Understanding Basic Statistics, Essential Package

Evaluation for 1.1a
Materials include an alignment guide outlining the TEKS, ELPS, and concepts covered, with a rationale for learning paths across grade levels (vertical alignment) and within the same grade level (horizontal alignment) as designed in the materials.

The materials include an Understanding Basic Statistics: Texas Teacher Resources Combined Guide, which contains an alignment guide and a scope and sequence document that outlines the alignment of the TEKS and the ELPS for each section, the concepts covered, and the suggested number of instructional days for each section.

The Understanding Basic Statistics Student Edition includes a “Table of Prerequisite Material” that lists the prerequisite sections for each chapter. In addition, each section in the Student Edition includes a “Looking Forward” note explaining how the concepts in that section connect to future topics in the course. For example, in the chapter 1 “Looking Forward” section, the materials say, “In later chapters, we will use information based on a sample and sample statistics to estimate population parameters (chapter 8) or make decisions about the value of population parameters (chapter 9).” In addition, the Understanding Basic Statistics: Texas Teacher Resources Combined Guide contains a section titled “Rationale for Vertical Alignment” that explains which grades provide the foundational understanding for statistics and how the course extends this understanding.

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use, such as just-in-time supports, advanced learning, or as a course.

The materials include an implementation guide with usage recommendations and strategies for effective educator usage. For instance, the Understanding Basic Statistics Instructor Manual includes each chapter’s purpose and perspective, chapter objectives, and a chapter outline, which allows the educator to “see how all the content relates to the topics covered in the text.”

The WebAssign Educator Guide provides instructors with tools to customize the course to the different needs of their students, including question types and relevance. This guidance helps educators adapt materials to meet diverse student needs and structure instruction. For example, “Select Your Scenario” questions increase relevancy and give students agency by allowing them to choose the context in which to answer a question. In addition, the Guide to Teaching Online encourages educators to consider a “flipped classroom model” for some lessons. This model allows students to complete some of the lower-level cognitive tasks (such as viewing the lectures and content videos) before coming to class so that class time can be spent completing higher-level analytic, synthetic, and/or creative activities. This model allows the educator to focus time on addressing student’s specific needs rather than providing basic content delivery.

Evaluation for 1.1c
Materials include a TEKS correlation guide with recommended skill entry points based on diagnostic assessment results.

The Texas Teacher Resources Combined Guide provides a Texas Alignment Guide and Texas Scope and Sequence with Pacing guide. The guides are broken down into sections, the number of days to cover each section, and which TEKS and ELPS are covered in each section. These guides provide support for teachers as they plan for instruction.

The Student Edition includes “Preview Questions” at the beginning of each chapter, which align with the big ideas for each section of the chapter. Learning objectives listed at the beginning of every chapter section give students a preview of the coming content. Students can revisit these objectives after each section to evaluate if they learned the intended content for each section. However, the materials do not provide recommended entry points based on these student self-evaluations. The materials do not include a diagnostic assessment, nor recommendations on skill entry points based on district diagnostic assessment results.

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

The Texas Teacher Resource Combined Guide provides educator guidance for unit (chapter) and lesson internalization. The guide includes lesson plans that have learning objectives with their TEKS and ELPS alignment, a suggested timeframe for a 50-min class period, and assessment resources aligned to the lesson. During the suggested timeframe, teachers are guided through the components of the lesson, including a focus problem, direct instruction, guided practice, independent practice, and lesson closure. The purpose of each component is also stated so that teachers understand why each component is necessary.

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

The materials do not include resources and guidance for instructional leaders to support educators with implementing the materials as designed. The Understanding Basic Statistics Instructor Manual provides educator-facing implementation resources and guidance, including the chapter’s purpose and perspective, chapter objectives, and an outline to support educators in planning instruction. These resources do not provide guidance for instructional leaders to enhance their ability to support educators with curriculum implementation.

The materials do not include guidance for instructional leaders to support educators in implementation, such as look-fors, coaching guidance, meeting protocols, observation rubrics, or implementation checklists.

Evaluation for 1.2a
If designed to be static, materials include detailed lesson plans with learning objectives, teacher and student materials, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

The Understanding Basic Statistics: Texas Scope and Sequence with Pacing document lists the TEKS and ELPS addressed in each section and how these standards align with the course materials. The materials include detailed lesson plans with learning objectives, suggested timeframes, as well as educator and student materials. For example, each chapter in the Student Edition includes a “Chapter Review” with a summary, a list of important words and symbols, review problems, and group projects.

Educator materials include the Understanding Basic Statistics Instructor’s Manual, which provides chapter outlines that organize activities and assessments by chapter and topic, aligned to the TEKS and ELPS. The educator materials also include PowerPoints with suggested discussion questions and supplemental activities. Student materials include a student textbook with practice problems for each section.

Evaluation for 1.2b
If designed to be adaptive, materials include detailed lesson overviews with learning objectives, lesson components with suggested timeframes, and assessment resources aligned with the TEKS and ELPS.

This guidance is not applicable because the program is not designed to be adaptive.

Evaluation for 1.2c
Materials contain support for families in Spanish and English for each unit, with suggestions on supporting the progress of their student(s).

The materials do not include communication with families. The available Understanding Basic Statistics documents include educator-facing chapter guidance, student downloads, WebAssign resources, online teaching guidance, analytics, and student support tools. The materials do not provide family-facing supports in Spanish or English, nor do the materials include unit-specific activities, questions, vocabulary, progress supports, or guidance that families can use to support student learning at home.

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

The materials include instructional formative assessments within the lessons but do not provide a purpose or definition. The materials include formative assessments, such as “Critical Thinking” problems, “Statistical Literacy” problems, “Basic Computation” problems, and “Linking Concepts: Writing Projects,” as opportunities for students to demonstrate understanding of terminology, methods, computation, interpretation, and written communication. However, the materials neither define these as formative assessments nor state their intended purpose.

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

The Texas Teacher Resources Combined Guide includes guidance to ensure consistent and accurate administration of instructional assessments. On each lesson plan, teachers are given aligned assessment resources that may be used for that section. For example, in Chapter 3, Section 3.3 suggests teachers assess using the following: Section 3.3 Basic Computation for quartiles and summaries; Interpretation problems for percentile meaning; Chapter 3 Review Problems 15-20; Linking Concepts; Writing Projects; Cumulative Review Problems (Chapter 1-3) for delayed retention across the first three chapters.

Evaluation for 2.1c
Digital assessments include printable versions and accommodations, including text-to-speech, content and language supports, and calculators, that educators can enable or disable to support individual students.

The materials provide a Cognero Test Generator platform that enables educators to generate assessment items that can be assigned digitally or printed.

