How the College Board College Readiness Pathway Aligns to Texas Report on the Alignment of the SAT, PSAT/NMSQT and ReadiStep to the Texas Essential Knowledge and Skills May 2010
Mission Statement The College Board s mission is to connect students to college success and opportunity. We are a notfor profit membership organization committed to excellence and equity in education. The College Board: Inspiring Minds The College Board is a not for profit membership organization whose mission is to connect students to college success and opportunity. Founded in 1900, the organization is composed of more than 5,700 schools, colleges, universities and other educational organizations. Each year, the College Board serves seven million students and their parents, 23,000 high schools, and 3,800 colleges through major programs and services in college readiness, college admission, guidance, assessment, financial aid and enrollment. Among its widely recognized programs are the SAT, the PSAT/NMSQT, the Advanced Placement Program (AP ), SpringBoard and ACCUPLACER. The College Board is committed to the principles of excellence and equity, and that commitment is embodied in all of its programs, services, activities and concerns. For further information, visit www.collegeboard.com.
Contents Executive Summary 2 Background 3 Alignment Methodology 4 Key Findings 6 Alignment Analysis and Summary Tables: Mathematics 7 Alignment Analysis and Summary Tables: English Language Arts 22 Appendices 40 Appendix A: ReadiStep, PSAT/NMSQT, and SAT Skills Insight Categories Appendix B: Mathematics Side-by-Side Alignment Tables Appendix C: English Language Arts Side-by-Side Alignment Tables 1
Alignment of the SAT, PSAT/NMSQT, and ReadiStep to the Texas Essential Knowledge and Skills May 2010 Executive Summary The College Board s College Readiness Pathway represents the reading, writing, and mathematical skills that students need in order to be ready to succeed in college. The College Readiness Pathway, a series of integrated assessments and supporting tools, consists of ReadiStep, administered in grade eight, PSAT/NMSQT, administered in grades 10 11, and the SAT, administered in grades 11 12. This report provides an analysis of how the content and skills measured by ReadiStep, PSAT/NMSQT, and SAT align with the expectations defined in the Texas Essential Knowledge and Skills (TEKS). This comparison is provided as a resource to Texas school districts as they prepare to implement the College Readiness Pathway assessments. Effective assessments should serve to inform instruction in the classroom and should be an element of an instructional plan that provides teachers, administrators, and students with feedback on current success and tools to gauge future success as students progress through the grades. The College Readiness Pathway assessments can fulfill these assessment needs. Using the enclosed alignment tables, Texas educators can connect ReadiStep, PSAT/NMSQT, and SAT skills to their local curricula and state standards to monitor student learning and to build a coherent instructional plan for their students. To conduct this alignment study, the College Board compared the TEKS to the ReadiStep, PSAT/NMSQT, and SAT Skills Insight Categories (Skills Categories). The Skills Categories outline the academic content and skills measured on each assessment, and as these Skills Categories were developed using released test items and forms, they fully represent the spectrum of content and skills found on each assessment. For the SAT essay, this evaluation relied on the scoring guide to articulate the key writing skills required by the essay section of the SAT. The Skills Categories are part of the Skills Insight tool for each assessment. The Skills Insight tool helps teachers and students identify skills that require further development. The Skills Insight report also allows teachers and students to identify areas in which students excel, a circumstance that may demonstrate their readiness for more rigorous course work. See Appendix A for a more detailed description of each skill category. Overall, there is strong alignment between the TEKS and ReadiStep, PSAT/NMSQT, and SAT in mathematics. At the overarching standard level of the TEKS in mathematics, almost every standard statement is addressed by the College Readiness Pathway assessments. In English language arts, there is good alignment between the College Readiness Pathway assessments and the TEKS in reading and writing specifically, vocabulary development; comprehension and analysis of literary, expository, and informational texts; writing conventions; and the writing process (which links to the SAT essay). Every reading and writing skill measured by the College Readiness Pathway assessments aligns to one or multiple performance expectations within the TEKS. Please see the Alignment Methodology section on page 4 for a description of the summary alignment ratings. These summary ratings should be interpreted and considered in conjunction with the more detailed alignment tables and content analyses that are provided in this report. 2
Background ReadiStep ReadiStep is the first step in the College Readiness Pathway. Developed by College Board professionals in partnership with middle school teachers and other education experts, this low stakes grade eight assessment provides early feedback on a student s academic progress and can serve to identify skills that students need in order to be college ready. The ReadiStep assessment helps schools and teachers measure student achievement, monitor progress, and gain information that enables informed decisions about classroom instruction. The ReadiStep program also provides detailed performance feedback to middle school students and parents so that students can identify academic strengths and address weaknesses before they enter high school. PSAT/NMSQT The intermediate step in the College Readiness Pathway, PSAT/NMSQT is a preliminary version of the SAT. This comprehensive assessment program places students on the path to college with SAT practice, skills