Elementary Statistics: Picturing the World, 8e, Texas Edition

Evaluation for 1.1a
Materials include a scope and sequence outlining the TEKS, ELPS, and concepts taught in the course.

The materials include a scope and sequence that outlines the concepts taught in the course, but scope and sequence does not address the TEKS or the ELPS. Within the MyLab digital platform’s instructor tools and resources, the pacing and activity guide outlines the math concepts by chapter and section. This guide schedules the instructional course content by providing a weekly chapter focus and a list of topics covered per class meeting. For example, the “Descriptive Statistics” (weeks 3–5) table in chapter 2 itemizes the chronological order of lessons and explicitly shows when frequency distributions are taught.

The materials reference the Mathematical Association of America (MAA), American Association of Two-Year Colleges (AMATYC), and National Council of Teachers of Mathematics (NCTM) standards rather than the TEKS or the ELPS. While the lessons include multilingual learner supports (MLS)—listing specific English language learner (ELL) activities and designating them as listening, writing, or speaking activities—the pacing and activity guide omits any reference to these linguistic standards.

Evaluation for 1.1b
Materials include suggested pacing (pacing guide/calendar) to support effective implementation for various instructional calendars (e.g., varying numbers of instructional days - 165, 180, 210).

The materials include suggested pacing to support effective implementation. Within MyLab, a pacing guide maps a chapter-by-chapter progression from chapter 1 through chapter 11. The Pacing and Activity Guide organizes the course into four parts: “Descriptive Statistics,” “Probability and Probability Distribution,” “Statistical Inference,” and “More Statistical Inference.” Each part identifies the corresponding chapters, objectives, suggested pacing, and weekly instructional timeframes. The companion guide further directs teachers to use the Pacing and Activity Guide when reviewing suggested pacing, lesson objectives, instructional activities, differentiated instruction, multilingual learner supports, and assessments during instructional planning.

The materials do not include various instructional calendars, including at least two instructional calendars, aligned to differing instructional-day totals, such as 165, 180, or 210 instructional days. The materials do provide multiple pacing options through scheduling tracks that assign recommended quantities of instructional days to content sections, chapter reviews, and cumulative tests. Within chapters and weekly plans, the Pacing and Activity Guide includes alternative pacing options, educator notes for flex and review days, and guidance for combining lessons or adjusting day allocations. For example, the materials provide recommendations for reducing multi-day topics to single-day blocks and shortening or omitting advanced topics when instructional time is limited.

Evaluation for 1.1c
Materials include an explanation for the rationale of unit order as well as how concepts to be learned connect throughout the course.

Introductory components, such as “Where You’ve Been” and “Where You’re Going,” at the start of each chapter demonstrate connection pathways across units. For example, chapter 6 introduces confidence intervals, which serve as a foundation for the single‑sample hypothesis testing developed in chapter 7. Chapter 8 then builds on both of these concepts by extending hypothesis testing to two samples, and chapter 9 connects these ideas to comparing multiple populations and analyzing relationships between ordered pairs.

The materials do not include an explicit rationale for the sequence of the units. Within MyLab, the pacing and activity guide provides alternative pacing directives to support instructor focus rather than a structural justification for the course layout. For example, the week 11 notes direct educators to omit one class by substituting technology for hand calculations and to omit a subsequent class by prioritizing standard deviation over variance and interpreting binomial distribution graphs over constructing them. Together, these features show that the materials support conceptual connections across chapters but do not provide a rationale for the sequence of the units.

Evaluation for 1.1d
Materials include protocols with corresponding guidance for unit and lesson internalization.

On the lesson level, the pacing and activity guide within MyLab provides pacing, objectives, and activities for each section to support internalization. These materials include structured chapter pacing and activity overviews within the educator resource guide that serve as an internalization protocol to support lesson preparation. For individual daily lesson design, the guide includes preplanned differentiated‑instruction activities tailored to specific student proficiency levels, such as foundational and advanced tracks. Additionally, the guide includes educator notes, common misconceptions, and MLS—such as explicit “ELL Activities” designated as listening, writing, or speaking—to assist the educator with lesson internalization.

The materials include protocols with corresponding guidance for unit internalization. The Texas High School Implementation and Planning Companion provides a recommended planning process that directs educators to review the TEKS correlation, ELPS correlation, pacing and activity guide, instructional resources, and assessment resources when preparing instruction. In section 2, “Preparing for Each Unit,” educators review the instructional sequence, chapter objectives, suggested pacing, mathematical background, differentiated instruction, multilingual learner supports, teaching tips, common misconceptions, classroom activities, and assessments before instruction. Additionally, the “Recommended Lesson Preparation Process” outlines steps for reviewing prerequisite knowledge, selecting instructional resources, and examining assessment opportunities prior to teaching.

Evaluation for 1.1e
Materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed.

Within the MyLab digital platform, the “Training & Implementation” tab under “Instructor Tools” includes educator-facing materials, such as how-to videos, recorded online training sessions, and implementation practices for instructors using the software. Additionally, the pacing and activity guide provides educator-facing lesson plans and planning materials designed exclusively for classroom educators. These resources support teachers with implementing the materials and provide instructional planning and implementation guidance.

The materials include resources and guidance for instructional leaders to support teachers with implementing the materials as designed. In section 3, “Supporting Instructional Leadership,” the companion guide provides a leadership support cycle for department chairs, instructional coaches, curriculum specialists, and campus administrators. Leaders use the TEKS Correlation to confirm lesson alignment, the Pacing & Activity Guide to review pacing, objectives, instructional supports, and assessments, and chapter assessments, TestGen, and MyLab reports to analyze student performance. Additionally, the guide includes collaborative reflection guidance and coaching reflection questions that support classroom observation, instructional decision-making, and continuous improvement.

Evaluation for 1.2a
Materials include comprehensive unit overviews that provide the background content knowledge and academic vocabulary necessary to effectively teach the concepts in the unit.

Within the pacing and activity guide, each chapter overview contains a “Suggested Approach” section with a dedicated “Math Background” summary that explains prerequisite content and maps out current and upcoming chapters. For example, the chapter 5 overview (“Normal Probability Distributions”) details how the upcoming content connects vertically to chapter 4 topics, noting that students previously studied discrete probability distributions, discrete and continuous random variables, binomial probabilities, geometric distributions, and Poisson distributions. The overview then details current learning—such as normal curves, z-scores, and the Central Limit Theorem—before outlining chapter 6 skills, such as confidence intervals for means, variance, and standard deviation.

The chapter overviews explicitly embed the mathematical academic vocabulary necessary for the unit, along with guided instruction and chapter flash cards. The materials integrate academic vocabulary through lesson procedures and MLS. For example, the chapter 5 overview targets terminology, including discrete and continuous random variables, normal probability distributions, standard normal distribution, z-score, x-value, sampling distributions, Central Limit Theorem, and binomial probabilities.

Evaluation for 1.2b
Materials contain supports for families in both Spanish and English for each unit with suggestions on supporting the progress of their student.

The materials provide families with support in English and Spanish for each unit, including suggestions to help their students’ progress. In the pacing and activity guide, a dedicated “Parent Letters” section features identical parallel letters for each chapter. These documents provide families with an overview of the curriculum objectives, along with a dedicated section outlining concrete methods to reinforce learning at home. For example, chapter 2 includes identical parent-facing letters in both languages to keep families informed of unit goals.

The family letters provide specific, unit-aligned suggestions to support student progress in both languages. For example, chapter 5 outlines curriculum objectives, such as the “Central Limit Theorem” and normal approximations, and features a “How You Can Help Your Student” section in the English letter, titled “Dear Parents and Guardians.” This component provides actionable guidance, such as prompting students to explain mathematical processes aloud and encouraging them to complete “Try It Yourself” and exercise set problems. The exact parallel Spanish family letter, titled “Estimados padres y tutores,” outlines the same normal probability distribution (“distribuciones de probabilidad normales”) objectives. It includes an identical “Cómo puede ayudar a su hijo” (“How You Can Help Your Child”) section with unit-specific suggestions, such as asking the student to explain how to find the area under a standard normal curve or to find real-world articles that contain a population mean and standard deviation to calculate a z-score.

Evaluation for 1.3a
Materials include comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments required to meet the content and language standards of the lesson (aligned with the TEKS and the ELPS).

The materials include comprehensive, structured lesson plans with daily objectives, questions, tasks, materials, and instructional assessments. The Pacing and Activity Guide provides section-level objectives through the “What You Should Learn” feature and includes exercises scaffolded as “Building Basic Skills and Vocabulary,” “Using and Interpreting Concepts,” and “Extending Concepts.” In Chapter 8, “Hypothesis Testing with Two Samples,” the planning framework maps daily instruction with objectives, tasks, materials, and embedded assessments. For example, in Section 8.1, objectives require students to distinguish between independent and dependent samples and perform two-sample z-tests. Instructional questions and activities directly align to these objectives by having students classify sample pairs, develop hypotheses, calculate test statistics, and interpret results from real-world datasets. These application tasks serve as embedded assessments of the stated objectives and are further supported by Chapter Summaries, Review Exercises, Chapter Quizzes, Chapter Tests, and daily skills checks.

The materials do not have comprehensive, structured, detailed lesson plans that include daily objectives, questions, tasks, materials, and instructional assessments aligned with the TEKS and the ELPS. Although the materials include a “Math Process Standards” section highlighting student communication and justification of mathematical ideas, the lesson plans fail to include explicit TEKS correlations anywhere within the section plans, tables, or unit overviews. Furthermore, while the curriculum provides language supports through its dedicated MLS activities for novice, developing, and advanced learners, the lesson plans do not formally identify, cross-reference, or tag the specific ELPS associated with those tasks.

Evaluation for 1.3b
Materials include a lesson overview listing the teacher and student materials necessary to effectively deliver the lesson, and the suggested timing for each lesson component.

