Statistics and Probability with Applications (5E)

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 outlining the concepts taught in the course. Within the “Getting Started” section of the table of contents, the materials organize the core statistical concepts into both 90‑day and 180‑day course outlines. These pacing guides map out the chronological progression of topics for educators across different school calendars. Because these outlines appear within separate digital components of the platform, educators must navigate multiple locations to view the full progression of course concepts.

The materials do not provide a comprehensive scope‑and‑sequence document that integrates these concepts with the Texas Essential Knowledge and Skills (TEKS) or the English Language Proficiency Standards (ELPS). Instead, the Statistics and Probability with Applications (SPA), 5th Edition TEKS Correlation Guide and the Statistics and Probability with Applications, 5th Edition ELPS Correlation Guide both appear as separate files in the “Correlations” subsection, disconnected from the primary course outlines. Because these elements are located in different digital files, the program lacks a single overview that details the chronological progression and alignment of skills.

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 across various instructional calendars. In the introductory pages of the Teacher’s Edition, the materials provide comprehensive 180‑day and 90‑day pacing calendars, mirrored in the chapter planning pages preceding each chapter. These schedules offer operational guidance for daily and block class periods and help educators plan lessons efficiently across different school calendars.

The 180‑day pacing guide is designed for standard 50‑minute daily class periods, while the 90‑day pacing guide is tailored for block schedules of 75 to 90 minutes or compressed half‑year courses. The materials outline how to adjust instruction for these different calendars, including explicit directives indicating when an educator should omit an entire chapter in the condensed 90‑day pacing schedule to maintain appropriate course progression.

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.

The materials explain the unit order rationale and describe how concepts connect throughout the course. Within the Teacher’s Edition introductory section, “Organizing Your Course,” the text outlines how the structural sequence intentionally builds student confidence and conceptual mastery. This rationale is reinforced at the unit level, where each chapter introduction explains how the lesson order connects to prior and future statistical strands throughout the course, establishing the macro-trajectory of learning.

To support these conceptual connections, the materials divide each chapter into five to eight specific sections grouped around two to three core learning topics. The opening pages of each chapter feature a comprehensive description of the overarching goals, along with a breakdown of each section. This layout tracks how the skills relate across units, establishing a clear mathematical progression through chapter overviews that map out the curriculum’s conceptual connections.

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

The materials include protocols with corresponding guidance for unit internalization. The Teacher’s Edition provides chapter planning pages that support unit‑level preparation through essential background content and pacing frameworks. These resources include a high-level chapter overview, evidence-based instructional practices aligned to each chapter topic, and a detailed lesson-by-lesson content breakdown with assignment recommendations and guidance on using textbook exercises. Together, these tools help educators understand each chapter’s structure and intent before planning daily instruction.

For daily lesson preparation, materials also include instructional supports for lesson internalization. The curriculum embeds background guidance focusing on statistical vocabulary and core content. Detailed instructional support, professional insights, and educator talk notes frame the pages within the Teacher’s Edition margins. These planning sections also list available chapter resources, interactive statistical applets, and digital educator tools to help educators navigate the online platform and prepare for classroom instruction. While these components function as internalization supports, the materials do not include a single, explicit, step‑by‑step internalization protocol. Instead, the guidance is distributed across chapter planning pages, embedded margin notes, and digital resources.

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

The materials provide administrative visibility into educator resources via the Teacher’s Edition introductory sections, “Using the Teacher’s Edition and Resources Effectively” and “Program Resources Available with SPA5e.” These sections outline the rationale, location, and intended audience for all print and digital assets, enabling instructional leaders to verify that classroom pacing aligns with the 90-day or 180-day guides. Additionally, leaders can observe embedded classroom supports such as Teaching Tips, Common Errors, and targeted differentiation strategies directly within the instructional margins.

The materials do not include dedicated guidance, protocols, or frameworks specifically designed to help instructional leaders support educators in implementing the materials. While the Achieve platform provides robust digital dashboards that track assignment and course performance and student goal-setting reflections, it lacks leader-focused support. The platform delivers raw student metrics and data visualizations. However, it fails to pair these analytics with concrete observation rubrics, data-driven meeting protocols, or strategic coaching actions. Because the program lacks these explicit administrator protocols, the materials do not provide actionable tools to help instructional leaders coach or guide educators based on classroom data.

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.

The materials include comprehensive unit overviews that give educators the background content knowledge needed to teach the concepts in the unit effectively. At the start of each chapter, the Teacher’s Edition includes a professional development (PD) overview featuring a video that explains where the chapter fits within the course, highlights the big ideas, and provides global instructional guidance. In chapter 1, the “Chapter Fits” section describes how the unit connects to previous and future chapters. Planning pages outline each lesson and summarize the major statistical ideas and conceptual foundations educators will address. These overviews also embed targeted Teaching Tips, integrated Common Error alerts to preempt misconceptions, and differentiation strategies that deepen educator understanding of the content. The See Yourself in Stats feature further supports instructional context by introducing careers connected to statistics, helping educators frame the relevance of the unit’s concepts.

The materials also include comprehensive unit overviews. These overviews provide the academic vocabulary needed to teach the unit’s concepts effectively. The Teacher’s Edition planning pages supply lesson‑by‑lesson vocabulary lists and highlight key terms in both educator guidance and student materials. For example, chapter 2, lesson 2.4 identifies the empirical rule as essential academic vocabulary for assessing normality. In chapter 9, lesson 9.1 introduces foundational inference terminology, including significance test, null hypothesis, alternative hypothesis, one‑sided alternative hypothesis, two‑sided alternative hypothesis, and p‑value. The materials pair these terms with Teaching Tips and Common Error alerts. The materials include guidance that “the p‑value is key to determining statistical significance” and advise first considering evidence for the null hypothesis before evaluating evidence for the alternative. These structured vocabulary supports ensure educators have the precise mathematical language needed to scaffold statistical reasoning throughout the unit.

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 include supports for families in both Spanish and English for each unit, with suggestions for supporting their student’s progress. In Spanish, the materials include a complete Guía de Acompañamiento Familiar that provides families with a weekly routine aligned to unit content. This guide outlines concept checks, homework monitoring steps, and structured conversation prompts that help families reinforce statistical reasoning and visual interpretation skills. The Spanish Guía para el Estudiante and the bilingual Glosario further support families by clarifying unit concepts and academic vocabulary, giving Spanish‑speaking families accessible tools to discuss lessons and monitor progress.

Each unit’s materials also include English-language supports for families, with clear strategies for supporting student learning. The Family Companion Guide provides a parallel weekly routine that includes concept checks, homework checkpoints, and real‑world conversation starters tied to each chapter. It explains what students learn in every unit, such as analyzing distributions, evaluating sampling methods, or interpreting regression models. It offers families actionable prompts to reinforce understanding at home. The English Student Guide and bilingual Glossary complement these resources by helping families navigate program features and discuss statistical concepts with their student. These resources ensure families have clear, accessible tools in both languages to engage with each unit and support their student’s learning.

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, detailed lesson plans with daily objectives aligned to the lesson’s content and language standards. Each lesson begins with clearly stated learning targets in both the Teacher’s Edition and Student Edition, clarifying instruction and supporting student goal setting. The chapter’s introductory pages list the objectives for each lesson and identify suggested practice. For example, in chapter 1, the planning pages present a structured overview that includes lesson‑level objectives, specialized vocabulary, and required materials. The program also supplies standalone TEKS and ELPS correlation documents in the Achieve platform’s “Correlations” section, mapping standards to specific lessons and pages. These correlations work alongside the chapter planning pages to clearly identify instructional goals, vocabulary, and standards alignment for each lesson.

The materials also include tasks, questions, and instructional assessments aligned to the lesson objectives. The planning pages outline daily tasks, required materials, and recommended assignments for each instructional day. In chapter 2, the Pacing Guide provides a table listing instructional days, lesson focus, and aligned practice. The guide includes a designated flex day for remediation, technology use, or reteaching difficult learning targets. Recommended assignments reference specific exercises such as Optional Assignment 2.1 (Exercises 20 and 23), Exercise 2.2 (Exercises 20 and 22), and Exercise 2.4 (Exercises 18 and 20), ensuring alignment between tasks and objectives. Lessons also embed formative assessments. For example, lesson 5.2 includes a student‑facing “What Did You Learn?” table that pairs learning targets with examples and corresponding practice problems, enabling educators to monitor student understanding and progress.