feedback, scholarship opportunities, information from colleges, and online college and career planning tools. It is used by schools and districts to identify more students who may be successful in Advanced Placement (AP ) courses. A widely used assessment in Texas, the PSAT/NMSQT also provides detailed reporting tools that schools and districts can use to identify skill weaknesses and make curricular adjustments. SAT The final step in the College Readiness Pathway is the nation s most widely used admission test among colleges and universities. The SAT is typically taken by high school juniors and seniors. It tests students core knowledge of subjects they have learned in the classroom such as reading, writing, and mathematics in addition to assessing how students think, solve problems, and communicate. The SAT also tells students how well they apply the skills and knowledge they have attained in and outside of the classroom. Through curriculum surveys and alignment analyses, the College Board regularly surveys classroom instructional practices, state standards, and district curriculum frameworks for grades 9 12, as well as the course content of first year college courses, to ensure that its assessments measure the content knowledge and skills that students need in order to be ready for college. 3
Alignment Methodology In order to illustrate the alignment continuum across middle school and high school, the College Board targeted the alignment of ReadiStep, PSAT/NMSQT, and SAT to focus on the following grades/ courses within the TEKS: Table 1: Grade levels/courses for Each Assessment Alignment Subject Area ReadiStep PSAT/NMSQT SAT Mathematics Grades seven and eight Algebra 1, Geometry, Algebra 2, Precalculus*, Mathematical Models with Applications Grades 9 12 Algebra 1, Geometry, Algebra 2, Precalculus*, Mathematical Models with Applications Grades 9 12 English Language Arts Grades seven and eight and III (Grades 10 11) and IV (Grades 11 12) *Precalculus skills aligned to the PSAT/NMSQT are not necessarily at the same level of rigor as the Precalculus skills measured on the SAT. The full breadth of the Precalculus TEKS will certainly include some standards that are beyond those of the PSAT/NMSQT and SAT. There are several organizing levels to the TEKS within each grade level or course. For the purpose of generating alignment tables, the following terminology was applied to the TEKS organizing structure: Table 2: TEKS Organizing Structure Grade/ Course Strand Standard Performance Expectation Establishes the grade level or course designation Examples:, Algebra 1 or Category within the standard (Math only) Example: Foundations for Functions Broad statement of knowledge and/or skill Example: 2. Reading/Vocabulary Development. Students understand new vocabulary and use it when reading and writing. More specific statement of finer grain size Example: (A) determine the meaning of grade level academic English words derived from Latin, Greek, or other linguistic roots and affixes. During the alignment process, the College Board aligns to the most specific grain size whenever possible, and for the TEKS, this would generally be at the level of the performance expectation. There are some instances in the TEKS where only the broad standard statements exist, and in those cases, the College Board determined whether there was an appropriate alignment to that level. College Board content specialists have extensive content knowledge of the College Board assessments as well as of state standards and district curriculum and instructional practices. In addition to applying content and curriculum expertise, content specialists use rigorous and researchbased methodologies to study the relationships between College Board assessment programs and state and national standards. 4
For this comparison, the College Board determined which concepts and skills from the TEKS are directly measured by ReadiStep, PSAT/NMSQT, and SAT. A successful alignment results when a skill (or skills) identified in a standard statement matches a skill in a related Skills Category. There are many instances where a TEKS standard statement may partially align to a ReadiStep, PSAT/NMSQT or SAT Skill Category, but this comparison details the areas of thorough alignment, not just partial alignment. Table 3: Description of Summary Alignment Ratings Strong Alignment Good Alignment Partial/ Weak Alignment This rating indicates that the skills and content measured on the assessments map to performance expectations within most or all of the broad standard statements. This rating also indicates that within each standard statement, multiple state performance expectations are thoroughly addressed. This rating indicates that the skills and content measured on the assessments map to performance expectations within the majority of the broad standard statements, but certain standards are not addressed due to the design and content of the assessment. This rating also indicates that within each standard statement, multiple state performance expectations are addressed. This rating indicates that the skills and content measured on the assessments map to performance expectations within a limited number of the broad standard statements. This rating also indicates that within each standard statement, single or few state performance expectations are addressed. Note: Many exceptions to an alignment between the College Readiness Pathway assessments and the TEKS arise from standards not being assessable in standardized group settings (such as monitoring fluency rates when reading aloud), standards requiring measurement over an extended period of time or through a variety of performance tasks (such as research tasks), or standards requiring the use of external resources beyond the testing materials (such as dictionaries or forms of education technology). See Appendix B for complete side by side alignment tables comparing the TEKS and the College Readiness Pathway Assessments in English Language Arts. 5