The lesson overviews list the educator and student materials needed to deliver the lesson effectively, as well as the suggested timing for each component. Within the pacing and activity guide and individual daily section plans, the materials feature structured, standalone tasks—such as the “Split-Second Differences” and “Data Detectives” activities in chapter 2—that outline the classroom resources and instructional guidance required for instruction. Under the specific material headings, the planner lists explicit item requirements for the educator and the student, including stopwatches, sample data sheets, answer keys, index cards, rulers, graphing calculators, normal curve sketches, and designated t-distribution tables.

The lesson overviews explicitly detail the recommended time allocations for each component to ensure that educators can manage instruction. In the activity guides, each lesson component is broken down into minutes to support pacing throughout the standard class period. For example, the “Split-Second Differences” activity details strict time limits for each part of the lesson cycle, allocating five minutes for the warm-up, 15 minutes for guided instruction, 25 minutes for the activity/independent practice, and five minutes for the closure.

Evaluation for 1.3c
Materials include guidance on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment).

The materials include guidance for educators on the effective use of lesson materials for extended practice (e.g., homework, extension, enrichment). The MyLab Statistics digital platform includes resources that provide educators with explicit strategies for selecting and managing targeted digital materials based on student performance. The platform includes customizable assignment settings, adaptive study plans, an automated gradebook, and interactive STEM activities that educators can assign for personalized homework, remediation, or enrichment. These tools provide instructors with active strategies for monitoring student mastery and adapting tasks, avoiding unguided or generic practice routines.

The materials incorporate specific homework, enrichment, and extension assets across both print and digital components to support extended learning. In the student eText chapter review, the curriculum includes a “Review Exercises” section with computational and conceptual problems, as well as individual online learning assignments and a skills review in the MyLab Statistics platform. Additionally, the pacing and activity guide and “Statistics with Integrated Review” section in MyLab highlight supplemental resources for advanced tracks. The materials explicitly guide educators to extended learning options. For example, in chapter 11, “Nonparametric Statistics,” the materials state that an extended learning option “is available online as supplemental material for enrichment,” thereby providing targeted academic pathways based on student needs.

Evaluation for 2.1a
Materials include a variety of instructional assessments at the unit and lesson level (including diagnostic, formative, and summative) that vary in types of tasks and questions.

The materials provide lesson-level formative assessments through section exercises, “Try It Yourself” tasks, and application-based activities that progress from foundational skill development to real-world problem-solving. For example, in chapter 5, section 5.2, exercises 27–32 require direct symbolic probability calculations, while exercises 33 and 34 present multipart, real-world scenarios using Environmental Protection Agency data that require interpretation, multistep reasoning, and the use of technology. At the unit level, chapter tests serve as summative assessments that evaluate student understanding across concepts. Additional assessment opportunities include case studies, technology labs, and cumulative activities, such as “Real Statistics, Real Decisions: Putting It All Together,” which engage students in analyzing authentic data and applying statistical reasoning across varied contexts.

The materials do not include diagnostic assessments at the unit and lesson level that vary in types of tasks and questions. While the materials include quizzes, study plans, and review assignments within the online platform, these tools function as brief prerequisite checks or practice opportunities rather than comprehensive diagnostic assessments. The available checks rely primarily on standard digital question formats and do not include a range of task types, such as open-ended responses, performance-based tasks, or conceptual reasoning prompts needed to identify specific misconceptions or gaps in prerequisite knowledge. In addition, the materials do not provide evidence of assessments designed to systematically measure baseline understanding before instruction begins or to differentiate entry points for instruction.

Evaluation for 2.1b
Materials include the definition and intended purpose for the types of instructional assessments included.

The materials include definitions and intended purposes for the instructional assessments embedded throughout the materials. In the “Review and Assessment” front matter, the materials outline the structure, organization, and purpose of chapter‑level and unit‑level assessments. Chapter summaries are described as aligning objectives with section examples and review exercises, and the chapter review exercises follow the chapter’s organizational structure to reinforce learning. The materials also define the role and format of chapter quizzes, tests, and cumulative reviews, including information about randomized question delivery and the location of solutions in the Annotated Instructor’s Edition and MyLab Statistics platform. In addition, the program explains how exercises are organized into categories, such as “Building Basic Skills and Vocabulary,” “Using and Interpreting Concepts,” and “Extending Concepts,” which establishes a clear progression from foundational understanding to application and extension.

The materials clarify the intended purpose of instructional assessments by connecting them to explicit learning goals and outcomes. Each section includes a “What You Should Learn” feature that defines the specific skills and concepts students are expected to master, which directly align with the content assessed in exercises, quizzes, and tests. For example, in chapter 7, section 7.3, these learning targets identify expectations, such as finding critical values in a t-distribution and conducting hypothesis tests for a population mean when σ is unknown. These clearly stated objectives establish the purpose of assessments as tools to measure mastery of defined skills and concepts. Together, the structural descriptions of assessment types and the alignment to explicit learning goals provide clear definitions and intended purposes for instructional assessments within the program.

Evaluation for 2.1c
Materials include teacher guidance to ensure consistent and accurate administration of instructional assessments.

The materials provide access to assessment tools, such as the TestGen test bank and the MyLab Statistics platform, along with a user’s guide that supports creating assessments, including selecting items and assigning point values. The materials also include multiple assessments with associated student-facing directions and solution sets. However, these resources do not include guidance on consistently administering the program across instructors or settings. The materials do not provide standardized procedures, administration protocols, timing expectations, or directions to ensure that assessments are delivered uniformly. As a result, educators must independently determine how to administer assessments, which does not support consistency in implementation.

The materials do not include educator guidance on ensuring accurate administration of instructional assessments. While the materials include performance analytics tools that allow instructors to monitor student performance through graphs and visualizations, these tools support analysis rather than administration. The resources do not include educator-facing guidance, such as scripts, step-by-step procedures, or directions to support accurate delivery of assessments. Additionally, supports, such as the TestGen user’s guide and digital platform features, focus on assessment construction rather than administration practices. Without explicit guidance to support accurate delivery, including clarification of expectations or procedures during assessment administration, the materials do not ensure accurate implementation of assessments.

Evaluation for 2.1d
Diagnostic, formative, and summative assessments are aligned to the TEKS and objectives of the course, unit, or lesson.

The materials include formative and summative assessments that align to the instructional objectives of the course, unit, and lesson. Lesson-level formative assessments, such as “Try It Yourself” tasks, are aligned with clearly stated learning objectives presented in the “What You Should Learn” sections. For example, in chapter 7, section 7.1, “Try It Yourself 4” requires students to evaluate claim statements and determine whether to reject or fail to reject a null hypothesis, which directly aligns with the lesson objective for hypothesis testing. Unit-level summative assessments, including chapter tests and cumulative exercises, evaluate student mastery of unit objectives. For example, in chapter 9, summative exercises require students to apply multiple linear regression equations to calculate predicted values, demonstrating alignment to unit-level objectives. Additional tools, such as the MyLab Statistics “Study Plan Manager,” support objective-based practice and track mastery of instructional goals.

The materials do not include diagnostic, formative, or summative assessments that are aligned to the TEKS or consistently aligned across the course, unit, and lesson levels. The materials do not reference the TEKS within assessment items and do not provide a correlation between assessments and TEKS expectations, preventing verification of standards alignment. In addition, the materials do not include diagnostic assessments designed to measure baseline understanding prior to instruction or to identify specific student strengths and misconceptions. While the program includes study plans, review assignments, and prerequisite activities, these serve as practice or reinforcement rather than as formal diagnostics aligned with objectives. Without assessments explicitly aligned to the TEKS and without diagnostic assessments aligned to course, unit, or lesson objectives, the materials do not include comprehensive alignment across assessment types.

Evaluation for 2.1e
Instructional assessments include TEKS-aligned items at varying levels of complexity.

The materials include instructional assessments that vary in levels of complexity and types of questions, but these items are not aligned to the TEKS. The materials include a range of assessment formats, including computational tasks, graphing and interpretation items, multiple-choice questions, free-response problems, and real-world application tasks. For example, chapter tests include questions that assess vocabulary, foundational understanding, and higher-level reasoning, requiring students to analyze data and construct solutions. Similarly, the test bank and Pearson Plus platform provide practice sets that include both multiple-choice and open-ended items. These assessments demonstrate a range of complexity, from routine procedures to multistep applications.

Instructional assessments do not include TEKS-aligned items at varying levels of complexity. The materials do not reference the TEKS within assessment items and do not provide correlation or alignment tools that would connect assessment questions to TEKS expectations. Although the assessments include a range of item types and levels of difficulty, the absence of alignment to the TEKS prevents verification that the complexity of the items reflects the progression and rigor of the standards. Without explicit identification of the TEKS for assessment items or documentation linking items to the TEKS, the materials do not meet the requirements for TEKS-aligned assessments at varying levels of complexity.

Evaluation for 2.2a
Instructional assessments and scoring information provide guidance for interpreting student performance.

The materials provide guidance for educators in interpreting student performance through digital tools available in the MyLab Statistics platform, which provides instructor-facing and student-facing gradebooks that display overall score percentages, assignment-level scores, and performance metrics for each assessment. In the student gradebook, users can view individual scores, completion status, and time spent on each assessment, along with visual progress indicators that track performance across assignments. Instructors can access aggregated scoring data through tools, such as the Instructor Gradebook and “Performance by Chapter” reports, which organize results by instructional unit and assessment type. These scoring features provide detailed, accessible information to support the evaluation of student performance across assessments.

The MyLab Statistics platform includes structured reporting tools and embedded support features, such as the “Study Plan Manager,” which explains how to interpret progress data, including visual representations of mastery and completion levels by objective or section. Dashboards and reports present performance analytics, including assignment completion rates, engagement metrics, and trends across chapters, enabling educators to identify patterns in student understanding. In addition, item-level analysis tools allow instructors to review student performance by question, helping to identify strengths, misconceptions, and areas for review. Student-facing features, such as access to completed assessment items and personalized study plan recommendations, further support interpretation by connecting results to targeted practice. Together, these tools provide clear guidance for interpreting student performance and supporting instructional decision-making.