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 materials include lesson overviews that list the educator and student materials needed to deliver each lesson effectively. In the Teacher’s Edition, margin‑level Activity Overview boxes provide the materials required for instruction. For example, the Activity Overview for chapter 3, lesson 3.6 identifies the technology needed for the activity, specifying an internet‑connected device for each student or group, or a single device with a projector when individual access is not available. The Activity Overview for chapter 6, lesson 6.1 lists classroom materials such as poster board or chart paper, dot stickers, and dice. The Teacher Resource Materials (TRM) button in the eBook links to STATsExtras, a collection of supplemental external resources, including articles, videos, applets, and data sets. Together, these margin-level Activity Overviews and the TRM-linked STATsExtras provide educators with both lesson-specific materials and broader supplemental resources that support effective lesson delivery.

Suggested timing for each lesson component is also included in the materials. At the course level, the introductory pacing guides provide 180‑day and 90‑day structures outlining the recommended progression of lessons throughout the year. Within individual lessons, the Teacher’s Edition includes margin‑level Activity Overviews that supply specific timing guidance for classroom tasks. For example, the Activity Overview for chapter 2, lesson 2.4 designates an eight- to 10-minute duration, chapter 3, lesson 3.6 provides a 10–12-minute range, and chapter 6, lesson 6.1 specifies a 15-minute activity. Additional Activity Overviews, such as those in chapter 4, lesson 4.4, and chapter 11, lesson 11.2, also include explicit minute‑by‑minute recommendations. These timing details help educators plan lesson flow and allocate instructional time effectively.

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 on effectively using lesson materials for extended practice (e.g., homework, extension, enrichment). The Teacher’s Edition provides course‑level and lesson‑level support for using exercises as practice and homework. In the chapter planning pages, the “Pacing and Recommended Assignments” section outlines 180‑day and 90‑day pacing options and explains how to structure assignments across the course. The Using the Exercises Effectively guidance describes five categories of end‑of‑lesson exercises: Building Concepts and Skills, Mastering Concepts and Skills, Applying the Concepts, Extending the Concepts, and Recycle and Review. The guidance then explains how to use each type for standard practice, homework, reinforcement, or extension. Wraparound margins embed Teaching Tips that clarify how particular problems connect to prior content and suggest patterns such as assigning even‑numbered exercises for additional practice or using Your Turn items and handouts for formative assessment.

To facilitate extended learning, enrichment, and differentiation, the materials provide advanced problem tiers, alternate examples, and educator notes. End‑of‑lesson assignments include an Extending the Concepts tier designed to challenge students who are ready for deeper application. For example, in chapter 5, lesson 5.6, the Extending the Concepts problems ask students to analyze whether events are mutually exclusive or independent using a two‑way table of ticket‑purchase data, and to apply geometric probability to repeated independent trials such as rolling doubles with dice. These tasks require students to extend core ideas beyond routine practice and apply them in more complex or novel contexts. Educator‑facing wraparound notes offer differentiation suggestions and highlight common errors to anticipate during independent work. Additionally, alternative examples embedded in the margins offer educators optional extensions or clarifications to enrich instruction or provide additional practice opportunities for students who need them.

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 include a variety of formative and summative assessments at the unit and lesson levels. These assessments include varying types of tasks and questions. The materials provide chapter reviews, section exercises, and daily Bell Ringers to check student understanding throughout the curriculum. Lesson‑level assessments include features such as Your Turn Exercises and Building Concepts and Skills. These are paired with varied task formats, including Recommended Assignment Exercises, Additional Exercises, and Open‑Ended Exercises, which require students to analyze data displays, interpret graphs, or respond to multi‑step statistical scenarios. Chapter 1, sections 1.7 and 1.8 contain these assignment types. At the unit level, the materials include cumulative evaluations such as the Chapter Review Exercises, Practice Tests, and chapter‑level projects. These features provide warm-up routines and end‑of‑unit evaluations that measure overall student progress using multiple question types. Question types include multiple-choice, free-response, simulations, and performance‑based investigations.

The materials do not include diagnostic instruments within these instructional assessment options. While the curriculum incorporates daily Bell Ringers, these exercises function strictly as brief introductory tasks. Other lesson‑level assessments also lack diagnostic features. For example, Building Concepts and Skills exercises “assess reading comprehension,” and Mastering Concepts and Skills exercises each “address a single learning target,” which limits their ability to identify underlying learning difficulties. Applying the Concepts exercises combine multiple learning targets. Recycle and Review exercises “reinforce concepts learned in previous lessons,” making them suitable for practice, but not for determining prerequisite readiness. Extending the Concepts tasks differentiate instruction for motivated students rather than evaluating foundational gaps. Unit‑level assessments such as Chapter Review Exercises and Practice Tests allow students to “check their work,” but measure cumulative understanding rather than diagnosing strengths or structural challenges. None of these assessment formats provide the detailed, targeted information required for diagnostic purposes.

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

The materials include definitions and the intended purposes of the instructional assessments included in the curriculum. The chapter planning pages define the role of several statistical applets used within lessons and describe how each supports instruction. For example, in chapter 5, the planning pages identify the applet used for the “Hiring Discrimination” activity in lesson 5.1 and explain that it helps students analyze hiring outcomes. The same section defines the applet used in the “What Is Probability?” activity to simulate repeated coin tosses and the applet used in lessons 5.7 through 5.8 to compute factorials, permutations, and combinations. These descriptions clarify each applet’s instructional purpose and how it supports lesson‑level practice.

The materials also define the purpose of unit‑level assessments. The guidelines explain that Chapter Review Exercises and Practice Tests are designed for student self‑evaluation, noting that answers appear at the back of the student edition so students can check their work. In addition, the pacing guides identify built-in flex days in both the 180-day and 90-day structures. According to the pacing guides, these days are intended for reteaching, quizzes, activities from the educator resource materials, or additional practice on difficult learning targets. By defining the roles of review exercises, practice tests, and flex days, the materials clearly describe the intended purposes of these assessment components.

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

The materials include digital educator guidance to support consistent administration and scoring of instructional assessments. In chapter 4, the Teacher’s Edition provides margin notes for the “Project on Response Bias.” The margin notes direct educators to a project description and evaluation rubric. The project description outlines specific requirements for student proposals, including a “detailed description of how you will obtain your subjects (minimum of 50),” ethical data‑collection precautions, and criteria for avoiding confounding variables. These parameters give educators clear expectations for administering the project and evaluating student submissions.

The Teacher Resource Materials (TRM) also include examples of completed student projects. The student projects are introduced with the statement, “Here are two examples of successful student projects.” These examples illustrate appropriate experimental designs and data summaries, helping educators apply consistent criteria when scoring student investigations. In addition, the digital platform offers an external test bank that supplies correct answers and statistical rationales for individual items, allowing educators to verify scoring decisions when assembling assessments. Together, these resources provide educators with clear guidance for administering and evaluating instructional 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 in the external test bank that align to specific course, unit, and lesson objectives. When instructors compile an exam within the test-building interface, they select the information icon to view the underlying statistical rationale and lesson-level goals for each question. This feature allows educators to verify that their compiled formative quizzes and summative unit exams align with the targeted instructional topics outlined across the curriculum.

The materials do not include diagnostic assessments aligned with the course objectives or the TEKS. Although the external test bank organizes items by lesson concepts, the program does not align these assessments to the state standards. Furthermore, while the material incorporates daily Bell Ringers, these exercises function strictly as brief, lesson-level warm-up routines rather than valid diagnostic instruments. Diagnostic assessments must yield detailed data to evaluate deep student knowledge, identify specific student strengths, and isolate structural learning difficulties. Diagnostic tools must also determine precise learning targets for foundational components—including vocabulary, comprehension, decoding, and encoding—or support a comprehensive evaluation process.

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

The materials provide instructional assessment items that vary in complexity, but they are not aligned to the TEKS. The materials include an external test bank that lets educators generate assessments by selecting questions based on topic and difficulty level. Within this system, educators can choose items using filters such as Difficulty. Individual questions include an information icon that displays attributes such as State Standards and Difficulty. However, the standards are not populated with TEKS alignment. They do not identify a direct connection between assessment items and the TEKS. As a result, the materials offer opportunities to select items at varying levels of complexity. However, they do not ensure that these items evaluate student understanding of TEKS-aligned expectations across levels of cognitive demand.

Instructional assessments do not include a variety of TEKS-aligned item types. The external test bank allows educators to create tests by selecting different question types and generating assessments from existing item sets. Educators can initiate this process through the Create Test feature and organize items by characteristics such as difficulty or question format. However, because the TEKS are not loaded into the system or explicitly identified, educators cannot select or verify items based on TEKS alignment. Without embedded TEKS alignment or clear identification of item types aligned with TEKS expectations, the materials do not provide the multiple TEKS-aligned item types required to assess student understanding across different formats.

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

The materials include scoring information to help educators score instructional assessments accurately. The Achieve platform allows teachers to access assignment-level data, including individual student scores and each item’s point value, supporting accurate scoring. Educators can view results across electronically assigned assessments and analyze performance for each student and each question. In addition, the Teacher’s Edition includes fully worked solutions for exercises, quizzes, and activities, as well as chapter-level learning target grids that clarify what each item assesses. The external test bank also provides item rationales and allows educators to adjust point values, further supporting consistent and accurate scoring. Together, these components provide sufficient scoring information to support accurate evaluation of student responses.