Key Findings As illustrated in the tables below, there is significant agreement between the content and skills measured by ReadiStep, PSAT/NMSQT, and SAT and the TEKS. Overall, the content and skills measured by ReadiStep, PSAT/NMSQT, and SAT correspond and align well with the TEKS. These assessments and supporting tools, such as Skills Insight, can be used as part of Texas s state and district college readiness initiatives. The tables below provide a summary of the number of broad TEKS standard statements that contain alignments to the College Board assessments. The College Board assessment(s) must align to one or more of the state performance expectations in order for the TEKS standard to be considered addressed. Table 4: Mathematics Alignment Summary 1 Assessment Targeted Grades/ Alignment Summary Courses ReadiStep Grades seven and eight 11 out of 16 TEKS standards are addressed PSAT/NMSQT and SAT PSAT/NMSQT and SAT PSAT/NMSQT and SAT PSAT/NMSQT and SAT PSAT/NMSQT and SAT Algebra I Geometry Algebra II Precalculus Mathematical Models with Applications 11 out of 11 TEKS standards are addressed 11 out of 11 TEKS standards are addressed 11 out of 11 TEKS standards are addressed 5 out of 6 TEKS standards are addressed 9 out of 9 TEKS standards are addressed See Appendix B for complete side by side alignment tables comparing the TEKS and the College Readiness Pathway assessments in Mathematics. Table 5: English Language Arts Alignment Summary 2 Assessment Targeted Grades/ Alignment Summary Courses ReadiStep Grades seven and eight 11 out of 19 TEKS reading and writing standards are addressed PSAT/NMSQT and III 10 out of 16 TEKS reading and writing standards are addressed SAT and IV 13 out of 16 TEKS reading and writing standards are addressed 1 Given the 9 12 grade band structure in the Mathematics TEKS, it was most appropriate to map both PSAT/NMSQT and SAT to the same 5 high school courses with the TEKS. 2 In English Language Arts, the College Board targeted the alignment to the most relevant reading and writing TEKS in order to communicate the relationship between the College Board assessments and the standards. The English Language Arts TEKS that address handwriting, spelling, using appropriate resources (i.e., dictionaries), the research process, listening, speaking, and teamwork are not included in these summary tables, as these standards are best addressed through local classroom measures or performance tasks. 6
Alignment Analysis and Summary Tables: Mathematics Alignment Analysis ReadiStep The ReadiStep mathematics section assesses how well students can apply the mathematics they know to solve both routine and nonroutine problems. The test consists of both calculator and noncalculator multiple choice questions designed to measure students middle school content knowledge and skills in the areas of Number & Operations, Geometry, Algebra, and Data, Statistics &Probability. There is very strong alignment between ReadiStep and the grades seven and eight TEKS. The majority of skills that are tested on ReadiStep correlates well to the TEKS performance expectations at the middle school level, and ReadiStep connects to all 16 standards within the grades seven and eight TEKS. Additionally, ReadiStep builds off of several foundational skills evident in the grades five and six TEKS. An example of the strength of the alignment of ReadiStep to the TEKS can be seen in the area of Number, Operation, & Quantitative. Listed below are the expectations for eighth grade students in the area of Number, Operation, & Quantitative. The student understands that different forms of numbers are appropriate for different situations. The student is expected to: A. compare and order rational numbers in various forms including integers, percents, and positive and negative fractions and decimals; B. select and use appropriate forms of rational numbers to solve real life problems including those involving proportional relationships; C. approximate (mentally and with calculators) the value of irrational numbers as they arise from problem situations; D. express numbers in scientific notation, including negative exponents, in appropriate problem situations; and E. compare and order real numbers with a calculator. The content assessed through ReadiStep fully engages with rational numbers (emphasized in performance expectations A and B), which sets the stage for continued assessment of the set of real numbers through the PSAT/NMSQT and SAT. Additionally, there is strong alignment between ReadiStep and the TEKS in the sub skills within Geometry and Number & Operations, as well as with the process skills inherent in, and skills. PSAT/NMSQT and SAT There is very strong alignment between the TEKS at the high school grade bands and the content and skills measured by PSAT/NMSQT and SAT. The alignment tables indicate the exemplary alignment in the areas of as well as Geometry. Probability and Statistics concepts are also clearly aligned to PSAT/NMSQT and SAT Skills Categories, with the most extensive alignment occurring in the coursework of Mathematical Models with Applications. Strong alignment exists 7
within the process skills, particularly in reasoning as well as representation. This is due to the rich algebraic and geometric curriculum that is evidenced throughout the TEKS. Significant gaps are not evident between the TEKS and PSAT/NMSQT and SAT, in that the College Board assessments address performance expectations found within almost every TEKS standard. In fact, the TEKS provide coherent, structured mathematical coursework appropriate for success on the PSAT/NMSQT and the SAT. Trigonometric and logarithmic functions are not included within the PSAT/NMSQT or SAT, yet are included within the content of the Algebra II TEKS. More generally, at first glance it might seem that the area of Number & Operations is significantly missing from the high school level TEKS, yet upon further investigation these skills are extensively embedded within the course work of as well as Geometry. An example of the strength of the alignment of the TEKS to the PSAT/NMSQT and SAT skills in, rather than merely to Number & Operations, can be seen in the Algebra I standard, Foundations for Functions strand: The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. (The student can) represent relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities This standard provides the opportunity for the use of and manipulation of numbers through operations but not solely within the realm of number and operation. A stronger alignment is seen within the PSAT/NMSQT and SAT skills in because of the application of the concepts within number and operation within an algebraic framework. Another aspect of the evaluation investigated the role of technology within the TEKS. This is important to the assessment program because of the ability of test takers to use a calculator during the administration of the PSAT/NMSQT and SAT, as well as during part of ReadiStep. It was found that technological tools are embedded within the high school level course work on a general level. On the middle school level, calculator use was clearly expressed within specific performance expectations on the seventh as well as eighth grade level. In summary, the in Mathematics evidence very strong alignment to the PSAT/NMSQT and SAT skills overall and align well to ReadiStep. This assessment pathway beginning in grade eight will serve to provide strong quantifiable support for students and teachers in developing education plans for effective mathematics instruction. 8
Table 6: ReadiStep Mathematics Alignment ReadiStep Aligned Skill Category and Description of Skills Grade Strand Performance Expectations Number & Operations: Students can understand numbers, number systems and operations. They can do arithmetic word problems, including those involving percent, ratio and proportion. They know properties of integers and elementary number theory. They can compute fluently with rational numbers expressed in fraction and in decimal form. They can solve problems involving sets and sequences of numbers. : Students can understand, write and simplify linear algebraic expressions. They can solve linear equations and inequalities. They can use mathematical models to represent and understand quantitative relationships. They can work with absolute value expressions involving a variable. : Students can analyze characteristics and properties of points, lines and angles in the plane. They can solve problems involving length, area and volume. They know and can apply angle sum property of triangles and the Pythagorean Theorem. They can identify points and work with translation and reflection of geometric figures in the coordinate plane. They are familiar with the concepts of parallelism, transversal and vertical angles, as well as similarity of geometric figures. Number, operation, and quantitative reasoning. Number, operation, and quantitative reasoning. Patterns, relationships, and algebraic thinking. Patterns, relationships, and algebraic thinking. Geometry and spatial reasoning. Measurement. Geometry and spatial reasoning. Measurement. 111.23.7.1.A 111.23.7.1.B 111.23.7.1.C 111.23.7.2.A 111.23.7.2.B 111.23.7.2.C 111.23.7.2.D 111.23.7.2.E 111.23.7.2.F 111.23.7.2.G 111.24.8.1.A 111.24.8.1.B 111.24.8.1.C 111.24.8.1.D 111.24.8.1.E 111.24.8.2.A 111.24.8.2.B 111.24.8.2.C 111.24.8.2.D 111.23.7.3.A 111.23.7.3.B 111.23.7.4.A 111.23.7.4.B 111.23.7.4.C 111.23.7.5.A 111.23.7.5.B 111.24.8.3.A 111.24.8.3.B 111.24.8.4.A 111.24.8.5.A 111.24.8.5.B 111.23.7.6.A 111.23.7.6.B 111.23.7.6.C 111.23.7.6.D 111.23.7.7.A 111.23.7.7.B 111.23.7.8.A 111.23.7.8.B 111.23.7.8.C 111.23.7.9.A 111.23.7.9.B 111.23.7.9.C 111.24.8.6.A 111.24.8.6.B 111.24.8.7.A 111.24.8.7.B 111.24.8.7.C 111.24.8.7.D 111.24.8.8.A 111.24.8.8.B 111.24.8.8.C 111.24.8.9.A 111.24.8.9.B 111.24.8.10.A 111.24.8.10.B 9
ReadiStep Aligned Skill Category and Description of Skills Grade Strand Performance Expectations Data, Statistics & Probability: Students can understand and interpret data displayed in tables and graphs, including bar graphs, pictographs and circle graphs. They can evaluate inferences and predictions that are based on data. They can understand and use descriptive statistics, including the mean and median. They can apply basic concepts of probability to solve problems. : Students can solve problems that arise in abstract as well as real contexts. They can apply and adapt a variety of appropriate strategies to solve problems, including both routine and nonroutine problems. They can monitor their process as they work toward the solution to a problem, and they can evaluate their answer in terms of the original question asked. Probability and statistics. Probability and statistics. Number, operation, and quantitative reasoning. Patterns, relationships, and algebraic thinking. 111.23.7.10.A 111.23.7.10.B 111.23.7.11.A 111.23.7.11.B 111.23.7.12.A 111.23.7.12.B 111.24.8.11.A 111.24.8.11.B 111.24.8.11.C 111.24.8.12.A 111.24.8.12.B 111.24.8.12.C 111.24.8.13.A 111.24.8.13.B 111.23.7.2.B 111.23.7.2.D 111.23.7.2.F 111.23.7.3.A 111.23.7.3.B : Students can create and use representations to organize, record and communicate mathematical ideas. They can select, apply and translate among mathematical representations, including the verbal, numerical, symbolic and graphical, to solve problems. Geometry and spatial reasoning. Measurement. Probability and statistics. Underlying processes and mathematical tools. Number, operation, and quantitative reasoning. Patterns, relationships, and algebraic thinking. Geometry and spatial reasoning. Measurement. Probability and statistics. Underlying processes and mathematical tools. Number, operation, and quantitative reasoning. Patterns, relationships, and algebraic thinking. Geometry and spatial reasoning. Probability and statistics. 111.23.7.8.C 111.23.7.9.A 111.23.7.9.C 111.23.7.10.B 111.23.7.13.B 111.23.7.13.C 111.23.7.13.D 111.24.8.1.B 111.24.8.2.A 111.24.8.2.D 111.24.8.3.B 111.24.8.5.B 111.24.8.7.B 111.24.8.8.A 111.24.8.8.C 111.24.8.9.A 111.24.8.9.B 111.24.8.11.A 111.24.8.14.B 111.24.8.14.C 111.24.8.14.D 111.23.7.1.B 111.23.7.1.C 111.23.7.2.A 111.23.7.2.C 111.23.7.2.E 111.23.7.4.B 111.23.7.4.C 111.23.7.5.A 111.23.7.5.B 111.23.7.7.A 111.23.7.7.B 111.23.7.8.A 111.23.7.8.B 111.23.7.11.A 10