The materials do not provide evidence that educators can enable or disable the required digital assessment accommodations for individual students. The WebAssign Educator Guide describes general learning tools, such as Master It, Watch It, and Read It, that can be turned on or off by assignment template or removed by question, but these tools are learning supports rather than the required accommodations of text-to-speech, content and language supports, and calculators for digital assessments. The guide also notes that the MindTap Reader includes ReadSpeaker text-to-speech and that eTextbook pages can be printed, but this guidance applies to the eTextbook, not to digital assessments.

Evaluation for 2.1d
Materials include diagnostic assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials do not include diagnostic assessments with TEKS-aligned tasks or questions. The materials include preview questions and focus questions at the beginning of each chapter, but these materials introduce chapter content and real-world context rather than diagnose student understanding or determine instructional needs.

Evaluation for 2.1e
Materials include a variety of formative assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels.

The materials include a variety of formative assessment opportunities through the Student Edition problem sets and educator-created WebAssign assignments. The Student Edition includes “Basic Computation,” “Statistical Literacy,” “Interpretation,” and “Critical Thinking” problems that provide opportunities for students to practice procedures, demonstrate conceptual understanding, interpret statistical results, and analyze statistical methods in context.

The WebAssign formative assignment provides additional digital formative assessment evidence. The assignment includes multiple-choice questions, select-all-that-apply items, numeric and symbolic entry fields, table-based data analysis, graph/sketch selection items, multi-part sequential tutorial exercises, and constructed-response explanation prompts. These tasks demonstrate more than two levels of complexity, ranging from recall and procedural understanding to application, statistical reasoning, hypothesis testing, and interpretation of conclusions in real-world contexts.

Evaluation for 2.2a
Instructional assessments include scoring information and guidance for interpreting student performance, including rationale for each correct and incorrect response.

The WebAssign Educator Guide describes the assignments, course packs, labs, project milestones, and tools, such as Master It, Watch It, and Read It, available on WebAssign.The guide notes that Master It provides graded step-by-step support to help identify where a student struggles. The Checks for Understanding and Feedback in the Texas Teacher Resource Combined Guide provide guidance for educators on interpreting student performance results. There are checkpoints spaced throughout the lesson sequence, with look-fors that state what a proficient response includes, and feedback that provides explanatory language tied to the likely error rather than a simple correction.

The materials provide rationales for correct responses through the Solution and Answer Guide. For example, in chapter 9, the guide explains why a statistical decision is appropriate, such as comparing the p-value to the significance level, rejecting or failing to reject the null hypothesis, and interpreting the result in context. However, the materials do not provide a rationale for incorrect responses.

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 Texas Teacher Resources Combined Guide guides educators in using the included tasks and activities to address student performance trends on assessments. Each chapter in the guide includes a section titled “Using Performance Data” that connects a common performance pattern to a specific instructional response. For example, if the data in chapter 3, “Averages and Variation,” shows that students are computing the mean and median accurately but miss selection items, it is likely because students did not have enough practice with the comparative judgment, only the arithmetic. The guide advises educators to reassign the “Interpretation” and “Critical Thinking” problems from 3.1 and require students to provide a written justification for every choice.

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 for educators to track student growth. For example, educators use the Cognero Test Generator platform to generate reports that track student progress, including grade book reports, progress reports, assignment results reports, question item analysis reports, prescription reports, proficiency charts and reports. There are also reports to compare classes and rosters.

The student view displays completed and in-progress assignments but does not include tools for students to monitor their own progress or growth.

Evaluation for 2.2d
If designed to be static, materials provide prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity.

The Texas Teacher Resources Combined Guide includes “Checks for Understanding” and “Feedback” sections for each chapter, providing explicit, timely guidance on feedback during lesson delivery. For example, the “Checks for Understanding” and “Feedback” sections for chapter 2, “Organizing Data,” include a chart that outlines when the assessment should take place, the prompt to ask students, what to look for in their responses, and the explanatory feedback to provide. For example, educators should pause after the frequency table in section 2.1 and ask students to state the boundary between two named classes. The guide explains that students should use the midpoint between the upper limit of one class and the lower limit of the next. If a student gives a limit instead, the guide advises educators to ask where a value falling between the two classes would go and explain that the boundary is what closes that gap.

In chapter 10, “Inferences about Differences,” the guide advises educators to pause mid-lesson in section 10.1 and ask students to explain why a paired test uses one column of differences. Students should recognize the paired test as a one-sample test, but if the student computes two separate means, the guide advises educators to ask what quantity the hypotheses are about.

Evaluation for 2.2e
If designed to be adaptive, materials provide frequent checks for understanding at key points throughout each lesson or activity.

This guidance is not applicable because the program is not designed to be adaptive.

Evaluation for 3.1a
Materials include explicit educator guidance for lessons or activities scaffolded for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills.

The Texas Teacher Resources Combined Guide contains explicit educator guidance for scaffolding lessons and activities for students who have not yet reached grade-level proficiency. Each chapter in the guide contains a section on “Differentiation,” which includes a chart that names the required requisite skills, a description of what it looks like when a student is missing that skill, and a scaffold to support students. For example, in chapter 1, “Getting Started,” one prerequisite skill is proportional reasoning for sample and population size. Students who lack this skill cannot judge whether a sample is a plausible size relative to a population. The guide suggests educators revisit grade 6 and 7 concepts on ratio reasoning with a concrete pair of numbers before discussing representativeness.

Evaluation for 3.1b
Materials include explicit educator guidance for language supports, including pre-teaching and embedded supports for developing academic vocabulary and unfamiliar references in text.

The Texas Teacher Resources Combined Guide provides suggestions for pre-teaching academic vocabulary so students can focus on mathematics. Section 8, “Academic Vocabulary and Classroom Discourse,” outlines the key vocabulary and language supports for each chapter before reading and using cognates to bridge meaning. In addition, the Understanding Basic Statistics Emergent Bilingual Support Guide includes a section on increasing comprehension and building background knowledge. When a chapter’s context is unfamiliar to students, the guide suggests “build[ing] the background briefly before the mathematics rather than allowing students to decode context and content simultaneously. Two minutes on what a wood duck is prevents twenty minutes of confusion in Chapter 10.”

Evaluation for 3.1c
Materials include explicit educator guidance for enrichment and extension activities for students who have demonstrated proficiency in grade-level and above grade-level content and skills.

The materials provide guidance for educators on assigning enrichment and extension activities to students who have demonstrated proficiency in grade-level content and skills. The Student Edition includes project-based extension opportunities through “Data Highlights: Group Projects” and “Linking Concepts: Writing Projects.” For example, the chapter 11 tasks ask students to apply chi-squared testing to DUI arrest data and to compare probability, two-proportion, and chi-squared homogeneity tests in the context of an ibuprofen/placebo study. These tasks require students to synthesize content, apply statistical methods, and communicate their reasoning in writing.