Instructional assessments and scoring information guide interpretation of student performance. The Achieve platform includes Insights and Reports dashboards that aggregate assessment data and present performance analytics through structured prompts such as “What are the top learning objectives to review?” and “What are the top assignments to review?” These dashboards organize results into categories such as “Performance by Unit,” “Performance by Learning Objective,” and “Performance by Student,” allowing educators to analyze trends and identify specific areas of need. In addition, item-level feedback explains incorrect responses and guides students toward correct reasoning, helping educators understand the nature of student errors. These reporting features and feedback mechanisms provide a clear framework for interpreting student performance and informing instructional decisions.

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 include data-tracking tools and instructional activities. However, these components do not connect to guide responses to student performance trends on assessments. The Achieve platform includes Insights and Reports dashboards that dynamically track student performance and identify areas of concern. The dashboards highlight “top learning objectives to review” and organize results by categories such as “Performance by Unit” and “Performance by Learning Objective.” In addition, the Teacher’s Edition includes a “Using the Exercises Effectively” section that categorizes tasks into functional types, including Building Concepts and Skills, Mastering Concepts and Skills, Applying the Concepts, Extending the Concepts, and Recycle and Review. These components provide access to performance data and a range of instructional activities that could support reteaching or differentiation.

The materials do not provide guidance on using the included tasks and activities to address student performance trends on assessments. While the Achieve platform displays performance data, including score distributions and identified areas for review, it does not include educator-facing guidance, recommendations, or instructional strategies for using this data to select or implement specific tasks or activities. The materials do not connect performance results to targeted instructional next steps, such as assigning specific exercises or reteaching strategies based on assessment outcomes. As a result, educators must independently interpret the data and determine how to respond to student needs without explicit support.

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.

The materials include tools that help educators track student progress and growth through the reporting features available in the Achieve platform. The platform provides access to the Reports dashboard, which allows educators to monitor performance at the individual student, instructional unit, and specific course learning objective levels. Educators can view assignment completion rates, student scores, and performance trends over time, including comparisons across assessments within a chapter. Additional reporting tools, such as the Insights dashboard and assignment performance reports, include data such as score distributions, time-on-task analysis, and learning objective trends. These tools provide educators with ongoing visibility into student progress and growth, supporting monitoring across the instructional cycle.

The materials include tools that help students track their progress and growth through the Achieve platform’s student-facing features. Students can access a gradebook that displays course totals, assignment scores, completion status, and due dates, allowing them to monitor their performance across tasks and assessments. The platform also allows students to filter assignments by resource type. Resource types include assessments, quizzes, and goal-setting activities, providing additional ways to review their progress. In addition, students receive immediate, item-level feedback on assessments that explains errors and prompts correct reasoning, supporting reflection on their understanding. These features give students continuous access to performance data and feedback, enabling them to track progress, identify areas for improvement, and take ownership of their academic 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 educator guidance to support students who have not yet reached proficiency through embedded instructional supports that address content misconceptions and provide alternative representations. Within the Teacher’s Edition, margin features such as Common Errors in chapter 1, section 1.3, alert educators to frequent misunderstandings, including the misconception that the standard deviation cannot be zero. Teaching Tip annotations provide contextual supports that connect statistical concepts to real-world situations, such as references to “the world’s highest ski jump,” helping educators anchor abstract content in accessible contexts.

The materials include guidance to support skill development for students below proficiency. This guidance relies on general differentiation suggestions that are neither systematic nor targeted. For example, in chapter 1, lesson 1.5, a Teaching Tip directs educators to allow students who struggle with constructing graphs by hand to use technology, providing an accessible scaffold for procedural skills. The Teacher’s Edition also recommends using Your Turn videos for remediation, reinforcement, or review. However, this guidance is repeated without differentiation across lessons and does not include explicit strategies tied to specific prerequisite skill gaps. As a result, the materials provide general suggestions rather than a cohesive approach to differentiated instruction for students who have not yet achieved grade-level 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).

The materials include pre-teaching and embedded supports to facilitate the acquisition of unfamiliar academic vocabulary. These supports are provided in both educator- and student-facing materials. Within the Teacher’s Edition, chapter planning pages include an “Effective Classroom Practice” section with guidance such as “Mind the Vocabulary” and “Pay Attention to the Vocabulary.” This guidance directs educators to organize discipline-specific terms into conceptual groupings, including sampling and experiments, and to provide explicit instruction for accurate use of terminology. Additional Teaching Tip annotations clarify discipline-specific language by explaining synonymous terms (e.g., individuals, cases, and subjects) and distinguishing related concepts such as categorical and qualitative variables. In the Student Edition, key terms are defined in highlighted boxes within lessons and reinforced through English and Spanish glossaries, supporting students as they learn and apply academic vocabulary in context.

The materials include embedded supports to clarify unfamiliar references in text. However, these supports are primarily contextual rather than systematic. For example, Teaching Tip annotations rephrase academic language to support comprehension, such as explaining that statisticians use “plausible” as a substitute for “reasonable.” Additional supports appear in lesson activities that connect abstract statistical concepts to real-world contexts. For example, the chapter 7 activity, “A Penny for Your Thoughts,” includes Teacher’s Edition guidance and linked resources to clarify scenario-based references. While these features help educators address potential confusion by making language and contexts more accessible, the supports are embedded within individual lessons and activities rather than presented as a structured approach to pre-teaching or systematically addressing unfamiliar references across the materials.

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.

Statistics and Probability with Applications, 5th Edition includes enrichment and extension activities that deepen students’ understanding of statistical content beyond grade-level expectations. In the Student Edition, each lesson includes an “Extending the Concepts” section at the end of the exercises that presents more complex tasks requiring conceptual reasoning. For example, in chapter 1, section 1.1, problem 21, “Quantigorical?” prompts students to analyze how age can function as a categorical rather than a quantitative variable, requiring justification and classification beyond procedural application. Additional extension tasks across lessons require students to interpret variations in data relationships and apply more advanced concepts. For example, extension tasks require students to analyze subsets within scatterplots or develop regression equations, extending conceptual understanding of statistical models.

The materials include educator guidance for differentiated instruction to extend student skills. However, this guidance is general rather than explicitly structured. Within the Teacher’s Edition planning pages, the “Using the Exercises Effectively” section directs educators to assign “Extending the Concepts” problems to advanced or motivated students to differentiate instruction. Additional Teaching Tip annotations occasionally suggest ways to extend procedural and analytical skills. For example, they guide students to explore different associations in the data or apply alternative solution methods. While these features support skill-extension opportunities, the materials do not include explicit instructional guidance, scaffolded enrichment pathways, or targeted differentiation strategies aligned with specific advanced skill development. As a result, the materials provide access to extension tasks but limited support for systematically advancing the skills of students who have demonstrated proficiency.

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 help educators model and explain concepts through structured examples, step-by-step directions, and scripted questioning. Within chapter 1, lessons on “Analyzing One-Variable Data” provide worked and alternative examples that model both processes and reasoning. For example, in the lesson on constructing bar charts, a highlighted three-step sequence directs educators to draw and label axes, scale axes based on frequency, and construct bars, providing a clear procedural model. The accompanying solution models explain the data distribution through sample narratives, offering educators a template for interpreting results. Additional prompts appear in activity overviews, including explicit directions such as “number the horizontal axis by 1s, starting at 0 and going up to 12.” Explicit directions also include scripted questions, such as asking students which labels apply to the axes, thereby supporting real-time instructional modeling and student engagement.

The materials include explicit guidance that helps educators model and explain concepts through planning resources, worked examples, and instructional commentary. Within the Teacher’s Edition, chapter planning pages provide “Effective Classroom Practice” guidance and lesson-by-lesson overviews that emphasize key ideas. For example, the overviews and guidance include integrating graphical and numerical understanding and selecting appropriate analyses based on variable types. Across lessons, worked examples aligned to learning targets include complete model solutions and “Voice of the Teacher” notes that demonstrate how to explain reasoning and address misconceptions. In chapter 4, the activity overview for “Who Wrote the Federalist Papers?” includes detailed instructions, required materials, and discussion prompts that guide educators in modeling concepts and interpreting results. Additional supports, including video-linked examples and solution sets, reinforce modeling by providing multiple representations of reasoning. Together, these features provide explicit guidance that enables educators to model and explain statistical concepts consistently.

