Progress Learning Statistics (TEKS)

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 a Statistics Scope and Sequence that provides a chart outlining the Texas Essential Knowledge and Skills (TEKS) for each lesson. In each lesson, the “Standards” section lists the TEKS and the English Language Proficiency Standards (ELPS) covered in that lesson.

The Statistics Scope and Sequence includes a “Statistics Sequence Rationale” section that explains how each lesson connects to prior and future learning. For example, this section explains that in lesson 1 “Sampling Techniques and Sample vs. Population,” students distinguish between sample statistics and population parameters and compare different sampling methods. The materials state, “This foundation is necessary to understand the ‘who’ and ‘how’ of data before moving into study designs.”

Each lesson includes “Looking Back” and “Looking Ahead” sections that list the aligned TEKS from previous and future courses. For example, the “Looking Back” section of lesson 3 “Steps in Statistical Study” states that students will build on skills such as solving problems using data represented in bar graphs, dot plots, and circle graphs, which aligns with 7.6G). The “Looking Ahead” section of the same lesson states that students will use the skills developed in this lesson when students design studies and experiments in AP statistics.

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 a High School Math Implementation Guide that provides clear usage recommendations and instructional strategies for educators. The lesson materials offer multiple delivery options, such as using videos paired with cooperative learning strategies (e.g., think-pair-share) and assigning independent practice with follow-up discussion. These supports demonstrate flexibility in instructional approaches and guidance for use in various contexts, including whole-group instruction and independent learning.

The materials include a Cooperative Learning Strategy Guide with Embedded Support for ELLs document that outlines all the cooperative learning strategies included in the materials and provides grouping suggestions for different math proficiency and emergent bilingual (EB) levels.

The materials also include recommendations for adapting instruction to meet varied student needs. The lesson plans provide intervention and enrichment activities for struggling and advanced students through additional precalculus videos and scaffolded practice opportunities. In addition, the materials provide just-in-time support by identifying common misconceptions and guiding educators in addressing them with students. For example, in lesson 3 “Steps in a Statistical Study,” the materials advise educators to project a problem with which students are struggling and model a mistake in the problem-solving process. Through error analysis, students identify multiple approaches to the problem and justify their answers.

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

The Statistics Scope and Sequence provides a chart outlining the TEKS for each lesson, which serves as a TEKS correlation guide. The scope and sequence paired with the “Student Diagnostic Strengths and Weaknesses Report” provide educators with recommended skill entry points based on diagnostic assessment results, which enables them to make instructional decisions aligned with student readiness.

For students who demonstrate mastery, the “Student Diagnostic Strengths and Weaknesses Report” directs educators to assign enrichment opportunities. These data-informed recommendations support flexible grouping, such as small-group instruction for intervention or enrichment, and help educators connect prerequisite skills to new content.

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

The materials include a High School Math Implementation Guide that supports lesson internalization. The “Explore” section of each lesson includes clearly labeled subsections, such as “Objective,” “Materials,” “Supports,” and “Implementation,” which guide educators in understanding lesson expectations, planning instruction, and anticipating student needs. Additional components outlined in the lesson plan, such as standards alignment, key vocabulary, and assessment guidance, provide further structure to support educator preparation and delivery.

In addition, each Teacher Guide provides guidance for unit and lesson internalization. For example, the Teacher Guide for lesson 15 “Analyzing Scatterplots and Line of Best Fit” provides lesson objectives, guiding questions, implementation strategies (including cooperative and collaborative learning strategies), and a “Guidance for Teacher” section.

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

The High School Math Implementation Guide includes a specific section titled “Guidance for Instructional Leaders” that says, “The overarching guide to verifying that these materials are being implemented with fidelity is observation of the student learning structure and the level of student engagement in a classroom.” The section also identifies what leaders should look for in implementation, including the 5E Instructional Model, cooperative learning structures, active student participation during the “Engage” and “Explore” sections, the use of instructional videos during the “Explain” section, individual practice in the “Elaborate” section, and formative feedback in the “Evaluate” section.

The materials include resources for instructional leaders to support educators in implementing the materials as designed. For example, the How-To Guides article “School Administrators Quick Start Guide” explains that administrators can customize account settings, manage both student and educator accounts, and access school-wide progress reports.