In addition, the Texas Teacher Resources Combined Guide contains more chapter-specific activities and projects for students who demonstrate proficiency in grade-level material. For example, in chapter 7, students can run a simulation that draws samples from a strongly skewed population at three different sample sizes and write an explanation of what changes and what does not as the sample size grows. Students can also find a published claim that treats a distribution as normal and evaluate whether the assumption is defensible, naming what feature of the data would reveal a problem.

Evaluation for 3.1d
Digital materials include accommodations, including text-to-speech, content and language supports, and calculators that educators can enable or disable to support individual students.

The materials do not allow educators to enable or disable text-to-speech, content, and language supports, or calculators for individual students. The digital materials include student-facing accessibility features, such as read-alouds, text highlighting, reading speed and voice adjustments, color scheme, font size, zoom, and calculator access.

Evaluation for 3.1e
Materials include educator guidance on offering options and supports for students to demonstrate understanding of mathematical concepts in various ways, such as perform, express, and represent.

The Understanding Basic Statistics Instructor Manual includes options for students to demonstrate understanding through discussion, data analysis, graphing, technology use, and interpretation. For example, chapter 3 includes a “Viewpoint Discussion” activity in which students analyze a histogram, determine which measure best represents the center of the data, and discuss skewness as a paired activity before class discussion.

The WebAssign Educator Guide lists several types of end-of-chapter questions that allow students to demonstrate their learning in various ways, including SALT, a dynamic data analysis tool. Additional resources include “Select Your Scenario” questions and “Concept Video” questions. The textbook offers a wide range of problem-solving options, including focus problems, guided exercises, technology-based problems, video problems, project-based learning, and real-world applications, allowing students to demonstrate their learning in various ways and formats. In addition, the Texas Teacher Resources Combined Guide includes a “Options for Demonstrating Understanding” section following each chapter that provides a list of alternative methods for students to show their mastery of the chapter’s objectives. The guide instructs educators to offer the choices to students rather than assigning a single mode.

Evaluation for 3.2a
Materials include explicit (direct) prompts and guidance for educators to build knowledge by activating prior knowledge, anchoring big ideas, and highlighting and connecting key patterns, features, and relationships through multiple means of representation.

The materials include explicit prompts and guidance for educators to build knowledge by activating prior knowledge and anchoring big ideas. In chapter 1, the materials guide educators to access prior knowledge by opening section 1.1 and asking students to recall a graph or average they made in middle school and to name what the numbers described. Also, in sections 1.2 and 1.3, the warm ups connect the learning from the previous section.

The Texas Teacher Resources Combined Guide includes a section for each chapter titled “Concrete, Representation, and Abstract Supports” that outlines the big ideas for the chapter and describes how those ideas progress from concrete understanding to representational thinking to abstract thinking. For example, in chapter 5, “Elementary Probability Theory,” the big ideas focus on calculating compound, conditional, and independent probabilities, as well as permutations and combinations. The guide explains that the formulas for calculating compound probability, permutations, and combinations are procedural, whereas conditional probability and independence are more conceptual. However, the materials do not include explicit prompts and guidance for educators to build knowledge by highlighting and connecting key patterns and features through multiple means of representation.

The Texas Teacher Resource Combined Guide includes explicit prompts and guidance for connecting key relationships through multiple means of representation. For example, in Chapter 4, section 4.2, students review least-squares line and prediction, which are concepts learned previously in 8th grade, using a trend line to predict, and Algebra 1, writing linear functions that fit data. This helps as students move on to section 11.4, where they learn to infer the slope of the regression line.

Evaluation for 3.2b
If designed to be static, materials include educator guidance for effective lesson delivery and facilitation using various instructional approaches.

The Texas Teacher Resources Combined Guide provides educator-facing guidance through chapter objectives, a chapter outline, discussion activities, technology-based activities, and applied interpretation tasks. For example, in chapter 8, the guide directs educators to use a “Critical Thinking” activity in which students discuss confidence intervals and solve related problems and to use a “Viewpoint Discussion” activity in which students use technology to analyze a body temperature dataset, compute a 95 percent confidence interval, and interpret the results. This supports discussion-based instruction, problem-solving, technology-based learning, and applied interpretation.

The materials include guidance for more than two instructional approaches through the WebAssign Educator Guide. The guide explains that educators can customize assignments for remediation or conceptual understanding using question types that include data analysis tasks, simulation questions, concept and application videos, scaffolded tutorials, labs, and project milestones. The guide also explains that Course Packs include pre-lecture assignments, homework, labs, and project milestones and that labs require students to analyze real-world data using instructor-selected technology tools, such as Excel, R, TI-83/84, Minitab, SPSS, or JMP. These resources support video-based instruction, scaffolded tutorials, simulations, real-world data analysis, independent practice, labs, projects, and technology-enhanced instruction. Through these various activities and resources, the materials provide educator guidance for effective lesson delivery and facilitation through various instructional approaches.

Evaluation for 3.2c
Materials include multi-tiered intervention methods for various types of practice and structures and educator guidance to support effective implementation.

The materials include lessons and activities designed to support students at different levels using various types of practice and structures. Each chapter of the Texas Teacher Resources Combined Guide contains guidance on multi-tiered interventions specific to that chapter, including setting and grouping options and a suggested activity. For example, in chapter 8, “Estimation,” the guide suggests that educators give tier-one instruction to the whole group and include direct instruction with the concrete–representational–abstract sequence built into section 7, especially the many-intervals capture-rate display. For tier two, the guide suggests providing 15 minutes of small-group instruction. During this instruction, the students who used probability language in their interpretations work on the correct-versus-incorrect wording pairs with four intervals and no computation. The guide suggests a three-step organizer to scaffold the correction of formula errors. Finally, for tier three, the guide suggests providing an individual, brief conference for a student who cannot identify the quantities in a problem, in which the educator uses a labeling checklist with two problems alongside the student before returning to the remaining problems in the section.

Evaluation for 3.2d
Materials include enrichment and extension methods that support various forms of engagement, and guidance to support educators in effective implementation.

The Student Edition includes “Data Highlights: Group Projects” that provide enrichment and extension opportunities through simulations, random sampling, technology use, comparisons of outcomes, ethical research, small-group discussion, and written or presentation-based products. These activities support various forms of engagement, including collaborative, technological, analytical, research-based, written, and oral engagement. The Understanding Basic Statistics Instructor Manual provides additional context by identifying related discussion activities, critical-thinking activities, WebAssign resources, concept videos, and labs to enrich and extend for students who demonstrate proficiency.

The Texas Teacher Resources Combined Guide provides guidance to help educators effectively implement enrichment and extension methods that foster various forms of engagement. For example, in chapter 5, it suggests having students analyze the lie detector Focus Problem quantitatively for a population with a low base rate of deception, and explain why a positive result can still be more likely to be false than true. This anticipates conditional-probability reasoning in medical testing. Also, ask students to design a simulation to estimate a probability that is too complex to compute directly, run it, and compare the empirical result with a theoretical value when one is available.