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

The materials include educator guidance that supports effective lesson delivery and facilitation through multiple instructional approaches. Within the Teacher’s Edition, chapter planning pages include Teacher Resources that provide instructional support through professional development tools such as “Chapter Overview” and “Lesson Overview” videos. These videos prepare educators to implement lessons. Lesson-level materials include instructional notes, Common Error annotations, and Teaching Tip features that guide educators in presenting content, addressing misconceptions, and supporting understanding during instruction. For example, in chapter 5, materials linked to Lecture Presentation Slides and activities such as “Stats Applied!” provide structured opportunities for whole-group instruction. These slides and activities are followed by guided discussion, supporting educators in facilitating concept development using multiple representations.

The materials include recommendations that support varied instructional approaches through embedded resources and flexible tools. Educators are directed to use a range of strategies, including digital tools such as interactive applets and external data sets; collaborative activities such as “Where Do You Stand?”; and print-based supports such as Alternate Examples and Your Turn handouts for exit tickets or group tasks. Additional recommendations include using bell ringers, “Tech Corner” activities, and chapter projects to extend learning and monitor progress. Comprehensive pacing guides, including 180-day and 90-day options, further support lesson structuring across instructional settings. Activity overviews also recommend facilitation moves, such as using chart paper to construct visual models and prompting student discussion to interpret results. Together, these recommendations provide educators with multiple, flexible approaches for delivering and facilitating instruction.

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 support multiple types of practice, including guided, independent, and collaborative learning opportunities across print and digital resources. Within the materials, worked examples and linked video solutions provide guided practice by modeling procedures and reasoning step by step. Independent practice is embedded through lesson exercises and supported by the Achieve digital platform, which provides immediate feedback to support self-monitoring and revision. Lesson activities include collaborative and mixed practice structures. For example, in chapter 1 activities, students work in pairs to simulate trials, record results independently, and contribute findings to a whole-class dot plot, integrating collaborative, individual, and whole-group practice. Additional activities, such as hands-on investigations using manipulatives, prompt students to complete tasks individually and then discuss results as a class. Together, these varied practice opportunities support student learning through multiple instructional formats and provide opportunities for both educator-guided and independent application of concepts.

The materials include guidance and recommended structures that support educators in implementing these varied practice types through whole-group, small-group, and individual instruction. Within the Teacher’s Edition, chapter planning pages and lesson resources direct educators to use Lecture Presentation Slides for whole-group instruction, followed by guided and independent practice through lesson exercises and Alternate Examples. In chapter 7, activity guidance such as “How many craft sticks are in the bag?” directs educators to organize students into whole-class and small-group settings to complete investigations and discuss results. Similarly, in chapter 8, activities such as “What proportion of beads are red?” guide educators in grouping students to explore probability concepts collaboratively and individually. Additional recommendations, including bell ringers, exit tasks, and digital tools, support flexible grouping and effective implementation of practice structures. Together, these features provide clear guidance that enables educators to organize and facilitate multiple types of practice across instructional settings.

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 include educator guidance on providing linguistic accommodations for students at beginning levels of English language proficiency as defined by the ELPS. The materials include supports such as an English/Spanish glossary, flashcards, translated resources, and a read-aloud eBook feature. However, the Teacher’s Edition does not explain how or when to use these supports to scaffold language for students with limited English proficiency. For example, the materials do not include guidance on introducing vocabulary, modeling academic language, or providing structured supports such as sentence stems, word banks, or visual scaffolds for students in the early stages of language acquisition. Additionally, differentiation features, such as Teaching Tip annotations and Lecture Presentation Slides, focus on content understanding rather than linguistic accommodations and do not address how to adapt instruction for students at beginning proficiency levels.

The materials do not include educator guidance on providing linguistic accommodations for students at intermediate or advanced English language proficiency levels. Although Achieve resources include ELPS correlation documents, these resources only identify alignment to standards and do not provide implementation guidance for differentiating instruction across proficiency levels or supporting students in using increasingly academic language. The materials do not include recommendations for scaffolding oral or written discourse, building academic vocabulary through structured language routines, or supporting cross-linguistic connections as students progress in language development. As a result, educators must independently determine how to provide linguistic accommodations and support language development across proficiency levels, as the materials lack explicit, ELPS-aligned guidance for engaging students in increasingly complex academic language use.

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 help educators use the materials effectively within state-approved bilingual or English as a Second Language (ESL) program models. The Teacher’s Edition and associated resources do not provide guidance for implementing instruction within program structures such as dual language immersion, transitional bilingual, ESL content-based, or ESL pull-out models. For example, the Teacher’s Edition lesson guidance and planning pages, including chapter-level “Effective Classroom Practice” sections, focus on content delivery and do not address how to adapt instruction for emergent bilingual (EB) students within bilingual or ESL program settings. Additionally, lesson features such as Your Turn activities and Lecture Presentation Slides do not include directions for modifying instruction or delivery within these program models.

The materials include limited linguistic resources. However, they do not provide educator-facing guidance for implementing these supports within bilingual or ESL program contexts. Student-facing supports, including an English/Spanish glossary, flashcards, translated chapter summaries, and video transcripts, are provided without accompanying recommendations for instructional use. Similarly, ELPS correlation documents are available through Achieve’s standards alignment, but do not include implementation guidance, instructional routines, or program-specific strategies for using the materials within bilingual or ESL settings. These resources do not address how to structure instruction, adapt materials, or support language development within state-approved program models. As a result, educators must determine independently how to use these materials with EB students, as the program does not provide explicit guidance for implementation in bilingual or ESL settings.

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 do not include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, or making cross-linguistic connections through oral discourse. The materials include vocabulary exposure within lessons, such as terms like population, census, and sample in chapter 4; however, the Teacher’s Edition does not provide guidance for facilitating structured oral language development that supports academic vocabulary acquisition or comprehension. The materials do not include discussion protocols, sentence stems, collaborative routines, or teacher guidance designed to help students build background knowledge through oral discourse. Additionally, available linguistic supports, including glossaries, flashcards, and translated resources, do not include educator-facing guidance for making cross-linguistic connections, such as comparing languages, identifying cognates, transferring meaning between languages, or leveraging students’ home languages during oral discourse.

The materials do not include embedded guidance for teachers to support emergent bilingual students in developing academic vocabulary, increasing comprehension, building background knowledge, or making cross-linguistic connections through written discourse. Although academic vocabulary appears throughout lessons, including terms such as chi-square goodness-of-fit test in chapter 11, the materials do not provide guidance for supporting students in writing about mathematical concepts in ways that develop academic vocabulary or increase comprehension. The program does not include structured writing supports such as sentence frames, guided writing tasks, graphic organizers, or opportunities for extended written responses that build background knowledge. Furthermore, available resources do not include recommendations for making cross-linguistic connections through written discourse, such as cognate instruction, language comparisons, bilingual writing supports, translation activities, or opportunities to connect meaning between a student’s home language and English. As a result, the materials do not provide educator guidance aligned to any indicator component through oral or written discourse.

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 across lessons and units that require students to demonstrate depth of understanding aligned to the Statistics TEKS. The publisher includes a “SPA 5th edition TEKS Correlation with Breakouts” document that links individual Statistics TEKS to textbook pages, activities, and projects. For example, Statistics TEKS 4(B), which requires students to summarize data, is correlated to multiple sections in chapter 1, lesson 1.1 requires students to “summarize the distribution of a variable with a frequency table or a relative frequency table,” and lesson 1.8, where students make and interpret boxplots. Statistics TEKS 7(D), which requires students to compare methods for determining a line of best fit, is linked to the chapter 3 activity in the TRM. Within the student materials, lessons are structured to build rigor across a sequence of tasks. In chapter 4, lesson 4.1 exercises progress from “Building Concepts and Skills” to “Mastering Concepts and Skills,” and finally to “Applying the Concepts,” supporting students as they move from foundational understanding to application aligned to Statistics TEKS 2(B). These structures give students opportunities to demonstrate increasing depth of understanding across lessons and units aligned to the TEKS.

Instructional assessments require students to demonstrate depth of understanding aligned to the Statistics TEKS. In chapter 2, the lesson 2.4–2.6 quiz increases rigor by moving from drawing the normal curve to verifying normality using standard‑deviation intervals and applying z‑score reasoning. In chapter 3, quizzes for lessons 3.1–3.4 emphasize conceptual interpretation. This includes justifying variable choices, explaining why correlation does not imply causation, describing scatterplot structure, and analyzing how outliers affect correlation. The document titled “SPA 5e TEKS Correlation with Breakouts” aligns the Statistics TEKS with specific units and lessons, rather than with individual assessment items. The BFW Test Generator organizes questions by difficulty and Bloom’s Taxonomy, but does not categorize items by TEKS. Educators need to use the correlation document to identify which assessment items correspond to specific TEKS expectations. Together, these assessment resources give students opportunities to demonstrate depth of understanding aligned to the Statistics TEKS.