Evaluation for 2.2b
Materials provide guidance for the use of included tasks and activities to respond to student trends in performance on assessments.

The materials provide guidance for educators on using tasks and activities to respond to student performance through adaptive and targeted instructional tools in the MyLab Statistics platform. The tools provide access to adaptive follow-up assignments and dynamic study modules, which are described within the platform’s “Need Help?” resources. These assignments are designed to become available after a “parent” assignment is completed or after the due date has passed and are structured to target areas where students need additional growth and practice. By automatically assigning follow-up tasks based on student performance, the platform ensures that instructional activities are directly connected to assessment results and aligned to student needs.

The materials provide guidance for educators on responding to student performance trends through system-generated recommendations and embedded support features. The MyLab Statistics platform identifies areas in which students “need help” and assigns adaptive activities that address those specific gaps in understanding. In addition, performance analytics tools allow educators to analyze trends, such as averages and performance distributions, while the adaptive system simultaneously delivers targeted practice aligned to those trends. Within the platform, resources explain how these adaptive features function and how they support student learning. The resources also provide guidance on using tasks and activities to address performance data. Together, these features ensure that instructional responses are connected to assessment outcomes and support differentiation based on student performance.

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

Educators track student progress and growth through the reporting and analytics features available in the MyLab Statistics platform. The platform provides access to the Instructor Gradebook and “Performance by Chapter” reports, which organize student performance data by instructional unit and assessment type. These tools allow educators to monitor assignment completion, view average scores across homework, quizzes, and tests, and analyze performance trends over time. In addition, item analysis features enable instructors to review performance on an individual question basis and identify areas of strength and need. Performance analytics tools further support tracking through visualizations, such as score distributions and summary metrics, providing ongoing insight into both individual and class progress across the instructional cycle.

Students track their progress and growth through the MyLab Statistics’ student-facing features. The Student Gradebook allows students to view overall scores, assignment-level results, completion status, and time spent on each assessment, supported by visual indicators, such as progress bars and tracking lines. Students can access completed assignments to review responses and receive support through features, such as “Help Me Solve This,” which supports reflection on errors and next steps. In addition, the platform connects students to personalized study plan recommendations and adaptive practice tools that respond to their performance. These features provide students with continuous access to performance data and feedback, enabling them to monitor their progress, identify areas for improvement, and take ownership of their learning and growth.

Evaluation for 3.1a
Materials include teacher guidance for differentiated instruction, activities, and paired (scaffolded) lessons for students who have not yet reached proficiency on grade-level content and skills.

The materials include scaffolded content supports for students who have not yet reached proficiency through structured activities and targeted instructional guidance. Within the pacing and activity guide, “Differentiated Instruction Activities” and scaffolded lessons provide step-by-step support to help students access grade-level statistical concepts. For example, in chapter 3, section 3.2, “Conditional Probability and the Multiplication Rule,” students build understanding progressively from ratios to simple probabilities and then to conditional probability through structured development of ideas. In chapter 4, section 4.2, “Binomial Distributions,” the materials direct educators to provide a preformatted table with partial calculations so that students can focus on completing the remaining values while developing an understanding of the distribution. These scaffolded activities break complex concepts into manageable steps, supporting conceptual access to grade-level content.

The materials guide educators on supporting skill development for students below proficiency through structured processes and targeted differentiation tools. For example, in chapter 7, section 7.4, the materials direct educators to outline the sequential steps of a Z-test, support interpretation using the rejection region method, and incorporate graphing calculator validation of p-values, building procedural accuracy through scaffolded instruction. Additional supports within the MyLab Statistics platform strengthen skill development through dynamic study modules, which provide adaptive guided practice and generate reports identifying student misconceptions and areas of need. Skills check assessments diagnose prerequisite gaps and allow educators to assign targeted remediation, while “Integrated Review” resources provide structured refreshers aligned to lesson content. Together, these features provide actionable guidance for educators to support the development of procedural and analytical skills for students who have not yet reached proficiency.

Evaluation for 3.1b
Materials include pre-teaching or embedded supports for unfamiliar vocabulary and references in text (e.g., figurative language, idioms, academic language).

Pre-teaching and embedded supports guide educators in teaching unfamiliar academic vocabulary through structured definitions, contextualization, and multilingual supports. Within the Student Edition, new terms appear in dedicated definition blocks with examples and visual representations to build understanding. For example, in chapter 3, section 3.1, the materials define terms, such as probability experiment, outcome, sample space, and event, and connect the terms to real-world contexts, such as weather forecasting and medical decision-making. Additional supports reinforce vocabulary development, including definitions such as “mutually exclusive” paired with diagrams and prior knowledge. The pacing and activity guide extends these supports through MLS, including routines that connect symbols to language (e.g., “Point to each symbol as you say the formula”) and sentence frames (e.g., “I see the symbol ____”), which help students develop precise academic vocabulary.

The materials include embedded supports to help educators clarify unfamiliar references in text through explanations of notation, terminology, and technology-based resources. For example, in the pacing and activity guide, the MLS restate symbolic expressions in words, such as explaining that “the population mean (μ; mu) equals the sum (Σ) divided by N.” This presentation supports the interpretation of statistical notation. “Study Tip” features clarify language used in context, including explanations of terms, such as or to indicate inclusive sets within probability. In the MyLab Statistics platform, the video and resource library provides reference tools, such as key formulas, statistical tables, and technology study cards, that guide students in interpreting formulas, notation, and software-based procedures. Together, these supports provide multiple entry points for understanding unfamiliar references in both print and digital formats.

Evaluation for 3.1c
Materials include teacher guidance for differentiated instruction, enrichment, and extension activities for students who have demonstrated proficiency in grade-level content and skill.

Enrichment and extension activities deepen students’ conceptual understanding beyond grade-level expectations through advanced-level tasks embedded throughout the chapters. For example, the “Differentiated Instruction Activity: Advanced” tasks in chapter 3 require students to generate additional probability statements, critique problem design, and justify classifications, extending conceptual reasoning. In chapter 4, section 4.1, students create graphic organizers to analyze and classify discrete and continuous random variables, requiring written explanations and conceptual comparisons. Extension tasks increase in complexity, such as in chapter 7, section 7.5, in which students design and solve original hypothesis-testing scenarios, establishing parameters, such as sample size and significance level, and completing all analytical steps. These activities require students to synthesize concepts, justify reasoning, and apply statistical ideas in new contexts.

The materials explicitly guide educators on implementing enrichment and extension through structured directions and differentiated activity frameworks. Within the pacing and activity guide, each advanced activity includes clear instructions, prompting educators to guide students in generating examples, constructing models, and justifying solutions. For example, in chapter 8, section 8.1, the materials direct educators to have students create and categorize their own examples of independent and dependent samples using tables or graphic organizers and justify their classifications. Additional chapter-level guidance, such as in chapter 9, section 9.1, provides recommendations for questioning and facilitating advanced student thinking during extension tasks. These structured directions ensure that educators can effectively implement enrichment activities, supporting students who have demonstrated proficiency in extending both conceptual understanding and analytical skills.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance to support the teacher in modeling and explaining the concept(s) to be learned.

The materials include explicit prompts that support educators in modeling and explaining statistical concepts through structured questioning, scripted language, and step-by-step procedures. Within the pacing and activity guide, lessons embed direct prompts that guide educator-student interaction and model thinking processes. For example, in chapter 3 activities, the materials prompt educators to ask questions, such as “What are you being asked to find?” and “How will you know whether or not the event is simple?” to guide students’ reasoning. In chapter 8, section 8.1, “Testing the Difference Between Means (Independent Samples, σ₁ and σ₂ Known),” educators have scripts to model precise explanations, such as stating that “the samples are dependent because the groups of patients consist of the same 70 patients” and “the samples are independent because the groups of people . . . are not related.” These explicit prompts provide clear models for how educators should communicate and reinforce key statistical concepts.

The materials provide educators with planning resources, instructional tools, and multiple representations to explain concepts. For example, the pacing and activity guide provides structured routines and teaching tips, such as setting up parts of a ratio for students and anticipating common errors to inform their explanations. Educator presentation slides further support modeling by providing sequenced lesson delivery from vocabulary introduction to concept development and guided practice. Additional supports in the MyLab Statistics platform, including study prep resources, video explanations, and the AI tutor, provide step-by-step demonstrations and reinforce conceptual understanding through multiple modalities. Together, these features offer consistent guidance that enables educators to model procedures, explain reasoning, and support student understanding of statistical concepts.

Evaluation for 3.2b
Materials include teacher guidance and recommendations for effective lesson delivery and facilitation using a variety of instructional approaches.

The materials guide educators on effective lesson delivery through a variety of instructional approaches. The pacing and activity guide provides educators with structured routines for moving between whole-group instruction, independent work, and collaborative partner or small-group activities. For example, in chapter 3, the materials direct educators to “follow with a series of questions,” and the provided tips help educators anticipate common errors when students divide incorrectly. These strategies support real-time instructional adjustments. Additional resources, including presentation slides, provide sequenced lesson delivery from vocabulary development to guided practice, while “Study Prep” tools and video supports reinforce educator-led instruction through modeled explanations. These features guide educators in facilitating instruction using multiple approaches, including direct instruction, guided inquiry, and collaborative learning.

The materials support educators on varied instructional approaches through multimedia integration, real-world applications, and structured discussion. The StatTalk Instructor Guide provides recommendations for incorporating video-based learning, including summaries of statistical concepts and structured discussion questions that prompt analysis and conceptual reasoning. The materials encourage educators to connect content to real-world scenarios and facilitate discussions that deepen understanding. For example, in chapter 6, the “Marathon Training” case study requires students to analyze data within an authentic context, which requires interpretation, evaluation, and decision-making. Additional digital resources in the MyLab Statistics platform include performance-monitoring tools that help educators adjust instruction based on students’ understanding and progress. Together, these resources provide actionable recommendations that support educators in delivering and facilitating instruction through a range of instructional approaches.