Evaluation for 3.2e
Materials include prompts and guidance to support educators in providing timely feedback during lesson delivery.

The Texas Teacher Resources Combined Guide includes “Checks for Understanding” and “Feedback” sections for each chapter, providing explicit, timely guidance on feedback during lesson delivery. The “Checks for Understanding” and “Feedback” sections for chapter 6, “The Binomial Probability Distribution and Related Topics,” include a chart that outlines when checks for understanding should take place, the prompt to ask students, what to look for in their responses, and the explanatory feedback to provide. For example, in section 6.1, educators should pause after the introduction of distributions and tell students, “Given a table, state whether it is a valid probability distribution.” Educators should look for students to check both conditions, not only the sum. If the student checks only the sum, the educator should respond by asking whether a negative probability could still sum correctly with others.

In chapter 7, “Normal Curves and Sampling Distributions," the guide advises educators to pause in section 7.3 mid-lesson and ask students to state whether a problem goes from value to area or from area to value. The guide advises educators to look for students who identify the correct direction before computing. If a student begins computing immediately, educators should ask students what the question gives and what it asks for.

Evaluation for 3.3a
If designed to be static, materials include educator guidance on providing and incorporating linguistic accommodations for all 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 include an Understanding Basic Statistics Emergent Bilingual Support Guide that includes educator guidance on what each ELPS proficiency level looks like in the course. The guide states that a student at the pre-production level can sort study descriptions into observational and experimental piles, point to the region of a curve, or place a value on a number line. The guide goes on to remind educators that students at the pre-production level should not yet be asked to explain things such as a p-value in words.

In addition, the guide provides linguistic accommodations by proficiency level for each of the ELPS domains. For example, in the Listening domain, an educator would support a pre-production student by pairing every spoken direction with a gesture, a written word, or an image. In the Speaking domain, an educator would support a high intermediate student by providing discussion stems that invite justification and comparison, such as “I choose the median-median line because _____, although the least-squares line _____.”

Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all 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.

This guidance is not applicable to the program because it is not designed to be adaptive.

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

The materials include implementation guidance to support educators in effectively using the materials in state-approved bilingual and English as a Second Language (ESL) programs. The Understanding Basic Statistics Emergent Bilingual Support Guide includes a section that describes each of the six state-approved program models used in Texas, as well as suggestions of how to implement the program in each of the models. For example, the guide states that ESL content-based and ESL pull-out are the two most commonly used models in high schools. The materials suggest that, in an ESL content-based model, the educator delivers vocabulary, comprehension, and discourse supports during regular instruction. However, in an ESL pull-out model, the guide recommends sharing the “Key Terms” list with the ESL educator in advance, so that pre-teaching occurs before the mathematics lesson rather than after the lesson.

Evaluation for 3.3d
Materials include embedded guidance 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 Understanding Basic Statistics Emergent Bilingual Support Guide provides embedded guidance to help emergent bilingual (EB) students develop academic vocabulary through oral and written discourse. The guide separates academic vocabulary terms into three distinct categories, each requiring a different instructional approach, as detailed in part 4. In addition, the guide provides a vocabulary routine educators can implement in every lesson, prioritizing five of the most important terms and to pre-teach and continually reinforce them through instruction. Part 7 of the guide describes a discourse routine that gives all students the opportunity to improve comprehension through oral and written discourse. In this routine, students spend one minute of individual writing, then engage in a pair exchange in which each partner restates the other’s reasoning before responding. This routine provides students with the opportunity to refine their mathematical language after listening to their peers. Then, the educator selects and sequences two contrasting responses so that the class can compare them with a focus on the reasoning involved rather than on the answer. Finally, students close the discussion with a written response. The materials provide sentence frames specific to each course phase to support EB students in engaging in the language.

Part 5 of the Understanding Basic Statistics Emergent Bilingual Support Guide provides embedded guidance to help educators support EB students in building background knowledge through oral and written discourse. The materials provide a chart listing common barriers, their location, and a remedy for each. For example, the course contains multiple dense multi-clause problem statements. The remedy reminds educators to provide a structured breakdown of what information the materials provide, what the question asks, and which procedure applies. Students must answer these questions before completing the computation.

Part 6 of the Understanding Basic Statistics Emergent Bilingual Support Guide helps students make cross-curricular connections through oral and written discourse. The materials include a chart of English statistical terms alongside their Spanish cognates, as well as a “False Friends” chart listing common English statistical terms and their false cognates. Students engage with these terms by using sentence stems to talk and write about their meanings and applications in everyday life.

Evaluation for 3.3e
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 throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

The materials provide practice opportunities throughout learning pathways that require students to demonstrate depth of understanding aligned to the TEKS. At the end of each section, students can practice by answering the “Statistical Literacy,” “Basic Computation,” “Critical Thinking,” “Interpretation,” and real-world connection problems. For example, the “Basic Computation” problems in section 2.1 require students to create frequency tables, while the “Interpretation” problems require students to analyze histograms.

At the end of each chapter, instructional assessments throughout learning pathways require students to demonstrate depth of understanding aligned with the TEKS. The “Chapter Review” sections cover a wide range of problems, from basic computation to data analysis and the creation of various graphs and diagrams. The “Data Highlights: Group Projects” provide opportunities for students to work in groups and discuss the scenarios. There are also “Linking Concepts: Writing Projects” that require students to write essays, including graphs and formulas as needed.

Evaluation for 4.1b
Questions and tasks, including enrichment and extension materials, increase in rigor and complexity, leading to grade-level and above grade-level proficiency in the mathematics TEKS.

The materials contain questions and tasks that increase in rigor and complexity toward grade-level proficiency through a sequence of guided practice, section problems, chapter review problems, interpretation tasks, and critical-thinking tasks. In chapter 2, section 2.1, “Frequency Distributions, Histograms, and Related Topics,” students move from organizing quantitative data into frequency tables to constructing and interpreting histograms, relative-frequency histograms, ogives, and dotplots. Students determine class width, class limits, class boundaries, midpoints, frequencies, relative frequencies, cumulative frequencies, distribution shape, and possible outliers. These tasks require students to represent, analyze, and interpret data rather than only perform routine calculations.

Every lesson or section in each chapter includes “Guided Exercises” and critical-thinking prompts of increasing complexity. At the end of each section and chapter, there are problem sets designed to extend students’ thinking. These problems require students to demonstrate statistical literacy, basic computations, critical thinking, and problem-solving across different fields, showing the relevance of these concepts to real life. For example, in section 6.1, “Binomial Probabilities,” students list the features of a binomial experiment and apply the binomial distribution formula to calculate probabilities from a list and a table by hand before using technology.

Evaluation for 4.2a
Materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships.