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 within and across lessons, supporting students as they move toward proficiency in the Statistics TEKS. Lesson exercise sets typically include 25–30 questions, organized in a deliberate progression: “Building Concepts and Skills,” “Mastering Concepts and Skills,” “Applying the Concepts,” “Extending the Concepts,” and “Review and Recycle.” Quizzes also show progressive complexity. In chapter 2, questions move from drawing the normal curve to verifying normality using raw data and finally to non‑integer z‑score and percentile calculations. In chapter 3, quiz questions progress from identifying variables and describing bar charts to interpreting scatterplots, estimating correlation, evaluating causation, and analyzing the effects of outliers. Across lessons and assessments, questions consistently increase in complexity to support mastery of the Statistics TEKS.

Tasks increase in rigor and complexity, helping students demonstrate proficiency in the Statistics TEKS. In chapter 2, tasks progress from drawing and labeling the normal curve to verifying normality using historical data and calculating percentiles with non‑integer z‑scores, aligned to Statistics TEKS 2(B) and 2(D). In chapter 3, tasks advance from describing relationships in scatterplots to estimating correlation, evaluating causation, and analyzing the effect of outliers, aligned to Statistics TEKS 3(A)–3(D). In chapter 4, lesson 4.7, tasks move from outlining a completely randomized design to explaining statistical significance and conducting simulations to determine whether observed differences are meaningful, and are aligned with Statistics TEKS 4(A)–4(C). The publisher’s “SPA 5e TEKS Correlation with Breakouts” document identifies these TEKS connections at the lesson level, allowing educators to confirm which tasks support specific TEKS expectations.

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 recurring patterns in statistical reasoning. In chapter 3, the “Big Picture” section explains how the chapter extends ideas from chapters 1 and 2, showing a consistent pattern of moving from graphical displays to numerical summaries to mathematical models. In chapter 4, the materials build on these earlier patterns by showing how working with graphs, summary statistics, and models prepares students for understanding randomness and data‑collection methods. In chapter 8, lesson 8.1 continues this pattern by connecting confidence intervals to students’ prior work with sample proportions and sample means from chapter 7, reinforcing that sampling variability consistently underpins inference across units.

The materials also demonstrate coherence across units by explicitly connecting big ideas and relationships between statistical concepts. In chapter 3, the STATS Applied! essential question (“When will the cherry trees blossom?”) introduces the big idea that understanding one variable often requires examining its relationship with another. The chapter’s resolution revisits this idea as students apply earlier concepts to make and justify predictions. In chapter 8, lessons develop the big idea of estimating population parameters through confidence intervals, which chapter 9 extends to determine whether results are statistically significant. In chapter 10, lesson 10.1 builds directly on the relationships developed in lessons 8.3 and 8.4, extending students’ understanding from confidence intervals for a single proportion to comparing two population proportions. These chapter introductions, educator notes, and lesson explanations help students experience statistics as a connected progression of big ideas rather than isolated topics.

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 language learned in previous courses to content in the current course. In the Teacher Edition’s chapter 3, lesson 3.2, a Teaching Tip guides educators to reference students’ prior algebra experience with the terms x‑axis and y‑axis when discussing coordinate axes, even when the horizontal axis in a statistical graph is not technically the x‑axis. This intentional use of familiar terminology supports continuity in mathematical communication and helps students access new statistical representations through vocabulary learned in earlier coursework. Additional guidance in chapter 3, lesson 3.5 reinforces this language connection by anchoring the regression equation y = a + bx to past learning, identifying a as the y‑intercept and b as the slope, terms first introduced in Algebra 1 and Algebra 2.

While these examples use familiar language consistently, they do not demonstrate coherence across units by connecting content learned in previous courses or grade levels to the content learned in the current course. The materials reference axis labels and slope/intercept terminology, but they stop at vocabulary reinforcement rather than linking the underlying content to earlier coursework. Students previously encountered correlation and linear modeling in middle school mathematics and Algebra 1, yet the materials do not explicitly draw on those content progressions to build coherence in the current course.

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 students have already learned in the current course to new statistical ideas. In chapter 3, lesson 3.1, the STATS Applied! activity asks students to draw on the knowledge and problem‑solving strategies developed in chapter 1 as they reason through an introductory question revisited throughout the chapter. As students progress through chapter 3, lessons extend ideas introduced earlier in the course, such as moving from graphical displays to numerical summaries and then to mathematical models. This helps students build on a foundation of concepts already developed in the current course. These structures support students in applying familiar representations and procedures as they encounter more advanced statistical reasoning.

The materials demonstrate coherence at the lesson level by connecting students’ prior grade‑level knowledge to new mathematical skills. In chapter 1, lesson 1.3, students use “what [they] may have learned as the median in previous math classes” to support their understanding of the distributional center. This explicitly activates earlier learning to build new statistical reasoning. In chapter 3, lesson 3.5, the materials reference the familiar algebraic form, y = mx + b, to help students connect prior algebra coursework to the statistical regression model ŷ = a + bx, reinforcing how foundational graphing and slope‑intercept concepts extend into statistical modeling. Educator notes and instructional routines further leverage students’ prior experience graphing two-variable data, guiding them to use familiar procedures to interpret and predict with regression lines. For example, familiar procedures for interpreting and predicting regression lines include mapping x‑values to y‑values. Through these explicit connections, the materials help students transition from earlier mathematical learning to new statistical ideas.

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

The materials provide spaced retrieval opportunities with previously learned skills across lessons and units. In chapter 5, lesson 5.8, the guided solution directs students to use methods introduced earlier in chapter 4, lesson 4.7, creating a spaced opportunity to retrieve and apply procedural skills across units. Program‑level structures reinforce this distributed practice: cumulative practice sets integrate skills from earlier units, lesson‑level checkpoints require students to bring forward previously taught procedures, and Recycle and Review exercises prompt students to retrieve and apply skills learned in prior chapters. For example, chapter 6, exercises 24 and 25, reference sections 2.6, 5.7, and 6.1. Together, these features support spaced retrieval of previously learned skills across lessons and units.

The materials include spaced retrieval opportunities with previously learned concepts across lessons and units. In chapter 2, lesson 2.1, students recall their prior understanding of quartiles as they interpret percentiles, creating conceptual spaced retrieval across lessons. In chapter 3, lesson 3.6, the text prompts students to recall earlier conceptual learning by stating, “Recall that regression to the mean is the tendency for extreme values… to be paired with less extreme values.” The text connects this idea to the foundational concept of standard deviation from chapters 1 and 2, demonstrating conceptual spaced retrieval across units. Unit reviews, mixed‑format assessments, and reengagement tasks further require students to retrieve concepts taught earlier in the course.

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

The materials provide interleaved practice opportunities with previously learned skills across lessons and units. Lesson‑level exercises consistently include a “Recycle and Review” section that integrates earlier procedural skills with new content. For example, in chapter 3, lesson 3.4, items require students to apply skills from earlier lessons involving correlation and distribution. Interleaving also occurs in chapter 11, where exercises alternate between constructing hypotheses, creating conditional distribution graphs from chapter 1, and performing computational routines for expected counts and chi‑square statistics. This requires students to shift flexibly among multiple procedural methods. Across the program, mixed‑problem sets, investigations requiring multiple statistical tools, and unit assessments that blend new procedures with previously taught ones provide structured opportunities for students to revisit and apply skills in interleaved formats across lessons and units.

The materials also provide interleaved practice opportunities with previously learned concepts across lessons and units. In chapter 11, lesson 11.4, exercise 26 introduces a cumulative review titled “How well does a line fit? (2.4, 3.5, 3.7),” requiring students to revisit conceptual ideas from chapters 2 and 3 while engaging with new inferential content. For example, some of these ideas include residual plots, regression models, and the conceptual meaning of regression to the mean. Interleaving is further supported through “Flex Day” lessons, such as the activity for chapter 10, lessons 10.1–10.2. This activity integrates conceptual understanding of confidence intervals and significance tests from chapters 8 and 9 with new ideas about comparing population proportions. Performance tasks, mixed‑format assessments, and real‑world investigations also blend conceptual demands from multiple units, ensuring students regularly revisit and apply previously learned concepts in interleaved formats 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 statistical models and representations. In chapter 2, students compute standardized scores and interpret their meaning within distributions of daily market changes, evaluating whether values are typical or unusual. Chapter 3 includes questions that ask students to interpret scatterplots and correlation coefficients in activities such as “Guess the Correlation,” analyzing the direction and strength of relationships, and evaluating the accuracy of model estimates. In chapter 4, lesson 4.8 prompts students to examine real statistical studies, interpret study design, analyze supported inferences, and evaluate ethical considerations. Chapter 7 extends this work by asking students to analyze graphs and tables to determine production‑process efficiency, requiring interpretation and evaluation of mathematical representations in applied contexts.

