (Calculator)

Of the 18- to 34-year-olds who reported voting, 500 people were selected at random to do a follow-up survey where they were asked which candidate they voted for. There were 287 people in this follow-up survey sample who said they voted for Candidate A, and the other 213 people voted for someone else. Using the data from both the follow-up 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.

Skill-Building Strategies Brainstorming Exercise

  • Review the Sample SAT Math Questions – Answer Explanations
  • Use the Skill-Building Strategies Brainstorming Guide to brainstorm ways to instruct and assess Heart of Algebra and Problem Solving and Data Analysis.

Additional Skill-Building 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



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
  • 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 subscore 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)

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 cross-test scores

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.



Measure of Success:





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?

Redesigned SAT Teacher Implementation Guide

See the whole guide at

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
  • Skill-Building 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?


Exit Survey

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