ReadiStep Aligned Skill Category and Description of Skills Grade Strand Performance Expectations : Students can create and use representations to organize, record and communicate mathematical ideas. They can select, apply and translate among mathematical representations, including the verbal, numerical, symbolic and graphical, to solve problems. : Students can recognize reasoning and proof as fundamental aspects of mathematics. They can make and investigate mathematical conjectures, and they can develop and evaluate mathematical arguments and proofs. They can use what they know and build a logical progression of statements to explore the truth of their conjectures. They can break things down into cases, can recognize and use counterexamples, and use logic to justify their conclusions. Connections: Students can recognize and use connections among different areas in mathematics, particularly between geometry and algebra. They can understand how mathematical ideas interconnect and build on one another to produce a coherent whole. They can also recognize and apply mathematics in applied contexts. Underlying processes and mathematical tools. Number, operation, and quantitative reasoning. Patterns, relationships, and algebraic thinking. Geometry and spatial reasoning. Measurement. Probability and statistics. Number, operation, and quantitative reasoning. Patterns, relationships, and algebraic thinking. Geometry and spatial reasoning. Probability and statistics. Underlying processes and mathematical tools. Number, operation, and quantitative reasoning. Patterns, relationships, and algebraic thinking. Geometry and spatial reasoning. Measurement. Probability and statistics. Underlying processes and mathematical tools. Number, operation, and quantitative reasoning. Measurement. Underlying processes and mathematical tools. Geometry and spatial reasoning. Measurement. 111.23.7.14.B 111.24.8.1.A 111.24.8.1.C 111.24.8.1.D 111.24.8.2.D 111.24.8.4.A 111.24.8.5.A 111.24.8.6.A 111.24.8.6.B 111.24.8.7.A 111.24.8.7.C 111.24.8.7.D 111.24.8.8.A 111.24.8.11.C 111.24.8.12.C 111.23.7.1.A 111.23.7.2.F 111.23.7.2.G 111.23.7.4.A 111.23.7.6.B 111.23.7.6.C 111.23.7.11.B 111.23.7.12.B 111.23.7.13.C 111.23.7.15.A 111.23.7.15.B 111.24.8.2.A 111.24.8.2.B 111.24.8.2.C 111.24.8.3.A 111.24.8.5.A 111.24.8.7.C 111.24.8.10.A 111.24.8.10.B 111.24.8.11.B 111.24.8.12.A 111.24.8.12.B 111.24.8.13.A 111.24.8.13.B 111.24.8.14.C 111.24.8.15.B 111.24.8.16.A 111.24.8.16.B 111.23.7.2.C 111.23.7.9.B 111.23.7.13.A 111.24.8.7.B 111.24.8.8.B 11
ReadiStep Aligned Skill Category and Description of Skills Grade Strand Performance Expectations Communication: Students can use the definitions, symbols and notation of mathematics to express mathematical ideas precisely. They can organize and consolidate their mathematical thinking through communication. They can communicate their mathematical thinking coherently and clearly. They can analyze and evaluate the mathematical thinking and strategies of others. Underlying processes and mathematical tools. Patterns, relationships, and algebraic thinking. Geometry and spatial reasoning. Probability and statistics. Underlying processes and mathematical tools. Number, operation, and quantitative reasoning. Patterns, relationships, and algebraic thinking. Geometry and spatial reasoning. Measurement. Probability and statistics. Underlying processes and mathematical tools. 111.24.8.14.A 111.23.7.4.C 111.23.7.6.A 111.23.7.6.B 111.23.7.6.C 111.23.7.6.D 111.23.7.7.A 111.23.7.10.A 111.23.7.12.A 111.23.7.12.B 111.23.7.14.A 111.23.7.14.B 111.24.8.1.E 111.24.8.5.B 111.24.8.7.D 111.24.8.10.A 111.24.8.10.B 111.24.8.12.A 111.24.8.12.B 111.24.8.15.A 111.24.8.16.B 12
Table 7: PSAT/NMSQT and SAT Mathematics Alignment PSAT/NMSQT and SAT Aligned Skill Category and Description of Skills Course Strand Performance Expectations Number & Operations: Students can understand numbers, number systems and operations. They can do arithmetic word problems, including those involving percent, ratio and proportion. They know properties of integers and elementary number theory. They can compute fluently with real numbers, including rational numbers expressed in fraction and in decimal form. They can solve problems involving sets and problems involving sequences and series. : Students can understand, write and simplify algebraic expressions, including those involving exponents. They can solve linear, quadratic, rational and radical equations, as well as systems of equations and inequalities. They are familiar with the concept of function and with functional notation and can use mathematical models to represent and understand quantitative relationships. They can work with absolute value as well as with direct and inverse variation. They can use algebra to solve word problems. Mathematical Models with Applications (5) The student uses functional relationships to solve problems related to personal income. (7) The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. 111.36.M.5.B 111.36.M.7.A 111.36.M.7.B 111.36.M.7.C Algebra I Foundations for functions. 111.32.A.1.A 111.32.A.1.B 111.32.A.1.C 111.32.A.1.D 111.32.A.1.E 111.32.A.2.A 111.32.A.2.B 111.32.A.2.C 111.32.A.3.A 111.32.A.3.B 111.32.A.4.A 111.32.A.4.B 111.32.A.4.C Linear functions. 111.32.A.5.A 111.32.A.5.B 111.32.A.5.C 111.32.A.6.A 111.32.A.6.B 111.32.A.6.C 111.32.A.6.D 111.32.A.6.E 111.32.A.6.F 111.32.A.6.G 111.32.A.7.A 111.32.A.7.B 111.32.A.7.C 111.32.A.8.A 111.32.A.8.B 111.32.A.8.C Quadratic and other nonlinear functions. 111.32.A.9.A 111.32.A.9.B 111.32.A.9.C 111.32.A.9.D 111.32.A.10.A 111.32.A.10.B 111.32.A.11.A 111.32.A.11.B 111.32.A.11.C Geometry Geometric patterns. 111.34.G.5.A Dimensionality and the geometry of location. 111.34.G.7.B Algebra II Foundations for functions. 111.33.2A.1.A 111.33.2A.1.B 111.33.2A.2.A 111.33.2A.3.A 111.33.2A.3.B 111.33.2A.3.C Algebra and geometry. 111.33.2A.4.A 111.33.2A.4.B 111.33.2A.4.C 111.33.2A.5.A 111.33.2A.5.B 13