The materials demonstrate coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. The materials include “Looking Forward” features that preview the use of current topics later in the course. For example, the “Looking Forward” note in section 4.1 previews that students will use linear regression in section 4.2 to fit a linear equation to paired data.

The table of contents shows a coherent course progression from foundational statistical ideas to more complex applications. Students begin with “Getting Started” and move into organizing data, averages and variation, correlation and regression, probability, normal curves and sampling distributions, estimation, hypothesis testing, differences between groups, chi-squared procedures, and inference for correlation and regression. This sequence supports horizontal coherence because concepts build on one another within the same course rather than appearing as disconnected topics.

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grades 3–12, by connecting patterns, big ideas, and relationships.

The materials demonstrate coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. The course demonstrates internal coherence, including “Looking Forward” features, cumulative review problem sets, prerequisite guidance, and alternative routes through topics such as regression, confidence intervals, and hypothesis testing.

The materials include a “Rationale for Vertical Alignment” section that shows three strands running continuously from grade 3 to grade 12. There is explicit guidance connecting current statistics concepts to prior grade-level mathematics standards. For example, students learned about frequency tables, dot plots, pictographs, bar graphs, and stem-and-leaf displays in grades 3–5. In chapter 2 of the text, students revisit the stem-and-leaf display and the frequency table as a formal tool with class limits, midpoints, and boundaries.

Evaluation for 4.2c
Materials demonstrate coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned in the current grade level and future grade levels.

The “Looking Forward” features preview how the course uses the current topic later. The text for this section includes procedure displays, examples, guided exercises, statistical literacy problems, interpretation problems, and cumulative review problems that connect concepts and procedures across chapters. For example, when the materials introduce the mean in section 3.1, the “Looking Forward” note explains that students later use the sample mean to estimate the population means in chapter 7 and to make decisions about it in chapter 8. This connects the current concept/procedure for calculating and interpreting the mean to later concepts in inferential statistics.

The Student Edition demonstrates coherence across lessons or activities by connecting students’ prior knowledge of concepts and procedures to the mathematical concepts to be learned at the current grade level. In section 7.2, students work with the standard normal distribution, connecting the normal distribution of x-values to z-values. The “Looking Ahead” states that the course will use this distribution repeatedly. For example, in section 7.4, students look for the sample distribution of the mean. In section 7.6, they look for the normal approximation of the binomial distribution. Students use the formula again in chapter 8 (for confidence intervals) and chapters 9 and 10 (for hypothesis testing).

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

The materials provide spaced retrieval opportunities with previously learned skills and concepts across the course. The Student Edition states that cumulative review problem sets occur after every third chapter and include key topics from previous chapters. Chapters 1–3 cumulative review problems require students to retrieve prior statistical procedures, formulas, and methods while also revisiting earlier concepts through statistical literacy, interpretation, and critical-thinking tasks.

The materials provide spaced retrieval opportunities with previously learned skills and concepts across learning pathways. Spaced retrieval opportunities are available in the Cognero Test Generator, in which educators can create and manage assessments and assignments on previously learned skills and concepts.

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

The Instructor Companion Site provides interleaved practice opportunities with previously learned skills and concepts across learning pathways. For example, the WebAssign course provides educators the ability to create assessments and assignments for remediation or to develop conceptual understanding.

The materials provide interleaved practice opportunities by requiring students to revisit and apply concepts from chapter 2, “Organizing Data,” throughout subsequent chapters. In this chapter, students develop their ability to represent data using different graphs and tables, such as histograms and frequency tables. Chapter 3 uses these concepts again when students display “Distribution Types and Averages.” Also, in chapter 6, Figure 6-1 uses histograms to graph the probability distribution of test scores.

Evaluation for 5.1a
Questions and tasks provide opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations.

The materials support opportunities for students to interpret mathematical concepts and complex, real-world situations. The preface for the Student Edition states that the course develops statistical methods in the context of applications and how the materials emphasize this interpretation throughout the text. The materials also include “Interpretation” problems that ask students to explain statistical results in the context of the application. For instance, chapter 1, section 1.3, asks students, “Do you expect the results to reflect how the Echo generation would classify items in 2020? Explain,” after students look at the 2006 results of how the Echo generations classified specified items as either luxuries or necessities.

The Student Edition states that “Critical Thinking” problems require students to analyze and comment on issues that arise in applying statistical methods and interpreting results. “Viewpoint” activities also use real data and ask students to analyze and interpret the data using what they learned. In the chapter 3, section 3.1, “Viewpoint” activity, students analyze a histogram of housing prices and answer questions, such as “When data is skewed, the balance point of the data is pulled in the direction of the skew. How does this explain the position of the mean in this example?” The materials support opportunities for students to analyze mathematical concepts and complex, real-world situations.

In hypothesis testing, students compare a p-value to the significance level, decide whether to reject or fail to reject the null hypothesis, and interpret the result in the context of the application. The text emphasizes that students should determine whether a statistical method or process is appropriate and understand the meaning of statistical results. This example shows how the materials support opportunities for students to evaluate mathematical concepts and complex, real-world situations.

Evaluation for 5.1b
Questions and tasks provide opportunities for students to create concrete models and representations of mathematical situations.

The materials provide opportunities for students to create representations of mathematical situations. In the Student Edition, students create a stem-and-leaf display, a frequency table, a histogram, a relative-frequency histogram, an ogive, and a box-and-whisker plot using a data set about West Texas water wells. In another technology task, the materials ask students to “make a scatter plot” and then “graph the line on the scatter plot,” which further supports opportunities to create graphical representations of data.

The materials provide opportunities for students to create concrete models of mathematical situations. For each chapter, the Texas Teacher Resources Combined Guide provides a table that explains how the main concepts for the chapter progress from concrete to representational to abstract representations. For example, in chapter 9, “Hypothesis Testing,” students engage with the concepts of null and alternative hypotheses at the concrete level by sorting cards that describe claims into two piles: the status quo claim and the claim requiring evidence. In that same chapter, when students learn about significance level, they do so initially by shading a fraction of a strip, which creates a model representing the sampling distribution.

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

The materials provide additional opportunities for students to apply conceptual understanding in unfamiliar statistical contexts. In the Student Edition, students apply their understanding of hypothesis testing, null and alternative hypotheses, and Type I and Type II errors to real-world situations, including a criminal justice case and a Starbucks business decision about opening a new location. These tasks require students to explain the meaning and consequences of statistical errors in context rather than only recall definitions or complete calculations.

In the Student Edition, students apply their understanding of confidence intervals for population proportions to a dormitory cafeteria context. Students estimate the proportion of students selecting the vegetarian meal option, calculate a confidence interval, interpret the interval in context, and explain whether the cafeteria can justify using the normal approximation. This example shows how the materials provide opportunities for students to apply conceptual understanding to new problem situations and contexts.