Evaluation for 3.2c
Materials support multiple types of practice (e.g., guided, independent, collaborative) and include guidance for teachers and recommended structures (e.g., whole group, small group, individual) to support effective implementation.

The materials include supports for multiple types of practice, including guided, independent, and collaborative learning opportunities across lessons and resources.The pacing and activity guide explains how lessons incorporate guided questioning routines, independent problem-solving tasks, and collaborative activities. For example, in chapter 3, students engage in guided inquiry through educator-led questioning, complete conditional probability calculations independently, and work in pairs or small groups to analyze results, providing varied practice experiences. Additional practice opportunities include “Try It Yourself” exercises for guided learning, independent exercises and quizzes for application, and adaptive online tools that reinforce understanding. These features ensure that students engage with statistical concepts through multiple practice formats aligned to different stages of learning.

The materials explicitly guide educators on instructional structures that support effective implementation of these practice types. The materials organize lessons into components, such as guided instruction, independent practice, and closure, with specific directions for facilitating each component. For example, in chapter 6, section 6.3, the materials guide educators to use whole-group instruction followed by targeted small-group support for students needing additional scaffolding when constructing confidence intervals, while digital study plans provide individual practice. The MLS also recommend partner-based activities, such as having students work together to write and justify statistical statements. Additionally, the StatTalk Instructor Guide provides structured whole-group discussion frameworks using sequenced prompts to facilitate class conversations. Together, these features provide clear guidance for implementing practice through whole-group, small-group, and individual structures.

Evaluation for 3.3a
Materials include teacher guidance on providing linguistic accommodations for various levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

The materials do not provide linguistic accommodations that are explicitly aligned to the ELPS proficiency levels or identify supports using the proficiency level descriptors established in the ELPS. However, the materials guide educators on providing linguistic supports for students with varying levels of English language proficiency through structured accommodations embedded in the pacing and activity guide. Within the MLS, lessons include explicit routines that guide educators in scaffolding language for novice learners. For example, in Chapter 6, Section 6.2, the materials direct educators to provide oral descriptions of a flowchart while students identify key sections visually, supporting comprehension through listening and pointing. Similarly, in Chapter 7, Section 7.5, novice-level tasks require students to highlight values, such as standard deviation or variance, in word problems and match the values to their corresponding symbols, reinforcing vocabulary recognition and connections between language and notation. Additional multilingual activities prompt educators to use visual prompts and scaffolded questions, such as “What do you see here?” to guide students in building foundational academic language.

The materials guide educators on supporting students at developing and advanced levels of language proficiency through activities that require increasing use of academic language and discourse. Within the Multilingual Learner Supports, the materials prompt educators to ask developing learners to describe processes using academic vocabulary and structured language supports. For example, in Chapter 6, Section 6.2, students work in pairs to verbally explain the steps of a flowchart using terms such as sample size and population standard deviation, promoting oral language development. In Chapter 7, Section 7.5, developing learners use a two-column graphic organizer to categorize values such as sample variance and population variance, supporting precise use of academic terminology. In Chapter 9, Section 9.1, advanced learners demonstrate understanding by explaining statistical concepts orally and engaging in partner discussions to synthesize learning. These tiered activities require students to move from identifying and matching vocabulary to explaining, justifying, and discussing concepts, with educators supporting increasingly complex academic language across proficiency levels.

Evaluation for 3.3b
Materials include implementation guidance to support teachers in effectively using the materials in state-approved bilingual/ESL programs.

The materials do not include implementation guidance to support educators in effectively using the materials within state-approved bilingual or ESL program models. Although the pacing and activity guide includes MLS and chapter-level overviews, these resources focus on general language development strategies rather than program-specific implementation. For example, chapter overviews and section-level activities, such as in chapter 4, section 4.3, “More Discrete Probability Distributions,” provide speaking routines and sentence frameworks for emergent bilingual (EB) students, but the materials do not include guidance for using these materials within program structures, such as dual language immersion, transitional bilingual, ESL content-based, or ESL pull-out models. The materials do not guide educators in adapting instruction, grouping students, or implementing lessons in these state-approved program settings.

The materials include MLS. However, the materials do not provide educator-facing implementation guidance aligned to bilingual or ESL program requirements. Within the pacing and activity guide, the MLS are organized by proficiency levels (novice, developing, and advanced) and include activities, such as oral descriptions, graphic organizers, and vocabulary supports. But these supports are not aligned to the ELPS proficiency level descriptors and do not include program-specific instructional routines or structures. For example, in chapter 7, section 7.4, the activity-level supports for novice and developing learners do not include guidance for how these supports should be implemented within bilingual or ESL instructional models. Additionally, ELPS-aligned resources identify connections to standards but do not provide guidance for instructional delivery within program contexts. As a result, educators must independently determine how to use these materials within bilingual or ESL programs, as the materials lack explicit implementation guidance aligned to state-approved program models.

Evaluation for 3.3c
Materials include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, and making cross-linguistic connections through oral and written discourse.

The materials provide educators with embedded guidance for supporting EB students in developing academic vocabulary and increasing comprehension through oral and written discourse. Within the pacing and activity guide, the MLS provide structured routines aligned to lesson content that scaffold language development across proficiency levels. For example, in chapter 5, section 5.1, novice students record observations about the mean and standard deviation of a normal distribution, while developing students extend this work by writing explanations that connect these parameters to real-world contexts, supporting written academic language. In chapter 6, section 6.1, students engage in oral and reading routines in which novice learners connect vocabulary, such as margin of error and population mean, to symbolic representations, while developing learners participate in partner discussions to identify and explain linguistic cues, such as “greatest possible distance.” Additional activities prompt students to explain vocabulary orally, write definitions in journals, and use sentence frames to justify reasoning, supporting both oral and written discourse and strengthening comprehension of statistical concepts. These embedded supports build academic vocabulary and support understanding through structured language use.

The materials do not provide educators with embedded guidance for supporting EB students in building background knowledge consistently or in making cross-linguistic connections through oral or written discourse. While some activities prompt students to recall prior mathematical knowledge, such as asking “What is a regression equation?” to connect to previously learned concepts, the materials do not include structured routines that systematically activate or develop background knowledge across lessons. More significantly, the materials do not include guidance for cross-linguistic connections, such as comparing languages, identifying cognates, or transferring meaning between a student’s home language and English. Activities and supports focus solely on English-language development and do not incorporate bilingual resources or metalinguistic strategies. As a result, although the materials provide embedded supports for academic vocabulary and comprehension through discourse, the materials do not fully address all components of the indicator, particularly the development of background knowledge and cross-linguistic connections.

Evaluation for 3.3d
If designed for dual language immersion (DLI) programs, materials include resources that outline opportunities to address metalinguistic transfer from English to the partner language.

This guidance is not applicable because the program is not designed for dual language immersion (DLI) programs.

Evaluation for 4.1a
Practice opportunities over the course of a lesson and/or unit (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The materials provide practice opportunities throughout lessons and units, but these opportunities do not align with the TEKS. Examples of practice tasks include the chapter 3 review exercises, in which students apply probability concepts, and chapter 9, section 9.3, in which students construct and describe models, analyze variance, communicate methods of analysis, and interpret confidence intervals. Additional practice appears in the “Try It Yourself” exercises, end‑of‑section practice, “Uses and Abuses,” “Applet Activities,” “Real Statistics,” and “Technology Projects.” All of these practice exercises support varying depths of understanding. Although the program aligns the materials to national mathematics organizations, the materials do not identify or reference the TEKS, so practice opportunities do not demonstrate depth of understanding aligned to the TEKS.

The materials provide instructional assessments throughout the course, but these assessments do not align with the TEKS. The MyLab Statistics platform includes assessments that educators can modify, adapt, and assign, as well as extended learning activities for Texas high school users. These assessments vary in depth and allow students to apply statistical concepts, reason with data, and demonstrate understanding. The materials do not identify the TEKS within assessments or provide a crosswalk showing how assessment tasks connect to the TEKS. Because the materials do not reference the rigor or cognitive expectations of the TEKS, educators must determine alignment independently.

Evaluation for 4.1b
Questions and tasks progressively increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS.

The materials include questions that progressively increase in rigor and complexity across lessons and units. For example, in chapter 2, questions move from foundational concepts, such as frequency distributions, graphs, and measures of central tendency, to deeper analysis through the “Applet Activity: Mean versus Median” and questions addressing measures of variation and standard deviation. Students extend their understanding through cumulative review questions in chapter 2, “Real Statistics, Real Decisions: Putting It All Together.” Here, students display, measure, and discuss data. This progression continues throughout the text. In chapter 9, section 9.2, questions begin with “Building Basic Skills and Vocabulary”—explaining residuals, interpreting slopes, and identifying meaningful prediction ranges—and advance through “Matching” items, “Graphical Analysis” items, and “Using and Interpreting Concepts” questions that require students to find regression equations, construct scatter plots, draw regression lines, and justify predictions. These sequences demonstrate a clear progression from conceptual understanding to higher-level reasoning across the materials.

The materials include tasks that progressively increase in rigor and complexity, supporting students as they move from procedural fluency toward advanced statistical application. For example, students begin chapter 6 by constructing confidence intervals for population means, progress to using statistical tables to support calculations, and culminate in “Extending Concepts” tasks in which students interpret confidence intervals in real-world scenarios. In chapter 9, section 9.3, the tasks progress from interpreting variation in regression lines to analyzing coefficients of determination, calculating standard errors, and making predictions using regression models. Section 9.4 extends this progression by asking students to interpret multiple regression equations, predict values using technology, and analyze quantitative and bivariate data. These task sequences demonstrate intentional increases in cognitive demand across lessons and chapters, supporting students as they develop toward grade-level proficiency in the TEKS.