PSAT/NMSQT and SAT Aligned Skill Category and Description of Skills Course Strand Performance Expectations : Students can understand, write and simplify algebraic expressions, including those involving exponents. They can solve linear, quadratic, rational and radical equations, as well as systems of equations and inequalities. They are familiar with the concept of function and with functional notation and can use mathematical models to represent and understand quantitative relationships. They can work with absolute value as well as with direct and inverse variation. They can use algebra to solve word problems. Precalculus Mathematical Models with Applications Quadratic and square root functions. Rational functions. Exponential and logarithmic functions. (1) The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise defined functions. (2) The student interprets the meaning of the symbolic representations of functions and operations on functions to solve meaningful problems. (3) The student uses functions and their properties, tools and technology, to model and solve meaningful problems. (4) The student uses sequences and series as well as tools and technology to represent, analyze, and solve real life problems. (5) The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations. (1) The student uses a variety of strategies and approaches to solve both routine and non routine problems. (5) The student uses functional relationships to solve problems related to personal income. (6) The student uses algebraic formulas, graphs, and amortization models to solve 111.33.2A.5.C 111.33.2A.5.D 111.33.2A.5.E 111.33.2A.6.A 111.33.2A.6.B 111.33.2A.6.C 111.33.2A.7.A 111.33.2A.7.B 111.33.2A.8.A 111.33.2A.8.B 111.33.2A.8.C 111.33.2A.8.D 111.33.2A.9.A 111.33.2A.9.B 111.33.2A.9.C 111.33.2A.9.D 111.33.2A.9.E 111.33.2A.9.F 111.33.2A.9.G 111.33.2A.10.A 111.33.2A.10.B 111.33.2A.10.C 111.33.2A.10.D 111.33.2A.10.E 111.33.2A.10.F 111.33.2A.10.G 111.33.2A.11.A 111.33.2A.11.B 111.33.2A.11.C 111.33.2A.11.D 111.33.2A.11.E 111.33.2A.11.F 111.35.P.1.A 111.35.P.1.B 111.35.P.1.C 111.35.P.1.D 111.35.P.1.E 111.35.P.2.A 111.35.P.2.B 111.35.P.2.C 111.35.P.3.A 111.35.P.3.B 111.35.P.3.C 111.35.P.3.D 111.35.P.4.A 111.35.P.4.B 111.35.P.5.A 111.35.P.5.B 111.36.M.1.A 111.36.M.1.B 111.36.M.1.C 111.36.M.5.A 111.36.M.5.B 111.36.M.5.C 111.36.M.6.A 111.36.M.6.B 14
PSAT/NMSQT and SAT Aligned Skill Category and Description of Skills Course Strand Performance Expectations : Students can understand, write and simplify algebraic expressions, including those involving exponents. They can solve linear, quadratic, rational and radical equations, as well as systems of equations and inequalities. They are familiar with the concept of function and with functional notation and can use mathematical models to represent and understand quantitative relationships. They can work with absolute value as well as with direct and inverse variation. They can use algebra to solve word problems. : Students can analyze characteristics and properties of points, lines and angles in the plane as well as of two and threedimensional geometric shapes. They can solve problems involving length, area and volume. They know and can apply the Pythagorean Theorem as well as special properties of isosceles, equilateral and right triangles. They can work with geometric figures in the coordinate plane and are familiar with the concepts of slope and similarity. They can develop mathematical arguments about geometric relationships. problems involving credit. (7) The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. (8) The student uses algebraic and geometric models to describe situations and solve problems. 111.36.M.6.C 111.36.M.7.A 111.36.M.7.B 111.36.M.7.C 111.36.M.8.B 111.36.M.8.C Geometry Geometric structure. 111.34.G.1.A 111.34.G.1.B 111.34.G.1.C 111.34.G.2.A 111.34.G.2.B 111.34.G.3.A 111.34.G.3.B 111.34.G.3.C 111.34.G.3.D 111.34.G.3.E 111.34.G.4.A 111.34.G.5.A 111.34.G.5.B 111.34.G.5.C 111.34.G.5.D Dimensionality and the geometry of location. 111.34.G.6.A 111.34.G.6.B 111.34.G.6.C 111.34.G.7.A 111.34.G.7.B 111.34.G.7.C Congruence and the geometry of size. 111.34.G.8.A 111.34.G.8.B 111.34.G.8.C 111.34.G.8.D 111.34.G.8.E 111.34.G.8.F 111.34.G.9.A 111.34.G.9.B 111.34.G.9.C 111.34.G.9.D 111.34.G.10.A 111.34.G.10.B Similarity and the geometry of shape. 111.34.G.11.A 111.34.G.11.B 111.34.G.11.C 111.34.G.11.D Algebra II Algebra and geometry. 111.33.2A.5.A 111.33.2A.5.B 111.33.2A.5.C Precalculus (1) The student defines functions, describes 111.35.P.1.C characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise defined functions. (2) The student interprets the meaning of the symbolic representations of functions and operations of functions to solve meaningful problems. 111.35.P.2.A 15
PSAT/NMSQT and SAT Aligned Skill Category and Description of Skills Course Strand Performance Expectations : Students can analyze characteristics and properties of points, lines and angles in the plane as well as of two and threedimensional geometric shapes. They can solve problems involving length, area and volume. They know and can apply the Pythagorean Theorem as well as special properties of isosceles, equilateral and right triangles. They can work with geometric figures in the coordinate plane and are familiar with the concepts of slope and similarity. They can develop mathematical arguments about geometric relationships. Data, Statistics & Probability: Students can understand and interpret data displayed in tables and graphs, including bar graphs, circle graphs, histograms and scatterplots. They can evaluate inferences and predictions that are based on data. They can understand and use descriptive statistics, including the mean, median and mode. They can apply basic concepts of probability to solve problems. : Students can solve problems that arise in abstract as well as real contexts. They can apply and adapt a variety of appropriate strategies to solve problems, including both routine and nonroutine problems. They can monitor their process as they work toward the solution to a problem, and they can evaluate their answer in terms of the original question asked. Mathematical Models with Applications (5) The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations. (8) The student uses algebraic and geometric models to describe situations and solve problems. (9) The student uses algebraic and geometric models to represent patterns and structures. 