The materials also include tasks that require students to interpret, analyze, and evaluate statistical models and representations. In chapter 2, students construct density curves and use them to reason about proportions and means. Chapter 3 includes Your Turn tasks in which students create scatterplots, identify explanatory and response variables, analyze associations such as sugar versus calories or femur versus humerus lengths, and evaluate regression models. In chapter 8, students compute and interpret confidence intervals, analyze factors that affect the margin of error, and evaluate population estimates using number lines, data displays, and interval models. Across these lessons, students generate, interpret, and critique graphical, numerical, and algebraic models representing authentic statistical situations.

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. In chapter 1, students construct histograms by hand and use the Tech Corner to generate them electronically, creating graphical models of data distributions. Chapter 3 includes questions in which students determine the equation of a line that models the relationship shown in a scatterplot, use the algebraic model to make predictions, and examine residuals. In chapter 5, lesson 5.3, the Your Turn activity asks students to construct a Venn diagram to model the sample space for the defined events A (attended college) and H (is a homeowner), requiring students to generate a visual representation of the probabilistic situation.

The materials include tasks that require students to create models to represent mathematical situations. Chapter 3 Your Turn handouts ask students to construct segmented bar charts, scatterplots such as sugar versus calories or femur versus humerus lengths, and regression plots for flowers and yogurt. This requires students to generate visual or algebraic models to communicate relationships in data. In chapter 8, students use given data to construct confidence intervals on normal distribution curves, creating interval models that represent population parameters and support the interpretation of the margin of error. Across these lessons, students build graphical, numerical, and algebraic models that represent authentic statistical situations.

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

The materials include questions that give students opportunities to apply conceptual understanding to new problem situations and contexts. In chapter 3, the chapter project on Lake Champlain water quality asks students to apply regression concepts to unfamiliar environmental data. Students accomplish this by creating scatterplots, calculating least‑squares regression lines, judging model appropriateness, comparing predictors, and justifying conclusions. In chapter 5, Extending the Concepts questions in lesson 5.8 require students to transfer their understanding of permutations and combinations to new real‑world situations without being told which method to use, and to interpret the meaning of combinations in unfamiliar contexts. These questions move beyond routine practice by asking students to apply conceptual understanding flexibly to new scenarios and justify their reasoning.

The materials also include tasks that give students opportunities to apply conceptual understanding to new problem situations and contexts. Chapter 4, lesson 4.5 asks students to use their understanding of observational studies, experiments, confounding, causation, and bias to interpret and evaluate unfamiliar real‑world scenarios, requiring them to transfer prior learning to new contexts. In chapter 7, lesson 7.5, students apply ideas about sampling distributions, variability, and the central limit theorem to new situations involving music libraries, insurance losses, traffic patterns, manufacturing defects, lightning strikes, and customer wait times. Chapter 8, lesson 8.4 asks students to construct and interpret a 99 percent confidence interval for data on U.S. teens’ daily TV habits and analyze conclusions based on the interval. Across these lessons, students apply conceptual understanding to unfamiliar scenarios, determine which statistical ideas apply, and justify conclusions in varied contexts.

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 student automaticity necessary to complete grade‑level tasks. In chapter 3, students repeatedly identify slope and y‑intercept in regression equations and distinguish predicted values from actual outcomes, building automatic recognition of core regression components through short, repeated practice. In chapter 4, students repeatedly identify simple random samples and distinguish them from other sampling methods, reinforcing automatic recall of sampling structures. Chapter 6 includes Bell Ringers that revisit foundational probability ideas, such as finding probabilities of independent events, providing quick, repeated warm‑ups that strengthen automaticity. Across these lessons, structured repetition supports rapid, accurate recall of essential statistical procedures.

The materials also include tasks designed to build the fluency students need to complete grade‑level tasks. In chapter 2, Recycle and Review problems ask students to determine how changes in data values affect the mean, median, standard deviation, and interquartile range, strengthening fluency with how statistical measures respond to variation. In chapter 3, Your Turn tasks require students to compute correlations, interpret regression slopes and intercepts, and calculate residuals, thereby reinforcing fluency with multistep statistical procedures. In chapter 5, students repeatedly compute theoretical and experimental probabilities in contexts such as dice, coins, and colored M&Ms, developing fluency with probability rules through varied applications. Across these lessons, students practice applying procedures accurately and efficiently in multiple contexts, supporting the development of fluency required for grade‑level work.

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.

The materials include opportunities for students to practice efficient, flexible, and accurate mathematical procedures. In chapter 2, lesson 2.2 asks students to convert units, apply transformation rules, and compute measures of center and variability. The linked practice exercise requires students to apply these procedures in a new context. In chapter 3, lessons 3.1–3.5 include Your Turn tasks that ask students to compute correlation step‑by‑step, construct segmented bar charts and scatterplots, and interpret regression slope and intercept, supporting efficiency, flexibility, and accuracy across multiple representations. In chapter 5, lesson 5.7, students calculate permutations using hand computation, a TI‑84 graphing calculator, and the applet, providing multiple procedural pathways and reinforcing efficient use of technology. Lesson 8.3 in chapter 8 guides students through calculating a confidence interval using both hand computation and a technology‑based method, reinforcing procedural accuracy and efficient use of digital tools.

The materials include opportunities throughout a unit for students to practice efficient, flexible, and accurate mathematical procedures. Each unit includes a cumulative practice test that requires students to choose appropriate methods and apply procedures across numerical, graphical, and contextual formats. In chapter 4, lesson 4.4 provides unit‑level procedural practice as students compute sample statistics, compare sampling distributions, and apply efficient methods for estimating population parameters across multiple sampling scenarios. In chapter 8, unit‑level activities such as “What Proportion of the Beads Are Red?” ask students to compute sample proportions, compare multiple solution methods, determine efficient and accurate approaches, and construct intervals of plausible values for a population proportion. Across units, students repeatedly apply procedures in varied contexts, strengthening efficiency, flexibility, and accuracy with core statistical methods.

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.

The materials include opportunities for students to evaluate procedures, processes, and solutions for efficiency, flexibility, and accuracy. In chapter 3, lesson 3.6 asks students to calculate the median‑median line and evaluate its efficiency by examining how the method responds to outliers. Additional tasks in chapter 3 require students to judge procedural suitability, such as determining whether a regression line provides an efficient basis for prediction, comparing how correlation changes with different explanatory variables, and using residual plots to evaluate a regression model’s accuracy. In chapter 4, lesson 4.8 asks students to examine real statistical studies and evaluate whether the sampling method, assignment process, data collection techniques, and ethical safeguards are appropriate and accurate, requiring students to judge the validity of the procedures used.

The materials also provide opportunities throughout a unit for students to evaluate the efficiency, flexibility, and accuracy of mathematical procedures. In chapter 7, lesson 7.1 asks students to use the sampling distribution of a statistic to evaluate whether claims about population parameters are reasonable, requiring judgment of whether the method, calculation, and interpretation are appropriate. In chapter 8, lesson 8.5 includes a simulation‑based activity in which students compare three different methods for estimating a population mean, evaluate long‑run capture rates, and determine which procedures are most accurate and efficient for constructing confidence intervals. Across units, students use technology tools, simulations, and comparative tasks to evaluate the appropriateness and effectiveness of statistical procedures in varied contexts.

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

The materials include embedded educator supports that guide students toward increasingly efficient approaches throughout the lesson. In chapter 2, Modeling One‑Variable Quantitative Data, Planning Pages, and Using Exercises Effectively help educators sequence problems so students progress toward streamlined methods for transforming distributions. In chapter 3, Analyzing Two‑Variable Data, the Teaching Tips model efficient procedures for making predictions and interpreting residuals, helping educators coach students toward more accurate and efficient approaches. In chapter 4, Collecting Data, Effective Classroom Practice guidance emphasizes precise statistical vocabulary. For example, it distinguishes random sampling from random assignment. This reduces procedural errors and supports efficient reasoning.

The materials include embedded supports that guide increasingly efficient approaches throughout a unit. In chapter 7, educator‑facing supports such as Teacher Tips, Activity Overviews, Alternate Examples, and Common Errors appear across lessons, helping educators reinforce efficient strategies for interpreting sampling distributions. In chapter 8, lesson 8.3 provides step‑by‑step guidance for calculating a confidence interval by hand and then using an applet to compute the interval more efficiently and accurately, supporting educators as students transition to technology‑supported methods. Across units, How‑To boxes, Tech Corners, and Activity Overviews help educators model streamlined procedures and guide students toward increasingly efficient statistical approaches.