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

The materials include “Statistical Literacy” problems that build automaticity of grade-level concepts. For example, in section 6.1, problem number 1 requires students to determine if the given variables are continuous or discrete. This requires students to understand the concepts of discrete and continuous variables and to build automatic recall of this understanding.

The materials include procedural activities and tasks that build students’ automaticity and fluency in mathematical skills and concepts. For example, in chapter 5, students study probability. In the “Guided Practice 1” activity, students assign a probability based on the information provided. There are three scenarios for students to consider, and students must determine which technique to use: intuition, relative frequency, or the formula for equally likely outcomes.

Evaluation for 5.2b
Materials provide opportunities for students to practice the application of efficient, flexible, and accurate mathematical procedures throughout learning pathways.

The materials include technology supports that help students carry out procedures efficiently. The “Tech Notes” and “Using Technology” sections provide point-of-use instructions for calculators, Excel, SALT, Minitab, and other tools. The text also explains that statistical technology can provide numerical results, but students must understand whether the process is appropriate and how to interpret the results.

The materials provide flexibility in procedure selection and learning pathways. The text notes that the course is flexible and offers alternate routes through the text, such as presenting linear regression after chapter 3 or later with inference topics, depending on course emphasis. The materials also allow instructors to determine how much probability content to cover based on course needs. In addition, the use of multiple tools and methods, such as Excel, SALT, Minitab, SPSS, TI calculators, and traditional formulas, gives students opportunities to approach statistical procedures in multiple ways.

The materials include examples, “Guided Exercises,” “Basic Computation” problems, “Statistical Literacy” problems, “Interpretation” problems, “Critical Thinking” problems, and a cumulative review, which supports accurate procedural use. The examples in the Student Edition show students how to select and use appropriate procedures. At the same time, “Guided Exercises” allow students to work with new concepts and include worked-out solutions for immediate reinforcement. The procedure also summarizes key statistical methods and the conditions required for their use.

Evaluation for 5.2c
Materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for efficiency, flexibility, and accuracy throughout learning pathways.

Students evaluate the efficiency of mathematical representations, models, strategies, or solutions by determining the main difference between situations in which the permutations rule and the combinations rule apply, requiring students to evaluate the efficiency of these strategies across various contexts. For example, the section 5.3 practice problems ask students, “What is the main difference between a situation in which the use of the permutation rule is appropriate and one in which the use of the combinations rule is appropriate?” and “Consider the following scenarios and determine whether to use the permutation rule or combinate rule to count the total number of outcomes.”

The materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for flexibility throughout learning pathways. In the Focus Problem “Say It with Pictures,” students analyze a misleading real-world graph, compare it to a corrected graph, explain how the representations communicate different messages, and create a revised graph. In chapter 3, students compare how changes to a data set affect measures such as standard deviation, allowing students to reason flexibly about formulas, transformations, and representations. These tasks support students in evaluating more than one way to represent, interpret, or approach statistical information.

The materials provide opportunities for students to evaluate the accuracy of mathematical representations, models, strategies, and solutions throughout learning pathways. In “Say It with Pictures,” students identify flaws in a misleading graph and revise the representation to communicate the data more accurately. In later inference sections, students repeatedly answer “Check Requirements” prompts before computing or interpreting confidence intervals and hypothesis tests, requiring students to determine whether the selected statistical model or method is appropriate.

Evaluation for 5.2d
Materials contain guidance to support students in selecting the most efficient approaches when solving mathematics problems.

The Student Edition contains guidance to support students in selecting increasingly efficient approaches to solve mathematics problems. For instance, “Guided Exercises” and “Procedures” in each section of the textbook walk students through step-by-step solutions to sample problems, ensuring that students implement increasingly efficient approaches to solving mathematical problems. In chapter 8, section 8.3, students have several formulas for confidence intervals for the population mean m. To choose the appropriate formula, the students “need to look at the sample size, the distribution of the original population, and whether or not the population standard deviation s is known.” Then, the materials give students guidance on using TI-84Plus/TI-83Plus/TI-Nspire calculators, Excel, SALT, and Minitab to construct confidence intervals using the Student’s t-distribution.

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

The Texas Teacher Resources Combined Guide explains the conceptual and procedural emphasis of the TEKS for each chapter. The guide explains that chapter 2, “Organizing Data,” contains a balance of conceptual and procedural tasks. Sections 2.1 and 2.3 are largely procedural as students construct frequency tables with correct class boundaries, histograms, and ogives and form stem-and-leaf displays. The guide states that the sections on marginal and conditional distributions are almost entirely conceptual. The procedural demand is minimal since students divide by single digits. Rather, students must decide what to divide by, which requires an understanding of correctly identifying the groups being described.

In another example, the guide explains that chapter 4, “Correlation and Regression,” also contains a balance of procedural and conceptual demands. Most of the procedural demands come from section 4.2 in which students compute r, the regression line, and r-squared. In contrast, the guide explains that the conceptual focus of the chapter is “the idea that a fitted line is a model, and that models are chosen rather than discovered.”

Evaluation for 5.3b
Questions and tasks provide opportunities for students to use concrete models, pictorial representations, and abstract models as required by the TEKS.

Questions and tasks in the Student Edition provide opportunities for students to use concrete models as required by the TEKS. In section 5.1, the students use a bag of three green, five red, and four white marbles to determine probability. The materials ask students to imagine drawing six marbles and determine the probability that none are red. The same page then shifts to statistics; students draw a sample of six marbles from a bag with an unknown composition, observe the colors, and make a conjecture about the full population.

Students also use pictorial representations, such as graphs and diagrams, to analyze data as required by the TEKS. In the Focus Problem “Say It with Pictures,” students analyze a misleading real-world graph, compare it to a corrected graph, and create a new graph to communicate what the data show. In section 2.1, students construct histograms, relative-frequency histograms, and ogives from data, providing repeated opportunities to represent statistical information visually.

Furthermore, students use scatter plots to represent bivariate data. In section 2.1, students organize raw numerical data into frequency tables and relative-frequency tables and follow procedures for constructing statistical displays. These tasks require students to use numerical, tabular, and procedural models to represent and analyze data.

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 Texas Teacher Resources Combined Guide provides systematic supports for connecting concrete and representational models to abstract statistical concepts. In every chapter, section 7 organizes key concepts in three columns: Concrete, Representational, and Abstract. The section gives a deliberate progression from physical or contextual experiences to models (diagrams, tables, graphs, or other visuals), and from models to formulas, notation, algorithms, and formal statistical reasoning. Throughout the Student Edition, students use box-and-whisker plots to connect visual representations to quartiles, the five-number summary, and IQR. Students use scatter plots and regression lines to connect visual data patterns to correlation, least-squares equations, and prediction. Students use tree diagrams to connect sample spaces to counting rules, and use shaded normal curves to connect area models to z-scores and probability notation. For example, in chapter 2, “Organizing Data,” students organize raw data into frequency distributions and graphical displays before calculating numerical summaries.