111.35.P.5.A 111.36.M.8.A 111.36.M.9.A 111.36.M.9.B Algebra I Foundations for functions. 111.32.A.1.B 111.32.A.2.D Algebra II Foundations for functions. 111.33.2A.1.B Mathematical Models with Applications (2) The student uses graphical and numerical techniques to study patterns and analyze data. (3) The student develops and implements a plan for collecting and analyzing data (qualitative and quantitative) in order to make decisions. (4) The student uses probability models to describe everyday situations involving chance. (5) The student uses functional relationships to solve problems related to personal income. 111.36.M.2.A 111.36.M.2.B 111.36.M.2.C 111.36.M.2.D 111.36.M.3.A 111.36.M.3.B 111.36.M.3.C 111.36.M.4.A 111.36.M.4.B 111.36.M.5.C Algebra I Foundations for functions. 111.32.A.4.A Linear functions. 111.32.A.5.B 111.32.A.6.E 111.32.A.6.G 111.32.A.7.B 111.32.A.8.B Quadratic and other nonlinear functions. 111.32.A.10.A Geometry Geometric patterns. 111.34.G.5.D Congruence and the geometry of size. 111.34.G.8.A 111.34.G.8.B 111.34.G.8.C 111.34.G.8.D 111.34.G.10.B Similarity and the geometry of shape. 111.34.G.11.B 111.34.G.11.C Algebra II Foundations for functions. 111.33.2A.1.A 111.33.2A.3.B Quadratic and square root functions. 111.33.2A.6.A 111.33.2A.8.B 111.33.2A.8.D 111.33.2A.9.C 111.33.2A.9.D 111.33.2A.9.E 111.33.2A.9.F Rational functions. 111.33.2A.10.C 111.33.2A.10.D 111.33.2A.10.E 111.33.2A.10.F Exponential and logarithmic functions. 111.33.2A.11.C 111.33.2A.11.D 111.33.2A.11.E 111.33.2A.11.F Precalculus (1) The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, 111.35.P.1.B 16
PSAT/NMSQT and SAT Aligned Skill Category and Description of Skills Course Strand Performance Expectations : Students can solve problems that arise in abstract as well as real contexts. They can apply and adapt a variety of appropriate strategies to solve problems, including both routine and nonroutine problems. They can monitor their process as they work toward the solution to a problem, and they can evaluate their answer in terms of the original question asked. : Students can create and use representations to organize, record and communicate mathematical ideas. They can select, apply and translate among mathematical representations, including the verbal, numerical, symbolic and graphical, to solve problems. Mathematical Models with Applications trigonometric, and piecewise defined functions. (2) The student interprets the meaning of the symbolic representations of functions and operations of functions to solve meaningful problems. (4) The student uses sequences and series as well as tools and technology to represent, analyze, and solve real life problems. (6) The student uses vectors to model physical situations. (1) The student uses a variety of strategies and approaches to solve both routine and non routine problems. (5) The student uses functional relationships to solve problems related to personal income. (8) The student uses algebraic and geometric models to describe situations and solve problems. 111.35.P.2.B 111.35.P.4.B 111.35.P.6.B 111.36.M.1.A 111.36.M.1.B 111.36.M.1.C 111.36.M.5.A 111.36.M.5.B 111.36.M.8.B Algebra I Foundations for functions. 111.32.A.1.B 111.32.A.1.C 111.32.A.1.D 111.32.A.2.A 111.32.A.3.A 111.32.A.3.B 111.32.A.4.A Linear functions. 111.32.A.5.C 111.32.A.6.D 111.32.A.6.F 111.32.A.7.A 111.32.A.7.B 111.32.A.8.A 111.32.A.8.B Quadratic and other nonlinear functions. 111.32.A.9.B 111.32.A.9.C 111.32.A.10.A 111.32.A.11.B 111.32.A.11.C Geometry Geometric structure. 111.34.G.4.A Geometric patterns. 111.34.G.5.A Dimensionality and the geometry of location. 111.34.G.6.A 111.34.G.6.B 111.34.G.6.C 111.34.G.7.A Algebra II Foundations for functions. 111.33.2A.1.B 111.33.2A.2.A 111.33.2A.3.A 111.33.2A.3.B Algebra and geometry. 111.33.2A.4.A 111.33.2A.5.B 111.33.2A.5.E Quadratic and square root functions. 111.33.2A.6.C 111.33.2A.7.A 111.33.2A.8.A 111.33.2A.8.D 111.33.2A.9.D 111.33.2A.9.E 111.33.2A.9.F Rational functions. 111.33.2A.10.B 111.33.2A.10.D 111.33.2A.10.E 111.33.2A.10.F 111.33.2A.10.G 17
PSAT/NMSQT and SAT Aligned Skill Category and Description of Skills Course Strand Performance Expectations : Students can create and use representations to organize, record and communicate mathematical ideas. They can select, apply and translate among mathematical representations, including the verbal, numerical, symbolic and graphical, to solve problems. : Students can recognize reasoning and proof as fundamental aspects of mathematics. They can make and investigate mathematical conjectures, and they can develop and evaluate mathematical arguments and proofs. They can use what they know and build a logical progression of statements to explore the truth of their conjectures. They can break things down into cases, can recognize and use counterexamples, and use logic to justify their conclusions. Precalculus Mathematical Models with Applications Exponential and logarithmic functions. (1) The student defines functions, describes characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise defined functions. (2) The student interprets the meaning of the symbolic representations of functions and operations of functions to solve meaningful problems. (3) The student uses functions and their properties, tools and technology, to model and solve meaningful problems. (4) The student uses sequences and series as well as tools and technology to represent, analyze, and solve real life problems. (5) The student uses conic sections, their properties, and parametric representations, as well as tools and technology, to model physical situations. (6) The student uses vectors to model physical situations. (2) The student uses graphical and numerical techniques to study patterns and analyze data. (6) The student uses algebraic formulas, graphs, and amortization models to solve problems involving credit. (8) The student uses algebraic and geometric models to describe situations and solve problems. 111.33.2A.11.D 111.33.2A.11.E 111.33.2A.11.F 111.35.P.1.B 111.35.P.1.D 111.35.P.2.A 111.35.P.3.B 111.35.P.3.C 111.35.P.4.A 111.35.P.5.A 111.35.P.5.B 111.35.P.6.A 111.36.M.2.D 111.36.M.6.B 111.36.M.6.C 111.36.M.8.A 111.36.M.8.B 111.36.M.8.C Algebra I Foundations for functions. 111.32.A.1.E 111.32.A.2.B 111.32.A.2.C 111.32.A.2.D 111.32.A.4.B Linear functions. 111.32.A.5.A 111.32.A.6.B 111.32.A.6.C 111.32.A.6.F 111.32.A.7.A 111.32.A.7.B 111.32.A.7.C 111.32.A.8.A 111.32.A.8.C 111.32.A.9.B 111.32.A.9.C 111.32.A.9.D Quadratic and other nonlinear functions. 111.32.A.11.A 111.32.A.11.B 111.32.A.11.C Geometry Geometric structure. 111.34.G.1.C 111.34.G.2.A 111.34.G.2.B 111.34.G.3.A 18