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 materials include detailed lesson plans that have clearly stated learning objectives at the beginning of each lesson, educator and student materials. and structured lesson components using the 5E Instructional Model (Engage, Explore, Explain, Elaborate, Evaluate). For example, the “Using Two-way Tables” lesson gives specific pacing of approximately 8 minutes for the “Engage” section, 20 minutes for the “Explore” section, 7 minutes for the “Explain” section, 15 minutes for the “Elaborate” section, and 15 minutes for the “Evaluate” section of a 65-minute lesson. The Statistics Scope and Sequence also provides a course-level pacing chart that has an estimated number of minutes for each 5E component across all 16 lessons.

Although each lesson plan states the TEKS and ELPS, the assessment components do not clearly align with the ELPS because the assessments primarily measure content understanding and do not require explicit evidence of language development expectations. The materials include an assessment builder that allows educators to select questions aligned with the TEKS. However, the assessment builder does not provide options to align questions with the ELPS, which limits educators’ opportunities to intentionally incorporate language development objectives.

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 include family support resources in both English and Spanish for each lesson, which ensures equitable access to instructional information. The resources provide families access to lesson slide shows and suggestions for supporting their student’s progress at home. For example, the lesson 3 “Steps in a Statistical Study” family support section invites families to explore a simple question like, "What is our favorite dinner?" The materials suggest that families discuss steps for collecting data from a larger group and create a simple chart to show results.

The materials include “Welcome Letters” in both English and Spanish and a “5 Things Every Family Member Should Know about PL (English and Spanish)” resource that answers questions, such as “How can I motivate my child to reach their best?”

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

The High School Math Implementation Guide includes an “Assessment Types and Implementation Guidance” section that defines and explains the purpose of formative Learning Snapshots, Assessment Reflection Tools, Study Plan practice, pre- and post-diagnostic assessments, and summative state practice assessments. For example, Learning Snapshots are described as formative assessments that evaluate student learning of the TEKS taught in each lesson and include item rationales to inform reteach opportunities or small-group instruction.

The materials include the definitions and intended purposes for the types of instructional assessments. For example, the How-To Guides article “What types of diagnostic tests are available in Progress Learning?” mentions “State Practice Assessments,” the “Question Quick Pick” option, “Summative Tests (Teacher-Assigned),” “Summative Tests (Student Dashboard),” and “Pre- and Post-Tests.” The article provides definitions and guidance for the use of each diagnostic test type.

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

The materials include guidance to ensure consistent and accurate administration of instructional assessments. For example, in the High School Math Implementation Guide, the Learning Snapshot guidance says “Administer either the print or digital assessment during the Evaluate phase of each lesson” and “Refer to the suggested assessment time listed in the Evaluate section of each lesson.”

The lesson plan for the “Analyzing Statistical Studies” lesson includes directions for administering the lesson-specific assessment. The “Evaluate” section allocates approximately 15 minutes and identifies “Learning Snapshot: Analyzing Statistical Studies” as the assessment with two administration options: printable or digital. The same lesson also includes “Learning Snapshot Rationales” and an optional “Learning Snapshot Reflection,” which help support the accurate use of assessment results after administration.

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.

In the High School Math Implementation Guide, the “Evaluate” section explains that educators can “locate and print the Learning Snapshots from within each lesson plan file or assign a digital version from the assignment center.” The printable and digital versions share the same name, items, and answer choices.

The materials provide an online platform that allows educators to enable/disable text-to-speech for individual students. This feature is available for both the diagnostic pre- and post-tests, as well as any educator-created 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 include a “Statistics Diagnostic Post-Test” with TEKS-aligned diagnostic assessment tasks/questions. The assessment shows a range of statistics content, including sampling methods, survey design, experimental design, variability, graphical displays, probability, confidence intervals, hypothesis testing, regression, residuals, outliers, and interpretation of statistical conclusions. The items also show more than two levels of complexity. For example, students identify sampling methods and sources of variability; interpret graphs such as boxplots, histograms, scatterplots, and bar charts; calculate or interpret probability and confidence intervals; evaluate p-values and Type I errors; analyze outliers and residuals; and justify conclusions based on study design.

The diagnostic assessment includes more than two unique interactive item types. In the “Statistics Diagnostic Post-Test,” students respond to multiple-choice items, multiselect items, inline text-entry/blank-response items, drag-and-drop response choices, table-based items, graph-interpretation tasks, and constructed-response-style explanation prompts. In addition, materials provide further evidence of the interactive item types available in the program, including bar graph, classification, constructed response, dot plot, drag-and-drop, drawing, equation editor, graphing, histogram, hot text, hotspot, inline choice, inline text entry, and label-image item types.