The materials provide supports for students in creating concrete and representational models to abstract. For example, chapter 2 in the Texas Teacher Resources Combined Guide explains that students engage with concepts such as random sampling by first drawing numbered slips or using a spinner to select from a class roster (concrete). Then, students use a numbered sampling frame with selected rows highlighted (representational), and, finally, students use a random-numbered table or generator applied to a labeled frame (abstract).

In addition, the materials help students define and explain concrete and representational models in relation to abstract concepts. In chapter 3, students define the concept of spread comparison by arranging two sets of counters, one tightly clustered and one dispersed, both with the same mean. In section 3.3, students interpret how a box-and-whisker plot shows center and spread, explain how scatter plots and regression lines model relationships between variables, describe how tree diagrams display possible outcomes, and interpret shaded regions under the normal curve as probabilities.

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

The materials provide opportunities for students to develop academic mathematical language through visuals, manipulatives, or other language-development strategies. The course uses illustrations for key vocabulary terms, such as normal curve, as shown in figure 7.1 of the chapter 7, “Normal Curves and Sampling Distributions” PowerPoint presentation.

Additionally, the Student Edition provides illustrations, when appropriate, and highlights key mathematical language. For example, chapter 2, section 2.1 defines frequency tables in words highlighted in a light blue box on the page, then provides illustrations of frequency tables in the subsequent example problems.

Evaluation for 5.4b
Materials include embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context when communicating with peers and educators.

The Texas Teacher Resources Combined Guide includes embedded educator guidance to scaffold, support, and extend students’ use of academic mathematical vocabulary in context. In each chapter, section 8, “Academic Vocabulary and Classroom Discourse,” includes a list of key vocabulary for the chapter, as well as a chart listing various vocabulary supports, directions for how to use them, and the associated ELPS for that support. In addition, the section provides discourse prompts to support students as they communicate about mathematics with their peers.

The Understanding Basic Statistics Emergent Bilingual Support Guide also includes educator guidance to scaffold, support, and extend students’ use of academic vocabulary. Although specifically designed for EB students, the scaffolds and supports described would benefit all students. Part 4 of the guide provides guidance for educators on how to develop academic vocabulary. The guide describes three tiers for all the vocabulary terms in the course. Tier one words are everyday words used technically, tier two words are general academic words, and tier three words are technical statistics terms. Each tier on the chart has a description and a suggested instructional approach. In addition, the materials provide a vocabulary routine that educators can use to introduce the key vocabulary for each lesson.

Evaluation for 5.4c
Materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse.

Chapter 1, “Linking Concepts Writing Review,” provides guidance for writing for each prompt. The directions state that students can discuss or write an essay. For example, question 2 says, “In your own words, explain the differences among the following sampling techniques: simple random sample, stratified sample, systematic sample, cluster sample, multistage sample, and convenience sample. Describe situations in which each type might be useful.”

“Data Highlights: Group Projects” in the Student Edition includes guidance to support student application of appropriate mathematical language and academic vocabulary in discourse. For example, after students learn about averages and variation in chapter 3, they apply the learning to specific scenarios. The guidance tells students to break into small groups, discuss the provided topic, and organize an outline summarizing the discussion’s main points. The first scenario concerns the effect of an earthquake on a volcano. The materials guide students by stating, “Do no calculations, just look at both graphs, and then explain which graph has the smaller and which has the larger standard deviation. Which distribution will have the larger coefficient of variation?” Students discuss the provided graphs using mathematical terms, such as frequency, mode, mean, standard deviation, distribution, coefficient of variation, and others.

Evaluation for 5.4d
Materials include embedded guidance to facilitate mathematical conversations allowing students to hear, refine, and use math language with peers.

There are “Critical Thinking” sections throughout the materials that prompt students to discuss specific problems and their solutions, which gives students the opportunity to hear and use mathematical language. For example, while learning about correlation and regression, students explore how outlier data points affect correlation and regression. Students then discuss why the effects of moving a point vertically differ for points at the ends of a graph than for points in the middle. End-of-chapter group projects in the Student Edition include guidance to facilitate mathematical conversations, allowing students to hear and use mathematical language with peers. For example, after students learn about the elementary probability theory in chapter 5, they have the opportunity to discuss how the theory applies to randomly selecting an orthopedic case and how the theory relates to the age of adults getting knee replacements.

Furthermore, the Understanding Basic Statistics Emergent Bilingual Support Guide provides an oral and written discourse routine that provides all students the opportunity to practice listening, speaking, and writing about the course content. In this routine, students engage in one minute of individual writing before engaging in a pair exchange in which each partner restates the other’s reasoning before responding. This routine provides students with the opportunity to refine their mathematical language after listening to their peers. Then, the educator selects and sequences two contrasting responses so that the class can compare the responses with a focus on the reasoning involved rather than the answer. Finally, students close the discussion with a written response. Sentence frames specific to each course phase support EB students as they engage with the language.

Evaluation for 5.4e
Materials include embedded guidance to anticipate a variety of student answers including exemplar responses to questions and tasks, including guidance to support and/or redirect inaccurate student responses.

The materials provide exemplar responses and correct answers for student activities. The Complete Solutions Manual includes solutions to textbook questions, and the Student Edition “Guided Exercises” provide fully worked-out solutions next to each exercise. For example, one of the “Guided Exercises” models how students classify real-world data by level of measurement and determine which operations are valid for each data type.

In addition, the Texas Teacher Resources Combined Guide provides explicit, timely guidance on feedback during lesson delivery. The “Checks for Understanding” and “Feedback” sections for each chapter include a chart that outlines when assessments should take place, which prompt to ask, what to look for in student responses, and the explanatory feedback to give when students give an incorrect response. For example, in chapter 5, “Elementary Probability Theory,” the “Checks for Understanding” and “Feedback” sections suggest that students might incorrectly conclude that a separate event is independent when they need to compare two or more events. In this case, the guide advises educators to ask students whether the sampling was with or without replacement.

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

The materials appropriately integrate the TEKS process standards. For example, in section 4.2, “Linear Regression and the Coefficient of Determination,” students analyze scatter plots, develop regression models, and interpret the coefficient of determination in context. The Focus Problem, worked examples, and “Chapter Review” problems require students to model data, analyze mathematical relationships (P.1(F)), evaluate the reasonableness of predictions (P.1(B)), and communicate statistical conclusions, integrating the TEKS process standards throughout the lesson.

Additionally, in section 10.2, “Inferences about the Difference of Two Means,” students compare two populations by selecting appropriate statistical procedures, interpreting results, and justifying conclusions using evidence from sample data. The worked examples, “Chapter Review” problems, and “Data Highlights: Group Projects” integrate the process standards by engaging students in problem-solving (P.1(B)), mathematical reasoning (P.1(D)), communication, and the application of statistics in real-world contexts (P.1(A)).