Evaluation for 4.2a
Materials demonstrate coherence across units by explicitly connecting patterns, big ideas, and relationships between mathematical concepts.

The materials demonstrate coherence across units by explicitly connecting patterns in statistical reasoning as students move through the course. The text is organized into four major parts—”Descriptive Statistics,” “Probability and Probability Distributions,” “Statistical Inference,” and “More Statistical Inference”—that intentionally build upon one another. Chapter openers reinforce these patterns by showing how earlier approaches reappear in new contexts. For example, in chapter 9, the “Where You’ve Been” section reminds students of the pattern of graphing paired data with scatter plots, illustrated through salaries and home-game attendance for Major League Baseball teams, before extending that pattern to regression lines and correlation in the “Where You’re Going” section. These structures help students recognize recurring statistical patterns and how they evolve across units.

The materials connect big ideas and relationships between mathematical concepts as students progress from one unit to the next. For example, in chapter 10, the opener revisits the big idea of comparing two population means using sample statistics and hypothesis testing, illustrated through chest-injury crash-test data for large pickups and midsize SUVs. The “Where You’re Going” section then extends this relationship by showing how similar reasoning applies when comparing three or more populations, using a new data set that adds large cars as a third group. By explicitly linking earlier inferential concepts to more advanced comparisons, the materials highlight how statistical ideas relate to and build on one another across units, supporting the coherent development of students’ understanding.

Evaluation for 4.2b
Materials demonstrate coherence across units by connecting the content and language learned in previous courses/grade levels and what will be learned in future courses/grade levels to the content to be learned in the current course/grade level.

The materials demonstrate coherence across units by connecting the content learned in previous courses or grade levels to the content to be learned in the current course. For example, in chapter 2, students revisit concepts on computing the mean, median, and mode that were introduced in earlier grade levels and use them to support understanding of statistical formulas and Greek notation. In chapter 5, video notes prompt students to review prerequisite algebra skills needed to interpret normal curves, and section 5.1 builds on geometric ideas about area to support the computation of probabilities under the standard normal curve. These features provide explicit instructional links that help students leverage prior mathematical content knowledge as they engage with new statistical ideas.

The materials demonstrate coherence across units by connecting the language learned in previous courses or grade levels to the content to be learned in the current course. Vocabulary cues, side notes, and teaching tips reinforce terminology students first encountered in earlier mathematics coursework, such as mean, median, mode, slope, and notation conventions. For example, in chapter 9, section 9.3, the “Extending the Concepts” feature prompts students to apply familiar terms—including slope, sample statistics, and population parameters—within more formal statistical procedures. These supports help students access new statistical representations through academic language learned in prior courses.

Evaluation for 4.2c
Materials demonstrate coherence at the lesson level by connecting students' prior knowledge of concepts and procedures from the current and prior grade level(s) to new mathematical knowledge and skills..

The materials demonstrate coherence at the lesson level by connecting concepts and procedures learned earlier in the current course to new statistical knowledge and skills. Each chapter begins with a “Where You’ve Been” opener and a “Chapter Skills Check” that reviews prerequisite ideas from previous lessons, helping students see how earlier content supports the new material. For example, in chapter 4, the opener explains how prior lessons on collecting and describing data and on computing basic probabilities in chapters 1 and 3 lead directly into constructing and interpreting probability distributions. Integrated review sections and “Study Prep” resources reinforce this within‑course coherence by revisiting essential procedures before students apply them in more complex statistical contexts, ensuring that new learning builds directly on skills developed earlier in the course.

The materials connect students’ prior grade‑level mathematical learning to new statistical concepts within individual lessons. For example, in chapter 3, section 3.2, students review the multiplication rule from geometry, helping them identify independent events and compute compound probabilities. This knowledge prepares students for Bayes’ Theorem in the “Extending Concepts” exercises. In chapter 9, Section 9.2, the text explicitly recalls algebraic concepts and procedures, instructing students to recall that slope is the ratio of rise over run and that equations of lines can be written in the form y = mx + b. Students then apply this prior Algebra learning to construct and interpret regression lines using predictive notation ŷ. These lesson-level connections help students apply concepts and procedures learned in prior grade levels to new statistical knowledge and skills developed in the course.

Evaluation for 4.3a
Materials provide spaced retrieval opportunities with previously learned skills and concepts across lessons and units.

The “Integrated Review Table of Contents” places prerequisite procedural skills at the beginning of each chapter, giving students repeated practice with earlier skills as they move through the course. Early chapters revisit procedures such as converting among number forms, simplifying expressions with exponents and square roots, calculating summations, rewriting inequalities, translating verbal phrases into mathematical expressions, and evaluating factorials. Later chapters continue this pattern by returning to skills such as solving linear equations and graphing on the coordinate plane. Cumulative reviews, such as for chapters 3 to 5, further reinforce procedural retrieval by requiring students to apply skills from multiple earlier units. These structures ensure that students repeatedly engage with previously learned skills across lessons and units.

The materials provide spaced retrieval opportunities with previously learned concepts across lessons and units. For example, the “Real Statistics, Real Decisions” activity in chapter 5 requires students to retrieve conceptual understanding of mean, standard deviation, and probability to analyze new data and make decisions. Later in the course, chapter 9 continues this pattern of conceptual recall. In chapter 9, section 9.3, the materials prompt students to “recall from section 9.1, example 7, that x and y have a significant linear correlation,” which reinforces earlier conceptual understanding before applying it to hypothesis testing. Section 9.2 also revisits conceptual ideas from prior courses, reminding students that “the slope of a line is the ratio of its rise over its run,” thereby connecting algebraic concepts to new statistical interpretations. These repeated opportunities to recall and apply previously learned concepts strengthen spaced retrieval across lessons and units.

Evaluation for 4.3b
Materials provide interleaved practice opportunities with previously learned skills and concepts across lessons and units.

The “Integrated Review Table of Contents” and the MyLab Extended Learning & Activities platform present mixed sets of prerequisite and current‑chapter skills within the same learning sequence, requiring students to switch among different types of procedures as they work. Early review topics combine skills such as converting among number forms, analyzing bar and pie charts, simplifying expressions with exponents and square roots, translating verbal phrases into mathematical expressions, and evaluating factorials. Additional tools, such as TestGen worksheets and test bank items, allow educators to generate mixed‑skill assignments that blend current‑chapter procedures with earlier skills on a daily or weekly basis. Cumulative reviews, such as those in chapters 9 and 10, further reinforce interleaving by requiring students to alternate among regression calculations, multivariate formulas, categorical data analysis, and measures of variability within a single assignment. These structures ensure that students repeatedly engage with mixed procedural skills across lessons and units.

The materials provide interleaved practice opportunities with previously learned concepts across lessons and units. The “Integrated Review” topics combine conceptual ideas from multiple chapters, prompting students to revisit earlier understandings as they learn new content. For example, cumulative reviews require students to contrast conceptual structures—such as interpreting two‑variable numeric tables, analyzing categorical frequencies, recognizing cues for variance tests, and identifying when a chi‑squared test is appropriate—within the same problem set. In later units, interleaving continues through activities that require students to apply conceptual knowledge of correlation, regression, population variability, and distributional reasoning in alternating sequences. By blending conceptual demands from different parts of the course into single assignments, the materials support interleaved practice with previously learned concepts across lessons and units.

Evaluation for 5.1a
Questions and tasks require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations.

The materials include questions that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. For example, chapter 2, section 2.3, includes questions that prompt students to interpret frequency distributions, analyze graphs and charts to determine measures of center, and explain when information cannot be determined from a representation. In chapter 5, section 5.1, the materials ask students to justify whether a graph could represent a normal distribution, while section 5.2 requires students to determine whether a selected value lies within a shaded region of a graph and evaluate control charts by deciding whether a process is in or out of control. Chapter 9 includes additional questions that deepen evaluation, such as interpreting scatter plots, analyzing explained and unexplained variation, and testing claims in regression contexts, including prompts such as “Test the claim that μ = 0. Use α = .05.” These questions collectively require students to engage with statistical models through interpretation, analysis, and evaluation.

The materials include tasks that require students to interpret, analyze, and evaluate models and representations for mathematical concepts and situations. For example, in chapter 5, section 5.1, the materials ask students to interpret graphical models of normal distributions by identifying the mean from the curve’s symmetry, estimating the standard deviation from the spacing of inflection points, and analyzing score ranges using the empirical rule. Section 5.2 provides additional opportunities for students to analyze and evaluate models by determining whether a selected value lies within a shaded region of a normal distribution graph and by examining control charts to decide whether a process is in or out of control. Chapter 9 extends these expectations by requiring students to construct scatter plots, analyze symbolic and graphical representations of variation, and evaluate regression models in real‑world contexts, such as wages, voter turnout, and vehicle sales. These tasks collectively engage students in interpreting, analyzing, and evaluating statistical models across multiple chapters of the course.

Evaluation for 5.1b
Questions and tasks require students to create models to represent mathematical situations.

The materials include questions that require students to create models to represent mathematical situations. For example, in chapter 2, section 2.5, the materials ask students to draw box‑and‑whisker plots to represent data distributions, requiring students to construct graphical models rather than interpret provided ones. In chapter 5, section 5.1, the materials prompt students to draw two normal curves with the same mean but different standard deviations and describe the similarities and differences, which requires students to create mathematical models that illustrate how changes in standard deviation affect the shape and spread of a distribution. In chapter 9, the materials ask students to construct scatter plots and draw regression lines, prompting students to generate graphical representations of relationships between variables. These questions collectively require students to create models that represent statistical situations across multiple chapters of the course.