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

The materials explicitly state how the conceptual emphasis of the TEKS is addressed. In the “Organizing Your Course” section, the program explains that lessons are structured to build conceptual understanding through learning targets, conceptual examples, and exercise types labeled “Building Concepts and Skills” and “Applying the Concepts,” which focus on reasoning, interpretation, and relationships. “Effective Classroom Practice” guidance reinforces this emphasis by stating, “conceptual understanding is valued more than formulas.” Essentially, educators should prioritize meaning, interpretation, and reasoning when introducing statistical ideas. Additional conceptual statements appear in chapter planning pages, which describe how students develop understanding of ideas such as association, distribution, sampling, and variability before applying procedures. These explicit descriptions show educators how instruction intentionally builds conceptual development aligned with TEKS expectations.

The materials also explicitly state how the procedural emphasis of the TEKS is addressed. Exercise structures such as Mastering Concepts and Skills and Recycle and Review identify where students practice procedures, and planning pages explain that these tasks focus on procedural accuracy, step‑by‑step methods, and targeted skill development. The Statistics and Probability with Applications, 5th Edition TEKS Correlation Guide specifies where procedural expectations are taught, and lessons include learning targets that state procedural goals directly, such as “Use a two‑way table to find probabilities.” Worked examples and How‑To boxes make procedural steps explicit, outlining numbered procedures for constructing graphs, selecting samples, computing statistics, and applying probability rules. Across these structures, the materials clearly articulate how procedural fluency develops and where TEKS-aligned skills are explicitly taught.

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 and manipulatives, pictorial representations, and abstract representations as required by the TEKS. In chapter 4, lesson 4.4 includes questions that prompt students to interpret results from hands‑on sampling activities using concrete manipulatives and physical simulations. Then, questions prompt students to interpret pictorial representations such as diagrams and dot plots. In chapter 5, lesson 5.5 includes questions that ask students to analyze tree diagrams and then apply abstract probability rules and notation. In chapter 6, lesson 6.1 includes questions that move students from concrete die‑rolling outcomes to pictorial dot plots of sample means and finally to abstract reasoning about plausibility using formulas. Across these lessons, questions intentionally progress from concrete to pictorial to abstract forms, aligned with TEKS expectations.

The materials include tasks that use concrete models and manipulatives, pictorial representations, and abstract representations as required by the TEKS. In chapter 3, the Candy Grab activity requires students to physically measure hand spans and collect candies (concrete), construct segmented bar charts and scatterplots (pictorial), and then analyze regression equations and residuals (abstract). In chapter 9, lesson 9.1, titled “I’m a Great Free‑Throw Shooter,” includes tasks that begin with a physical or simulated free‑throw model (concrete), transition to a graphical sampling distribution (pictorial), and conclude with symbolic inference procedures (abstract). Across units, tasks consistently move students through concrete, representational, and abstract forms to support conceptual understanding and problem‑solving in alignment with TEKS requirements.

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 include supports that help students connect, create, define, and explain concrete models as they transition to abstract statistical concepts. In chapter 6, lesson 6.1 begins with a concrete model: rolling a die and using dot stickers to create a class dot plot of sample means. Then, the lesson guides students to abstract reasoning as they compute theoretical and empirical probabilities and evaluate the plausibility of outcomes using symbolic formulas. In chapter 9, lesson 9.1 provides alternate versions of a simulation activity using physical paper‑clip spinners or digital applets, supporting students as they move from concrete simulation tools to abstract probability concepts and symbolic inference. These supports help students build understanding by grounding abstract statistical ideas in concrete experiences.

The materials also include supports that help students connect, create, define, and explain representational models as they transition to abstract concepts. In chapter 3, lesson 3.6 moves students from scatterplots to calculating residuals and comparing sums of squared residuals, helping them visualize and explain how representational graphs connect to the abstract concept of the least‑squares regression line. In chapter 5, lesson 5.6 guides students from a representational model to abstract symbolic probability expressions with prompts that support the transition from visual structure to formal notation. Across these lessons, the materials provide explicit supports that help students link representational models to symbolic, numeric, and algorithmic statistical ideas, aligned with TEKS expectations.

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

The materials give students opportunities to develop academic mathematical language using visuals. In chapter 2, lesson 2.3, the section “Describing Density Curves” requires students to interpret visual representations of distributions and describe characteristics such as skewness and symmetry using appropriate statistical terminology. Additional visual supports appear throughout the materials, including graphs, histograms, scatterplots, residual plots, and the target diagram in figure 7.5, which students use to describe the statistical concepts of bias and variability. These visual representations give students recurring opportunities to connect statistical vocabulary to graphical models and communicate mathematical ideas using academic language.

Students have opportunities to develop mathematical academic language through manipulatives and other language-development strategies. In lesson 4.4, students use a spinner to simulate random samples and investigate sampling variability. As students conduct repeated simulations and discuss the results, they apply academic vocabulary such as random sample, variability, simulation, and sampling distribution in context. Additional opportunities come through technological tools, including the One Quantitative Variable, Single Group applet and graphing calculator activities, which let students manipulate data displays while developing statistical language. The materials also include contextual language-development opportunities in which students explain statistical concepts, interpret results, and apply mathematical vocabulary to real-world situations such as earnings data, news articles, and data investigations. Across the materials, hands-on activities, technology-based tools, and contextualized discussions support the development and use of academic mathematical language.

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 include embedded educator guidance to scaffold and support students’ development and use of academic mathematical vocabulary in context. Effective Classroom Practice guidance in the “Planning” section reminds educators to have students answer questions within the context of the data, reinforcing statistical language during instruction. Additional educator guidance appears throughout lessons and activities. For example, chapter 3, lesson 3.5 includes teaching tips that clarify statistical terms such as residual and error and guide educators in connecting mathematical language to data analysis. Chapter resources also provide vocabulary lists, definitions, and main-point summaries that help educators introduce and reinforce key statistical terminology within instruction.

Embedded support for academic mathematical vocabulary also appears in instructional activities and educator-facing notes. In chapter 4, the activity “Who Wrote the Federalist Papers?” guides educators to discuss concepts such as variables, observational units, and sampling methods while students analyze dot plots and data displays. Educators note that the materials highlight key statistical concepts and support classroom discussions that connect vocabulary to graphical representations and real-world contexts. The materials include educator prompts, vocabulary references, and guidance for contextual discussion. These are incorporated into lessons and activities to support students’ development and use of academic mathematical language. However, much of the guidance focuses on contextual reasoning and clarification of statistical concepts rather than providing explicit strategies for introducing and reinforcing vocabulary, identifying language demands, or supporting students with varied language-development needs.

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. In chapter 3, lesson 3.3, the activity, “Guess the Correlation,” provides guidance for educators to help students develop and apply statistical vocabulary while interpreting applet-generated graphs. Students discuss their correlation estimates with group members and justify their reasoning using statistical language related to associations and data displays. Additional guidance in Effective Classroom Practice notes and Teaching Tips directs educators to attend to vocabulary and connect symbols, formulas, and statistical concepts. These supports give students opportunities to use appropriate statistical terminology, communicate mathematical ideas, and engage in mathematical discourse as they analyze data.

Guidance supports mathematical conversations and gives students opportunities to hear, refine, and use mathematical language with peers over time. In chapter 4, the activity “Who Wrote the Federalist Papers?” asks students to use a word list, create dot plots, analyze sampling methods, and discuss statistical concepts such as variables and observational units. Educator notes guide classroom discussions and prompt students to explain their reasoning using statistical language. As the activity continues into lesson 4.4, additional educator questions require students to apply and revisit concepts such as mean, sampling variability, standard deviation, range, and interquartile range, allowing them to build and extend their mathematical language over time. Educator guidance also includes discussion prompts, anticipated observations, and sample explanations to help educators facilitate conversations and respond to student thinking during statistical investigations.

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

The materials integrate TEKS process standards appropriately into instruction. The chapter planning pages include a “Using the Exercises Effectively” section that describes how students progress from developing foundational skills to applying statistical reasoning in increasingly complex contexts. Throughout the course, students engage in activities that require problem-solving, analysis, representation, and communication. For example, in lesson 1.6, students apply statistical concepts to a real-world situation, supporting the use of mathematics to solve problems in everyday life. Additional opportunities arise in lessons where students analyze the effects of changes in data values, interpret statistical notation, and draw conclusions from data displays. These activities embed TEKS process standards within the study of statistical concepts.

Opportunities to apply TEKS process standards are also embedded in investigations, technology activities, and statistical simulations throughout the course. In chapter 4, lesson 4.4, students conduct a simulation using a spinner, organize and represent results graphically, discuss findings, and evaluate evidence to support a conclusion. In chapter 6, students use applets to investigate normal distributions, discrete random variables, and binomial distributions, and use technology to analyze and verify results. The STATS Applied! investigation, “A Jury of Your Peers,” requires students to select appropriate models, use statistical tools, calculate and interpret measures, justify conclusions, and communicate reasoning using evidence from data. Across the materials, students engage in problem-solving, reasoning, communication, representation, and the strategic use of tools and technology, demonstrating the integration of the TEKS process standards throughout the course.