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

The materials incorporate process standards throughout the learning pathways through recurring features identified in the preface of the Student Edition, including “Guided Exercises,” “Procedure” displays, “Statistical Literacy” problems, “Interpretation” problems, “Critical Thinking” problems, “Viewpoints,” “Data Highlights,” “Linking Concepts,” and technology notes. These features require students to apply statistics in real-world contexts, use representations and technology, analyze information, interpret results, and communicate mathematical reasoning across chapters.

In addition, the materials connect process standards throughout the learning pathways through “Looking Forward” features, Focus Problems, and “Cumulative Review” problem sets. The preface explains that “Looking Forward” previews how the course uses a current topic later and how “Cumulative Review” problems revisit key topics from previous chapters. Students connect scatter diagrams and correlation coefficients to the later use of linear regression equations, and the Focus Problem connects real-world probability reasoning to later chapter work on conditional probability and interpretation. These examples show students connecting real-world contexts, representations, reasoning, and statistical interpretation over time.

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

The materials include an overview of the TEKS process standards incorporated into each lesson. The table in the Alignment Guide shows the integration of the process standards throughout the lessons. Students analyze problem situations, apply mathematics to real-world contexts, and represent mathematical concepts with tables, graphs, and diagrams. The Scope & Sequence with Pacing Guide lists the process standards by chapter.

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

The materials provide opportunities for students to think mathematically. In section 2.1’s “Critical Thinking” problems, students reason about histograms and the shape of a distribution rather than simply constructing a graph. Students must connect the visual shape of the distribution to the structure of the data, such as identifying whether equal rankings create a uniform distribution or whether combined city/highway mileage data can produce a bimodal display.

The “Interpretation” problems provide opportunities for students to persevere through solving problems. In section 1.2, problems 5–6 require students to reason through what can and cannot be concluded from random samples. This process involves sustained thinking beyond a single computation and persevering through solving problems.

The “Linking Concepts: Writing Project” allows students to explain their understanding of mathematics and make sense of mathematics through writing. In this chapter, students discuss three measures of the “goodness of fit” of the least-squares line for given data: the standard error of estimate, the correlation coefficient, and the coefficient of determination. Students compare and contrast how these measurements are similar and different. The materials remind students “to include a discussion of explained variation, unexplained variation, and total variation in your answer. Draw a sketch and include appropriate formulas.”

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

The Student Edition provides “Comment” notes when appropriate to support students’ understanding and explain that there can be multiple ways to solve problems. For example, in lesson 4.2, “Linear Regression and the Coefficient of Determination,” students learn that they can use formulas for the slope of least-squares lines or use a calculator or computer software. Students then learn that they can explain the coefficient of determination by the least-squares line, the linear regression model, and the variation in the explanatory variable x. In lesson 5.3, “Trees and Counting Techniques,” “Guided Exercise 10” illustrates how students can determine the possible wins from three tennis matches using both tree diagrams and the multiplication rule. The illustration shows the comparison of results from utilizing both methods. Later in the lesson, students learn the permutation and combination rules, as well as additional methods for determining the total number of outcomes when combining a sequence of events in specified ways. When students get to the lesson exercises, one problem asks students to explain the main difference between a situation in which the permutation rule applies and one in which the combination rule applies.

The Texas Teacher Resources Combined Guide provides a section for each chapter titled “Multiple Approaches and Structures Reflection” that provides opportunities for students to justify that there can be more than one approach to solving problems and completing tasks. For example, in chapter 8, students analyze competing approaches for reducing the margin of error by either increasing the sample size or by accepting a lower confidence level. Given a target margin of error, groups of students attempt to reach the target by increasing sample size and by lowering confidence level, then argue which trade-off they would accept for a stated purpose, such as a medical study versus a marketing survey.

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/or educators.

In chapter 5, “Data Highlights: Group Projects,” the materials require students to conduct statistical analysis using real-world graphical displays of the number of adults getting a knee replacement. Students determine the probability that a randomly chosen orthopedic case involves both a knee issue and the need for total knee replacement surgery. Then, students examine the age distribution of patients undergoing this procedure.

“Linking Concepts: Writing Projects” asks students to “write a brief but complete essay” that summarizes the main points of each chapter. Chapter 2 requires students to write about mathematics/statistics by composing essays that explain and compare graphical displays, including histograms, relative-frequency histograms, bar graphs, circle graphs, time-series graphs, Pareto charts, and stem-and-leaf displays. The materials ask students, “If you have nominal data, which graphic display might be useful? What if you have ordinal, interval, or ratio data?”


The “Data Highlights” require students to discuss mathematics/statistics through group projects and class discussions. In chapter 8, students examine figure 8-8, “Fall Back.” The data is a survey of 1,024 adults and their preference for daylight saving time or standard time. The graph shows that 66 percent reported favoring daylight saving time. The students must discuss, “How many people in the sample preferred daylight saving time?”

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

The Student Edition contains “Viewpoint” problems that educators can use to guide students in sharing their problem-solving approaches and explanations. For example, in chapter 3.1, students explore house prices. The instructions lead students to describe the shape of the data distribution and determine and explain whether the distribution makes sense in the context. The Texas Teacher Resource Combined Guide supports educators in helping students share and reflect on their problem-solving approaches, including arguments, in the Multiple Approaches and Structured Reflection Sections. For example, teachers are guided to "Ask students to argue both sides of whether the outlier in the landscaping data should influence the model, given that i represents a real job on rocky soil."

The materials include “Critical Thinking” exercises that guide students to share and reflect on their problem-solving approaches and explanations. One such example appears in the chapter 5 review problems, in which students must explain whether they have enough information to compute the probability of event A or event B [P(A or B)] and, if the events are mutually exclusive, the probability of event A or event B. To answer these questions correctly, students must reflect on their problem-solving method and explain and justify how it verifies the solution. However, the materials do not support educators in guiding students to share and reflect on their problem-solving approaches, including multiple points of entry.

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

The Texas Teacher Resources Combined Guide provides explicit, timely guidance on feedback during lesson delivery. The “Checks for Understanding” and “Feedback” sections for each chapter include a chart that outlines when the assessments should take place, the prompt to ask students, what to look for in their responses, and the explanatory feedback to provide. For example, educators should pause in section 10.3 before computing and ask students to verify the conditions for a two-proportion procedure. Students should check expected successes and failures in both samples. However, if a student only checks the combined sample, the guide provides explanatory feedback, telling the educator to ask which sampling distributions the procedure combines.

In addition, the Texas Teacher Resources Combined Guide also includes anticipated misconceptions and suggested responses for each chapter. For example, in chapter 11, “Additional Topics Using Inference,” the guide suggests that students might think expected counts must be whole numbers because counts of objects are whole numbers. The guide advises educators to redirect students by explaining that expected counts are computed from proportions and are frequently fractional. Rounding them introduces error into the statistic.