The materials include tasks that require students to create models to represent mathematical situations. For example, in chapter 3, students create tree diagrams to represent probability situations and construct bar graphs in section 3.3 to model categorical data. In chapter 6, section 6.3, the materials require students to create confidence‑interval models by identifying the sample proportion, calculating the margin of error, and constructing interval bounds within a structured representation. Additional tasks prompt students to write original confidence‑interval word problems using their own numbers and scenarios. In chapter 9, section 9.1, the “Correlation by Eye” task directs students to construct scatter plot models by adding, removing, and arranging data points to generate data sets with targeted correlation values, such as r ≈ 1, r ≈ 0, r ≈ –0.5, and r ≈ 0.9. These tasks collectively engage students in creating mathematical models across a range of statistical concepts.

Evaluation for 5.1c
Questions and tasks provide opportunities for students to apply conceptual understanding to new problem situations and contexts.

Through provided questions, students have opportunities to apply conceptual understanding to new problem situations and contexts. For example, in chapter 2, section 2.3, the materials require students to apply their understanding of the mean, median, and mode to varied real‑world contexts, such as sports scores, political debate responses, home‑sales data, and classroom scenarios. These questions ask students to determine how outliers affect measures of center, identify factors that influence the relationship between the median and the mean, and apply statistical reasoning to unfamiliar situations, demonstrating a flexible use of conceptual understanding. Chapter 8 includes “Real Statistics Real Decisions: Putting It All Together” questions that ask students to apply sampling concepts, identify appropriate sampling techniques, evaluate potential biases, and select and justify hypothesis tests using Medicare patient hospital‑stay data. These questions require students to use conceptual understanding in new contexts by determining sampling methods, analyzing assumptions, and interpreting results to make data‑driven decisions.

The materials provide students with tasks in which students apply conceptual understanding to new problem situations and contexts. For example, in chapter 6, section 6.3, students vary sample size, population proportion, and confidence level in repeated simulations to examine how these changes affect interval width and coverage, applying their understanding of confidence intervals to unfamiliar conditions. In chapter 7, section 7.3 includes the “Hypothesis Tests for a Mean” activity in which students vary parameters, such as sample size, distribution shape, population mean, population standard deviation, and alternative hypotheses, within a simulation environment to observe how these changes affect rejection rates. In this activity, students apply conceptual understanding of hypothesis testing to new scenarios. Across chapters, the “Real Statistics Real Decisions: Putting It All Together” tasks further support conceptual application by requiring students to plan approaches, interpret results, evaluate decisions, and draw conclusions using real‑world data.

Evaluation for 5.2a
Materials provide tasks that are designed to build student automaticity and fluency necessary to complete grade-level tasks.

The materials include tasks designed to build the automaticity necessary for students to complete grade‑level tasks. For example, in chapter 5, section 5.1, students have repeated procedural practice with computing z‑scores and using the standard normal table, including tasks that require finding areas to the left, right, and between z‑scores across multiple lessons. This pacing gives students repeated exposure to the same procedures over several days, supporting the development of automaticity with normal‑distribution calculations. Additional automaticity practice is available through the MyLab instructor tools, resources, homework resources, and online exercises. Students repeatedly compute sample means, summations, z‑scores, probabilities, confidence intervals, and hypothesis tests across structured items, such as “calculate the sample mean,” “binomial probability calculations,” “standard normal distribution,” and “hypothesis tests for a mean.” These high‑volume exercises provide the repetition students need to deliver correct responses quickly and accurately.

The materials include tasks designed to build student fluency necessary to complete grade‑level tasks. For example, in chapter 5, the “Uses and Abuses” section includes error‑analysis tasks, such as identifying mistakes in probability calculations, which prompt students to analyze procedural errors and refine their understanding of when and how to apply statistical procedures. Chapter 6, section 6.2, reinforces fluency through tasks that require students to repeat earlier exercises using the standard normal distribution with a known standard deviation, prompting students to transfer and adapt prior procedural knowledge to a new but related context. These opportunities to adjust calculations, compare results, and interpret procedural outcomes support the development of fluency with grade‑level statistical skills.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures within the lesson and/or throughout a unit.

Students have opportunities to practice efficient, flexible, and accurate mathematical procedures within lessons. For example, in chapter 1, example 3, and activity 1.3, students create and compare samples using simple random, stratified, cluster, and systematic sampling, prompting flexible use of multiple valid procedures within a single lesson. These tasks support accuracy as students analyze whether a sample is biased and determine which sampling method is most appropriate for a given context. In chapter 3, section 3.4, example 6 provides students with an initial worked example followed by additional practice in which students use both hand calculations and technology, such as Excel, allowing students to apply efficient procedures for computing probabilities and verify results using multiple methods. The “Try It Yourself” exercise that follows requires students to apply the same procedures independently, reinforcing accuracy through repeated computation. These lesson‑embedded opportunities help students practice efficient, flexible, and accurate procedures as students engage with new concepts.

Students also have opportunities to practice efficient, flexible, and accurate mathematical procedures throughout a unit. For example, in chapter 3, “Technology (Minitab, Excel, TI‑84 Plus): Simulation: Composing Mozart Variations with Dice,” students have recurring opportunities to apply efficient procedures by using technology to generate random values, flexible procedures by shifting between theoretical and empirical probability methods, and accurate procedures through repeated computation and comparison of probabilities within the simulation. Chapter 5 further extends unit‑level practice by requiring students to compute z‑scores, use the standard normal table, and apply technology tools, such as graphing calculators and applets, across multiple sections. These recurring opportunities across the probability and normal‑distribution units help students practice and strengthen efficient, flexible, and accurate mathematical procedures throughout the units.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within the lesson and throughout a unit.

Students have opportunities to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy within lessons. For example, in chapter 4, section 4.3, example 1, the materials ask students to compare hand‑computed geometric probabilities with technology‑generated results using the TI‑84 Plus, which prompts evaluation of procedural efficiency and accuracy. The “StatTalk” videos in the MyLab Statistics platform support evaluation by modeling multiple approaches to statistical procedures through real‑world examples, allowing students to judge the efficiency, flexibility, and accuracy of the methods demonstrated. These lesson‑embedded opportunities require students to assess how procedures were carried out and whether alternative methods may be more effective or precise.

Students also have opportunities to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy throughout a unit. For example, in the “Real Statistics Real Decisions: Putting It All Together” feature at the end of chapter 6, students compare confidence‑interval construction methods to determine whether the population standard deviation was used, evaluating both the accuracy and efficiency of each approach. The chapter 6 review questions extend this evaluation by asking students to determine the minimum sample size using different preliminary estimates, requiring judgment of procedural flexibility and accuracy. The chapter 9 review exercises continue this pattern throughout the regression unit, in which students evaluate the efficiency of regression equations, compare the flexibility of correlation and regression models, and assess accuracy using measures such as r² and the standard error of estimate. These recurring tasks across chapters help students evaluate procedures, processes, and solutions throughout the unit.

Evaluation for 5.2d
Materials contain embedded supports for teachers to guide students toward increasingly efficient approaches.

Educators have embedded supports to guide students toward increasingly efficient approaches throughout lessons. For example, in chapter 9, educator-facing guidance at the end of the “Independent Practice” section prompts instructional moves that help students refine their methods. The materials direct educators to “go over key points on the graph,” provide model values from both hand‑drawn and Desmos‑generated representations, and facilitate discussion using the prompt “Which method better describes the data and why?” These supports help educators lead students in comparing approaches, recognizing more effective strategies for representing data, and moving toward increasingly efficient methods during independent practice.

Educators have resources to guide students toward increasingly efficient approaches across lessons. For example, the presentation slides for chapter 6 scaffold instruction by first modeling symbols, formulas, and visual representations before guiding educators to present more efficient technology‑based methods using “Minitab” or “StatCrunch.” The pacing and activity guide supports efficiency by outlining steps for presenting streamlined approaches, such as scaffolding the process for finding the margin of error for a population mean. These embedded resources help educators introduce, model, and transition students toward increasingly efficient strategies using both paper‑and‑pencil and technology‑based methods.

Evaluation for 5.3a
Materials explicitly state how the conceptual and procedural emphasis of the TEKS are addressed.

The materials do not explicitly state how the conceptual emphasis of the TEKS is addressed. Although the textbook includes conceptual tasks, such as asking students in chapter 9 to explain correlation patterns and interpret the meaning of statistical relationships, these opportunities are not identified as addressing the conceptual expectations of the TEKS. The “Extended Learning & Activities for Texas High School Users” includes conceptual tasks, such as explaining observed versus expected frequencies and interpreting independence in chapter 10, but the materials do not connect these activities to conceptual requirements of the TEKS. Conceptual understanding is evident throughout the textbook, MyLab activities, and planning resources, yet the materials never explicitly state how these tasks align with the conceptual emphasis of the TEKS.


The materials do not explicitly state how the procedural emphasis of the TEKS is addressed. Although students engage in procedural work—such as calculating correlation coefficients, constructing frequency tables, creating graphs, and performing chi‑squared tests—the materials do not identify these procedures as fulfilling the procedural expectations of the TEKS. The “Extended Learning & Activities for Texas High School Users” includes tasks requiring students to create frequency tables and apply chi‑squared procedures, and the pacing and activity guide outlines procedural activities, such as conditional probability and hypothesis testing. However, the textbook, MyLab resources, and the planning materials do not reference the TEKS or explicitly state how these procedures align with TEKS requirements. As a result, procedural practice is present but not explicitly connected to the TEKS.

Evaluation for 5.3b
Questions and tasks include the use of concrete models and manipulatives, pictorial representations (figures/drawings), and abstract representations, as required by the TEKS.