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

The materials do not describe how TEKS process standards are incorporated throughout the course. The course includes projects, chapter reviews, STATS Applied! investigations, technology activities, and other instructional experiences that align with TEKS process standards. However, the materials do not explain how those standards are embedded in instruction throughout the course. The “SPA 5e TEKS Correlation with Breakouts” document identifies locations where specific TEKS, including process standards, are addressed. However, it serves as a correlation chart rather than describing how the process standards are incorporated into instruction. As a result, educators receive references to aligned lessons and activities but not a description of how TEKS process standards are incorporated throughout the course.

The materials do not describe how TEKS process standards are connected throughout the course. Although the materials give students opportunities to engage with process standards across lessons, activities, and assessments, they do not explain how those standards build on one another or recur throughout the course. The “SPA 5e TEKS Correlation with Breakouts” document lists lessons and activities associated with individual process standards, but it does not describe relationships among the standards or explain how students develop and apply them over time. Consequently, the materials provide evidence of alignment with individual process standards but do not describe how the TEKS process standards are connected throughout the course.

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 do not describe how each TEKS process standard is incorporated throughout the unit. Unit and chapter overviews summarize lesson content, instructional activities, and statistical concepts students will encounter. For example, the chapter 3 “Lesson-by-Lesson Content Overview” describes topics such as segmented bar graphs, scatterplots, and other statistical representations that students will use throughout the unit. While these activities align with process-standard skills such as reasoning, representation, and communication, the materials do not explicitly identify the TEKS process standards or explain how the unit incorporates them. The “SPA 5e TEKS Correlation with Breakouts” document provides references to lessons and activities associated with specific TEKS. However, it does not include a unit-level description that explains how the process standards are incorporated throughout the unit.

The materials do not describe how the TEKS process standards connect throughout the unit. Although lessons within a unit build statistical content knowledge and give students opportunities to engage in reasoning, representation, and communication, the materials do not explain how the TEKS process standards connect across lessons. The unit overviews and TEKS correlation document do not describe how process standards develop, recur, or build upon one another as students progress through a sequence of lessons. As a result, educators do not have a description of how the TEKS process standards connect throughout each unit.

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 materials include chapter-planning resources, lesson-by-lesson content overviews, and instructional guidance describing lesson topics, activities, and suggested teaching practices. For example, the chapter 1 “Lesson-by-Lesson Content Overview” identifies content on bar charts, pie charts, dot plots, stem plots, and histograms. However, these lesson descriptions do not identify the TEKS process standards incorporated into each lesson or provide a lesson-level overview of those standards. As a result, educators receive information about lesson content but not an overview of the TEKS process standards addressed in individual lessons.

The materials also do not provide lesson-level overviews of TEKS process standards through supporting resources. The “SPA 5e TEKS Correlation with Breakouts” document lists lessons, activities, and exercises associated with specific TEKS. However, it functions as a correlation chart rather than an overview of the process standards each lesson incorporates. Similarly, chapter planning pages, such as “Using the Exercises Effectively,” describe instructional features and assignment suggestions but do not identify or summarize the TEKS process standards for individual lessons. Consequently, the materials do not include an overview of the TEKS process standards incorporated into each lesson.

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

The materials give students opportunities to think mathematically, persevere through problem solving, and make sense of mathematics. In lesson 1.7, students analyze real data, compute measures of spread, justify their results, and compare statistics with and without an outlier, requiring multi-step reasoning. Students also apply mathematical thinking in chapter projects and STATS Applied! activities in which they select representations, calculate summaries, interpret data, and communicate findings. Additional opportunities in chapters 2 and 3 ask students to explain their processes, construct and compare representations, distinguish correlation from causation, and complete multi-step algebraic calculations, supporting sustained mathematical reasoning and perseverance.

In chapter 11, lesson 11.5, students determine the standard deviation of a simulated sampling distribution, increase the sample size, generate repeated samples, and explain why the standard deviation decreases. Students analyze sampling distributions, compare sample slopes to population slopes, and justify how changes in sample size affect variability. Chapter 4 further reinforces these expectations as students simulate random assignment, compute group means, interpret dot plots, and evaluate statistical significance. Across lessons and chapters, students consistently engage in multi-step analysis, interpret mathematical relationships, and justify their conclusions, providing repeated opportunities to think mathematically and persevere through complex problem solving.

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, explaining, and justifying that problems can be represented and solved in multiple ways. In lesson 4.2, students evaluate sampling methods by identifying sources of bias, explaining why certain approaches produce unrepresentative samples, and proposing improved designs. The worked video solution models the reasoning process and demonstrates how different sampling approaches affect the validity of statistical conclusions. In lesson 11.4, students conduct a chi‑square test for association by stating hypotheses, verifying conditions, calculating expected counts, interpreting results, and completing the test both by hand and with technology. The video solution shows multiple ways to compute expected counts. It provides a technology‑based method for performing the chi‑square test, reinforcing that statistical tasks can be represented and solved through verbal explanations, symbolic notation, manual calculations, and technological tools.

The materials further support multiple representations and solution methods through activities and exercises across chapters. In chapter 3, students use various approaches to find a line of best fit, including graphing calculators, applets, and hand‑drawn models. Students analyze residuals to justify which methods are more appropriate or more resistant to outliers. In chapter 6, students design a completely randomized experiment. They may choose different methods for random assignment, such as slips of paper or technology, before determining whether the results generalize to the U.S. population. Across lessons and chapters, students compare approaches, justify methodological choices, and explain how different representations and solution pathways support understanding and interpretation.

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 require students to make sense of mathematics through multiple opportunities to do, write about, and discuss mathematics with peers and educators. In chapter 3, students work in small groups to draw lines of best fit by hand, compute residuals, and compare their results to determine which model best fits the data. These tasks require students to justify computational choices in writing, such as explaining why residuals must be squared or why a least‑squares regression line is steeper than an absolute‑value line. Students also engage in mathematical discourse by debating which line provides a better fit and by justifying the use of a median‑median line for its resistance to outliers, thereby supporting sense‑making through hands‑on analysis, written reasoning, and peer discussion.

In chapter 4, students simulate random assignment, compute group means, and interpret a class dot plot to evaluate statistical significance. The activity requires students to analyze data, make sense of mathematical relationships, and explain why the results support or do not support a claim. Students write explanations to justify their reasoning and participate in structured peer discussion to compare interpretations and share findings. These designed opportunities ensure students actively do mathematics, write about their thinking, and discuss mathematical ideas with peers and educators as they work toward statistical conclusions.

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 opportunities focused on explanations. In chapter 2, STATS Applied! provides educator‑supported solutions that help educators prompt students to explain their reasoning when determining relative performance using density curves and summary statistics. In chapter 3, educators direct students to work in small groups to compare their regression equations and explain how they calculated their lines of best fit. Students reflect on their computational choices by explaining why residuals must be squared or why absolute values may be used. In chapter 4, the Your Turn activity asks students to describe how an experiment could be carried out and explain the purpose of random assignment, with educator‑provided responses that guide students in sharing and reflecting on their explanations.

The materials do not provide sufficient support for educators to guide students in sharing or reflecting on their problem‑solving approaches to arguments or justifications. Teaching Tips and FYI sidebars throughout the Teacher Edition provide background information and mathematical context but do not include prompts, discussion protocols, or guidance for facilitating student argumentation or justification. For example, notes in lessons 1.7 and 1.8 explain the mathematical significance of variability and hypothesis claims but do not direct educators to have students share arguments, compare solution strategies, or justify their conclusions. Similarly, while STATS Applied! activities require students to construct arguments or justify decisions, the educator guidance does not explicitly support students sharing or reflecting on those arguments. As a result, the materials lack structured educator support for arguments and justifications.

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 and guidance to help educators provide explanatory feedback based on anticipated misconceptions. In chapter 1, Common Error notes identify specific misunderstandings—such as confusing numerical values with counts or misinterpreting the range—and provide corrective clarification educators can use during instruction. Teaching Tips further support educators by explaining how to guide students in comparing dot plots and interpreting differences in variability, helping them address misconceptions before they affect students’ reasoning. These annotations help educators anticipate conceptual errors and provide targeted explanations that reinforce accurate statistical understanding.

The materials also include prompts and guidance to help educators provide explanatory feedback based on student responses. In chapter 3, Teaching Tips and Common Error callouts offer structured guidance for responding to student answers, including examples of reasonable predictions and prompts for helping students compare raw counts and percentages. Educators are guided to respond to incomplete explanations of associations by prompting students to address direction, form, and strength. In chapter 5, STATS Applied! activities include educator guidance that supports educators in prompting students to explain their reasoning, justify conclusions, and construct arguments using probability. These supports help educators react to student thinking, extend student explanations, and provide explanatory feedback tied to what students say or write.