PSAT/NMSQT and SAT Aligned Skill Category and Description of Skills Course Strand Performance Expectations : Students can recognize reasoning and proof as fundamental aspects of mathematics. They can make and investigate mathematical conjectures, and they can develop and evaluate mathematical arguments and proofs. They can use what they know and build a logical progression of statements to explore the truth of their conjectures. They can break things down into cases, can recognize and use counterexamples, and use logic to justify their conclusions. 111.34.G.3.B 111.34.G.3.C 111.34.G.3.D 111.34.G.3.E Geometric patterns. 111.34.G.5.A 111.34.G.5.B Dimensionality and the geometry of location. 111.34.G.7.B 111.34.G.7.C Congruence and the geometry of size. 111.34.G.8.C 111.34.G.8.F 111.34.G.9.A 111.34.G.9.B 111.34.G.9.C 111.34.G.9.D 111.34.G.10.A 111.34.G.10.B Similarity and the geometry of shape. 111.34.G.11.A 111.34.G.11.D Algebra II Foundations for functions. 111.33.2A.1.B 111.33.2A.2.A 111.33.2A.3.A 111.33.2A.3.C Algebra and geometry. 111.33.2A.4.C 111.33.2A.5.B 111.33.2A.5.C 111.33.2A.5.E Quadratic and square root functions. 111.33.2A.6.A 111.33.2A.7.B 111.33.2A.8.A 111.33.2A.8.B 111.33.2A.8.C 111.33.2A.9.A 111.33.2A.9.C 111.33.2A.9.F Rational functions. 111.33.2A.10.A 111.33.2A.10.B 111.33.2A.10.C 111.33.2A.10.F 111.33.2A.10.G Exponential and logarithmic functions. 111.33.2A.11.A 111.33.2A.11.B 111.33.2A.11.C 111.33.2A.11.F Precalculus (1) The student defines functions, describes 111.35.P.1.E characteristics of functions, and translates among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise defined functions. (2) The student interprets the meaning of the symbolic representations of functions and operations of functions to solve meaningful problems. 111.35.P.2.C Mathematical Models with Applications (3) The student uses functions and their properties, tools and technology, to model and solve meaningful problems. (1) The student uses a variety of strategies and approaches to solve both routine and non routine problems. (2) The student uses graphical and numerical techniques to study patterns and analyze 111.35.P.3.A 111.35.P.3.C 111.35.P.3.D 111.36.M.1.A 111.36.M.1.C 111.36.M.2.A 111.36.M.2.B 19
PSAT/NMSQT and SAT Aligned Skill Category and Description of Skills Course Strand Performance Expectations : Students can recognize reasoning and proof as fundamental aspects of mathematics. They can make and investigate mathematical conjectures, and they can develop and evaluate mathematical arguments and proofs. They can use what they know and build a logical progression of statements to explore the truth of their conjectures. They can break things down into cases, can recognize and use counterexamples, and use logic to justify their conclusions. Connections: Students can recognize and use connections among different areas in mathematics, particularly between geometry and algebra. They can understand how mathematical ideas interconnect and build on one another to produce a coherent whole. They can also recognize and apply mathematics in applied contexts. data. 111.36.M.2.C (3) The student develops and implements a plan for collecting and analyzing data 111.36.M.3.A 111.36.M.3.C (qualitative and quantitative) in order to make decisions. (4) The student uses probability models to describe everyday situations involving chance. 111.36.M.4.A 111.36.M.4.B (5) The student uses functional relationships 111.36.M.5.C to solve problems related to personal income. (6) The student uses algebraic formulas, graphs, and amortization models to solve problems involving credit. 111.36.M.6.A 111.36.M.6.B 111.36.M.6.C (7) The student uses algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. 111.36.M.7.A 111.36.M.7.B 111.36.M.7.C Algebra I Foundations for functions. 111.32.A.1.B 111.32.A.4.C Linear functions. 111.32.A.5.C 111.32.A.6.A 111.32.A.6.C 111.32.A.6.E 111.32.A.6.G Quadratic and other nonlinear functions. 111.32.A.10.B Geometry Geometric structure. 111.34.G.1.A Geometric patterns. 111.34.G.5.C Dimensionality and the geometry of location. 111.34.G.7.A 111.34.G.7.B Congruence and the geometry of size. 111.34.G.8.E Algebra II Algebra and geometry. 111.33.2A.4.B Quadratic and square root functions. 111.33.2A.6.B 111.33.2A.6.C 111.33.2A.7.A 111.33.2A.7.B 111.33.2A.8.C 111.33.2A.9.A 111.33.2A.9.B 111.33.2A.9.G Exponential and logarithmic functions. 111.33.2A.11.B Precalculus (1) The student defines functions, describes 111.35.P.1.D characteristics of functions, and translates 111.35.P.1.E among verbal, numerical, graphical, and symbolic representations of functions, including polynomial, rational, power (including radical), exponential, logarithmic, trigonometric, and piecewise defined functions. Mathematical Models with Applications (2) The student interprets the meaning of the symbolic representations of functions and operations of functions to solve meaningful problems. (5) The student uses conic sections, their properties, and parametric representations as well as tools and technology to model physical situations (5) The student uses functional relationships to solve problems related to personal income. 111.35.P.2.A 111.35.P.2.C 111.35.P.5.A 111.35.P.5.B 111.36.M.5.A 20