The materials include questions that use concrete models, pictorial representations, and abstract representations as required by the TEKS. For example, the exercises in chapter 3, section 3.1, include concrete models, such as rolling physical or online dice, to generate sums and compare theoretical and simulated probabilities. Questions incorporate pictorial representations, such as interpreting box‑and‑whisker plots to determine probabilities for stock prices. Abstract representations appear in questions requiring students to justify probability formulas, such as using the ratio p:q to show that P(A) = p/(p + q). These questions prompt students to engage with concrete manipulatives, visual models, and symbolic reasoning to understand and apply statistical concepts.

The materials include tasks that use concrete, pictorial, and abstract representations as required by the TEKS. For example, in chapter 2, sections 2.1, “Multilingual Activity,” and 2.3, “Extending Concepts,” the materials require students to construct and interpret pictorial representations, such as frequency tables, histograms, and other graphical displays. Students also work with abstract numerical summaries, including class widths, frequencies, and measures of center. Concrete models appear in tasks that use authentic data sets, such as educator salaries or stock revenues, allowing students to work directly with real‑world numerical information. Additional tasks in chapter 9 ask students to construct scatter plots and regression lines (pictorial) and compute correlation coefficients and coefficients of determination (abstract). These tasks provide recurring opportunities for students to use concrete, pictorial, and abstract representations to model, analyze, and interpret statistical situations.

Evaluation for 5.3c
Materials include supports for students in connecting, creating, defining, and explaining concrete and representational models to abstract (symbolic/numeric/algorithmic) concepts, as required by the TEKS.

The materials support students in connecting concrete models to abstract statistical concepts. For example, the activity in chapter 2, section 2.4, provides students with concrete data sets to manipulate by adding or removing values. As students adjust the data, the applet displays updated measures of center and spread, guiding them to connect hands-on changes to abstract numerical concepts, such as mean, median, and standard deviation. In the “Introduction to Normal Distributions” section in chapter 5, students work with concrete graphical models of the normal curve to identify standard‑deviation intervals and inflection points before linking these visual features to the abstract concept of the z‑score. These sequences support students in creating, defining, and explaining concrete models that lead directly to symbolic and algorithmic statistical ideas.

The materials support students in connecting representational models to abstract concepts. For example, in chapter 2, “Measures of Variation,” students interpret box plots and data tables and connect these visual representations to abstract numerical measures such as range, interquartile range, and standard deviation. In chapter 9, students construct scatter plots, draw regression lines, and use regression equations to justify predictions, moving from plotted data and drawn lines to abstract ideas, including correlation, functional relationships, and predicted values. Chapter 9 review tasks extend these representational‑to‑abstract connections by asking students to calculate correlation coefficients, determine coefficients of determination, and interpret the meaning of these values in context. Across these chapters, students analyze how features of graphical models correspond to underlying statistical quantities, supporting the creation, definition, and explanation of representational models linked to abstract concepts.

Evaluation for 5.4a
Materials provide opportunities for students to develop academic mathematical language using visuals, manipulatives, and other language development strategies.

Students have opportunities to develop academic mathematical language using visuals. For example, in chapter 1, section 1.1, students use a diagram representing a population and a sample to develop statistical vocabulary related to data collection and analysis. Additional visual representations, including histograms, frequency polygons, pie charts, scatter plots, and stem-and-leaf plots, require students to interpret graphical displays and communicate observations using precise statistical terminology. The MyLab study slides further support the development of academic language by presenting visual models of statistical concepts and prompting students to connect vocabulary to representations and data displays. These visual supports provide recurring opportunities for students to build and apply academic mathematical language while interpreting statistical information.

Students have opportunities to develop academic mathematical language using manipulatives and other language-development strategies. For example, in chapter 3, section 3.4, students use coins, dice, and playing cards to conduct probability experiments and discuss theoretical and experimental probability in context. The materials include additional language-development supports in chapter 1, section 1.1, “An Overview of Statistics,” in which the MLS provide sentence stems and word banks for terms, such as population, sample, parameter, and statistic. These activities encourage students to communicate statistical reasoning using academic vocabulary while connecting hands-on experiences and structured language supports to mathematical concepts. Manipulatives, sentence frames, and vocabulary supports provided across the materials help students develop and use academic mathematical language during statistical investigations.

Evaluation for 5.4b
Materials include embedded teacher guidance to scaffold and support students' development and use of academic mathematical vocabulary in context.

The materials guide educators in scaffolding and supporting students’ development and use of academic mathematical vocabulary in context. For example, in the differentiated instruction activity in chapter 1, section 1.2, educators help students classify data using the four levels of measurement: nominal, ordinal, interval, and ratio. The materials direct educators to use cards featuring real-world examples, and the materials guide educators in addressing common misconceptions as students learn and apply measurement vocabulary. This embedded support helps educators introduce statistical terminology in meaningful contexts while guiding students toward accurate use of academic mathematical language.

The differentiated instruction activity in chapter 10, section 10.4, guides educators on supporting students in learning and applying terms associated with analysis of variance (ANOVA) procedures. The activity recommends visual supports, including an f-curve and a rejection region, and identifies concepts that may require additional explanation, such as rejection regions and the interpretation of differences among population means. The guidance supports educators in helping students develop and use mathematical vocabulary for academic purposes while making decisions, interpreting statistical results, and communicating conclusions. Throughout the pacing and activity guide, scaffolded instructional supports provide educators with embedded guidance to develop students’ understanding and use of statistical language in context.

Evaluation for 5.4c
Materials include embedded teacher guidance to support the application of appropriate mathematical language to include vocabulary, syntax, and discourse to include guidance to support mathematical conversations that provide opportunities for students to hear, refine, and use math language with peers and develop their math language toolkit over time as well as guide teachers to support student responses using exemplar responses to questions and tasks.

The materials include embedded educator guidance to support the application of appropriate mathematical language, including vocabulary, syntax, and discourse. For example, a speaking activity in chapter 1, section 1.2, supports students in learning and applying vocabulary associated with nominal, ordinal, interval, and ratio data. Students use sentence stems to discuss real-world examples and justify classifications, providing structured opportunities to develop mathematical syntax while communicating statistical ideas. The materials include similar supports in chapter 11, section 11.3, which provides educators with questions, discussion prompts, and sentence stems that guide students in describing data and statistical procedures. Across these activities, embedded educator guidance supports the development of statistical vocabulary, complete mathematical responses, and academic discourse during mathematical conversations.

The materials guide educators in supporting mathematical conversations that allow students to hear, refine, and use mathematical language with peers. For example, in Chapter 1, Section 1.2, students discuss data classifications with partners, justify their responses, and share explanations with the class, providing opportunities to hear and refine mathematical language through discussion. Chapter 7 includes additional supports in which the materials direct educators to read scenarios aloud, facilitate student discussions, and provide sentence stems to help students communicate statistical conclusions. The Instructor Solutions Manual provides exemplar responses that model appropriate mathematical language and complete statistical explanations. For example, Chapter 7 solution sets include model responses such as, “There is enough evidence at the 5% level of significance to support the claim that the average speed is greater than 35 miles per hour,” and “There is not enough evidence at the 1% level of significance to support the claim that the mean number of workdays missed due to illness or injury in the past 12 months is different from 3.6 days.” These exemplar responses demonstrate how students should communicate conclusions using precise statistical vocabulary and reasoning and provide teachers with guidance for supporting student responses.

Evaluation for 5.5a
TEKS process standards are integrated appropriately into the materials.

The TEKS process standards are integrated appropriately into instruction. In the pacing and activity guide, each chapter includes a “Math Practices” section that identifies the TEKS process standards addressed within the chapter. For example, the chapter 2 overview explains how students will display, explain, and justify mathematical ideas using precise mathematical language in written and oral communication. Similarly, the “Math Process Standards” page in chapter 3 directs students to use technology strategically, select appropriate tools, and communicate and justify probability statements. These chapter-level supports explicitly connect instruction to the TEKS process standards and provide guidance for incorporating mathematical reasoning, communication, and tool use throughout the course.

The materials include opportunities to apply the TEKS process standards. For example, the “Extended Learning & Activities for Texas High School Users” resource includes activities designed to engage students in problem-solving, mathematical reasoning, communication, representation, and justification within statistical contexts. Students apply process standards while investigating real-world situations, selecting strategies, using technology, and explaining their conclusions. The instructional resources expect students to analyze information, communicate mathematical ideas, justify reasoning, and apply appropriate tools, which supports the integration of the TEKS process standards throughout the materials.

Evaluation for 5.5b
Materials include a description of how TEKS process standards are incorporated and connected throughout the course.

The materials describe how the TEKS process standards are incorporated throughout the course. For example, in chapter 1, the “Mathematical Process Standards” section within “A Suggested Approach” identifies specific TEKS process standards and describes how students apply mathematics to problems arising in everyday life, society, and the workplace. The guidance explains that students design surveys and experiments, collect data, and use precise mathematical language to display, explain, and justify their conclusions. Similar descriptions appear throughout the pacing and activity guide, in which chapter overviews and “Math Practices” sections identify the process standards embedded in instruction and explain how students engage in reasoning, representation, communication, and problem-solving as they learn statistical concepts.

Across the materials, recurring expectations for reasoning, communication, representation, and tool use demonstrate how the TEKS process standards are connected and reinforced throughout the course. The “Math Practices” sections consistently emphasize skills, such as creating and using representations, communicating mathematical ideas, justifying reasoning, and applying appropriate tools and technology, across multiple statistical topics. The “Extended Learning & Activities for Texas High School Users” resource provides activities that connect the process standards to real-world statistical investigations and applications. For example, chapter 8, section 8.1, includes activities that require students to classify study designs, justify their reasoning, and communicate conclusions using statistical language..

Evaluation for 5.5c
Materials include a description for each unit of how TEKS process standards are incorporated and connected throughout the unit.

The materials describe how TEKS process standards are incorporated throughout each unit. In the pacing and activity guide, each chapter includes a “Math Process Standards” section within “A Suggested Approach” that describes how students will apply process standards during instruction. For example, in chapter 8, the guidance explains that students apply mathematics to problems arising in everyday life, society, and the workplace as they investigate differences between means and proportions for independent and dependent samples. Students engage in reasoning, interpretation, communication, and problem-solving as they analyze statistical questions and draw conclusions from data. The materials provide similar descriptions throughout the course, demonstrating how TEKS process standards are incorporated into unit instruction and activities.

The materials do not describe how the TEKS process standards are connected throughout each unit. While the chapter guidance describes the process standards addressed within individual lessons and outlines the progression of statistical content, the chapter guidance does not explain how the process standards, such as representation, communication, justification, tool selection, and problem-solving, are intentionally developed and connected across lessons within a unit. For example, chapter 8 describes hypothesis-testing procedures and previews subsequent topics. However, the chapter guidance does not describe how the process standards build from one lesson to the next or how students’ use of these standards progresses throughout the unit. As a result, the materials describe how TEKS process standards are incorporated within units but do not explicitly describe how those standards are connected throughout the units.

Evaluation for 5.5d
Materials include an overview of the TEKS process standards incorporated into each lesson.

The materials do not include an overview of the TEKS process standards incorporated into each lesson. The preface includes an “Examples and Exercises” section that describes instructional features, including examples, exercises, and technology applications used throughout the course. In addition, chapter-level resources, such as “A Suggested Approach” in the pacing and activity guide, describe the mathematical practices and process standards addressed in a chapter. However, the materials do not provide lesson-specific overviews that identify or describe the TEKS process standards incorporated into individual lessons.

Although TEKS process standards are evident within lesson activities, the materials do not include lesson-level overviews of those standards. For example, chapter 11, section 11.2, includes tasks that require students to analyze information, select appropriate procedures, use technology, justify conclusions, and communicate statistical reasoning using precise mathematical language. These activities reflect the TEKS process standards through problem-solving, representation, tool use, communication, and justification. However, the lesson does not include an accompanying overview that identifies or explains the TEKS process standards incorporated into the lesson. Similar patterns occur throughout the materials, in which process standards are embedded in student tasks but are not described in a lesson-by-lesson overview.

Evaluation for 6.1a
Materials provide opportunities for students to think mathematically, persevere through solving problems, and to make sense of mathematics.

Students have opportunities to think mathematically through tasks that require conceptual reasoning, interpretation, and analysis of mathematical relationships. For example, in chapter 3, section 3.1, students identify sample spaces, determine outcomes, classify events, and explain their reasoning. They construct tree diagrams to represent probability situations and interpret how these representations connect to underlying concepts. Additional opportunities for mathematical thinking appear in chapter 9, in which students analyze real articles that confuse correlation and causation, interpret scatter plots and correlation coefficients, and evaluate residual plots to determine whether linear models are appropriate. These experiences require students to analyze patterns, justify relationships between variables, and apply statistical reasoning to real‑world contexts.

Students have opportunities to persevere through solving problems and making sense of mathematics through multistep tasks that require sustained reasoning and interpretation. Students complete detailed data tables, compute summations, and substitute values into multivariable formulas to calculate correlation coefficients, slopes, and intercepts, monitoring their workflow to ensure accuracy across multiple stages. Activities, such as the confidence intervals simulation in chapter 6, section 6.3, require students to run repeated trials, analyze interval behavior, and explain how sample size and confidence level affect results, reinforcing conceptual sense‑making. Additional opportunities appear in “StatTalk Video 21,” in which students discuss absolute versus relative risk and apply these ideas to real‑world scenarios, as well as in probability tasks that require students to interpret roulette odds without procedural guidance. These experiences prompt students to persist through complex reasoning and articulate mathematical meaning.

Evaluation for 6.1b
Materials support students in understanding, explaining, and justifying that there can be multiple ways to represent and solve problems and complete tasks.

The materials support students in understanding and explaining that there can be multiple ways to represent and solve problems through a variety of tasks, representations, and instructional features across the program. Students encounter multiple graphical, numerical, symbolic, and technological representations of statistical ideas, such as the wide range of graphs in chapter 2 (frequency distributions, histograms, bar graphs, Pareto charts, pie charts, dot plots, stem‑and‑leaf plots, and time‑series graphs) and the visual, numerical, and symbolic presentations of confidence intervals in chapter 6. Students also learn to compute measures of central tendency and construct confidence intervals using different methods, including hand calculations, graphing calculators, and Excel. Extended learning activities reinforce this understanding by having students model data using symbols, diagrams, graphs, and written explanations, then reflect on how each representation contributed to their understanding. These experiences demonstrate that statistical concepts can be represented and solved in multiple valid ways.

The materials support students in justifying and selecting among multiple solution methods as students explain why a particular representation or approach is appropriate for a given task. For example, in chapter 6, the materials ask students exercises 35 to 40 to choose between the standard normal distribution and the t distribution when constructing a confidence interval. Students then justify their decision based on the characteristics of the data. Chapter 9, section 9.2, allows students to determine the line of best fit using any method: formula, slope‑intercept form, graphing calculator, or statistical software. This activity reinforces that multiple approaches are acceptable and requires students to justify the method they selected. The pacing and activity guide strengthens this skill through activities in which students create their own hypothesis‑testing problems and explain how different tests or representations support their solutions. These tasks require students not only to use multiple methods but also to articulate why a chosen method is appropriate, demonstrating understanding, explanation, and justification that multiple approaches can be used to represent and solve problems.

Evaluation for 6.1c
Materials are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with peers and teachers.

The materials are designed to require students to make sense of mathematics through multiple opportunities to do and write about mathematical ideas. For example, in the MLS for chapter 1, section 1.1, students generate sample scenarios, identify populations and samples, organize data in tables, and write explanations that justify statistical relationships. In chapter 3, section 3.1, students complete probability tasks, including identifying sample spaces, determining outcomes, and constructing representations, such as tree diagrams, and write explanations to justify their reasoning. Other activities, such as the chapter 6, section 6.3, investigation, require students to run simulated samples, calculate proportions, analyze the behavior of intervals, and explain how changes in sample size affect the results. These tasks engage students directly in mathematical work and written explanation, supporting sense‑making through doing and writing.


Students have multiple opportunities to discuss mathematics with peers and educators through structured discourse routines embedded across chapters. For example, the MLS in chapter 1, section 1.1, direct students to discuss their reasoning with partners as they analyze populations, samples, and statistical relationships. The pacing and activity guide includes collaborative vocabulary activities in chapter 7, section 7.1, in which students listen to real‑world scenarios, identify statistical terms, and communicate their understanding with peers and educators. Section 7.4 requires students to work with a partner to write and discuss conclusions of hypothesis tests using academic vocabulary. The MLS in chapter 8 guide educators to facilitate conversations that help students interpret terms, compare ideas, and explain mathematical meaning. These opportunities for peer and educator discussion ensure that students make sense of mathematics through sustained mathematical discourse.

Evaluation for 6.2a
Materials support teachers in guiding students to share and reflect on their problem-solving approaches, including explanations, arguments, and justifications.

The materials support educators in guiding students to share and reflect on their problem‑solving approaches through structured activities that require explanation, argumentation, and justification. For example, in chapter 1, section 1.3, students work in pairs to explain relationships among components of an experimental design using complete sentences supported by sentence stems. The advanced differentiation activity extends this task by having students analyze a flawed experimental design, identify weaknesses, propose improvements, and justify their reasoning using conditional and argumentative language. Students present their solutions to the class and debate which confounding variables most affect the results, providing opportunities for educators to guide students in sharing and defending their approaches. Additional supports appear in chapter 2, section 2.5, in which students interpret unusual z‑scores, explain their solution process, and discuss real‑world meaning, with educator guidance prompting students to articulate and justify their reasoning.

The materials support educators in guiding students to reflect on their problem‑solving approaches through structured discourse and explanation prompts. For example, in chapter 7, section 7.1, the materials direct educators to have students state their hypotheses and test types to a partner, thereby supporting oral sharing of reasoning. In section 7.2, educators guide students through the steps to find a p‑value, then explain whether to reject the null hypothesis and justify their decision, prompting reflection on the meaning behind their computational work. In section 7.4, students work with a partner to write and discuss the conclusions of hypothesis tests using academic vocabulary, thereby reinforcing the explanation and justification of their reasoning. These activities provide explicit educator guidance to help students share, reflect on, and justify their mathematical approaches.

Evaluation for 6.2b
Materials include prompts and guidance to support teachers in providing explanatory feedback based on student responses and anticipated misconceptions.

The materials include prompts that support educators in providing explanatory feedback based on student responses. However, the materials do not include prompts to provide explanatory feedback based on anticipated misconceptions. For example, in chapter 5, section 5.4, educators receive prompts tied directly to student‑generated work, such as reminding students to use x̄ rather than x and to define the lower bound correctly when solving sampling‑distribution problems manually and with technology. In chapter 7, section 7.1, the materials provide educators with explicit questions to ask students—such as identifying the null and alternative hypotheses and determining the nature of the test—along with exemplar student responses to help evaluate precision and guide corrective feedback. In section 7.4, the materials prompt educators to guide students in checking manual calculations against graphing‑calculator output and using the p‑value to verify their decision. The materials support educators in how to respond to student thinking but not how to provide explanatory feedback based on anticipated misconceptions.

The materials include guidance to support educators in providing explanatory feedback based on student responses and anticipated misconceptions. For example, in chapter 4, section 4.2, educators receive guidance to address common errors, such as reminding students that 0! = 1 to prevent factorial mistakes. In chapter 7, section 7.2, the materials guide educators to have students complete the steps for finding a p‑value, then explain whether to reject the null hypothesis and justify their decision, thereby supporting reflection on student reasoning. Section 7.3 highlights a common misconception: confusing “reject” with “fail to reject” the null hypothesis. The materials advise educators to emphasize the conceptual purpose of hypothesis testing. These examples demonstrate that the materials provide guidance for addressing both student responses and anticipated misconceptions.