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 assessments with TEKS-aligned tasks or questions, including interactive item types with varying complexity levels. For example, the Premium Assessments provide a full suite of assessment and reporting tools that educators, campus administrators, and district leaders can use to build and deliver custom assessments and monitor student learning and mastery of the TEKS. These assessments contain Depth of Knowledge (DOK) level 2 and 3 item types. The materials also include multiple-choice, drag-and-drop, text-entry, and inline-choice question types.

The materials include Study Plan practice aligned with the standards taught in each lesson that provide immediate feedback when students answer incorrectly. In the “Evaluate” section, Learning Snapshots are described as formative assessments aligned with lesson standards that mirror the rigor, verbiage, and cognitive complexity of State of Texas Assessments of Academic Readiness End-of-Course assessment items.

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

In the High School Math Implementation Guide, an answer key for a Learning Snapshot includes item rationales for each item in the assessment, which help create small- or whole-group reteach. Each item rationale addresses both correct and incorrect responses to support reteaching decisions.

The How-To Guides article “How do I access and use my teacher progress report?” details the step-by-step process of generating assessment progress reports. Educators can choose to view either the “Class Dot Rank” or the “Student Dot Rank” reports. The reports contain color-coded dots that rank standards mastery for individual students. The article links to a video that provides educators quick remediations based on progress reports.

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 High School Math Implementation Guide states that after the lesson, the materials provide educators suggested activities for both intervention and enrichment and that educators can organize students into small groups based on their needs.

The “Quick-Click Remediation” guidance shows educators how to respond to assessment trends by selecting weak areas, choosing students, setting start and end dates, and assigning targeted remediation. Using the “Teacher Progress Report,” educators can select a standards-based area of weakness from the “Class Dot Rank” or “Student Dot Rank” views and assign remediation to students who need additional 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 for educators to track student progress and growth. Educators can view assessment results through the Results Report, including the overall assessment average, class-level filters, “Student Dot Rank” view, “Completion Status” tab, “Item Analysis” tab, “Assignment Mastery” tab, and “Student Attempts” tab. The “Item Analysis” tab shows class performance by individual question. In contrast, individual student reports identify areas of needed practice by domain or standard and provide videos and practice questions for areas of weakness. Educators can also assign remediation for students who scored 80 percent or lower on a standard.

The materials include tools for students to track their own progress and growth. The Statistics TEKS tracker allows students to record a beginning-of-year score, multiple practice attempts, whether they achieved a ribbon or green dot, and the educator’s initials for each Statistics TEKS. The tracker is organized by statistics content areas, such as statistical process sampling and experimentation and variability, with specific TEKS-aligned skills, including sampling techniques, studies/surveys/experiments, generalizations, statistics and parameters, communicating ideas, analyzing findings, models, variability, and distributions. In addition, the student “Graded Work Report” allows students to view their overall score, performance by domain and standard, and platform-suggested additional practice based on their results. Students can also review questions, read text explanations, or watch explanation videos to learn from mistakes and receive feedback.

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 materials include prompts and guidance to support educators in conducting frequent checks for understanding at key points throughout each lesson or activity. For example, in lesson 12 “Calculate and Interpret Confidence Intervals,” the “Engage” section begins with a think-pair-share that guides educators on how to conduct the activity and provides potential questions and guidance for potential feedback.

The materials provide guidance for educators on how to use the prompts to check student understanding. The Teacher Guide includes guiding questions, common misconceptions, and suggested educator responses. For example, during a quick write, the materials guide educators to ask, “What is the best method for this study?” and to clarify that bias and randomization are important when students do not consider them. During a “Rally Coach & Player” activity, the materials guide educators to look for misconceptions, such as missing control-group details and incorrectly skewing data, and to reinforce randomization, control protocols, and the meaning of right skew. During a “Brain Dump” activity, the guide prompts educators to ask whether the data support the conclusions and to remind students to consider other explanations and all components of a reliable study.

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 High School Math Implementation Guide includes 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 guide describes intervention videos that include two or three questions for students to work through. Educators may organize students into small groups based on their needs to complete the appropriate intervention activities. Additionally, the intervention videos may come from below-grade level or on-grade level.

Lesson 4 includes scaffolded educator guidance and activities for students who need support with grade-level concepts and skills. The Teacher Guide for this lesson identifies common misconceptions, such as students failing to consider selection bias, randomization, control-group details, or the limits of conclusions. The guide then provides specific educator feedback responses, including discussing why bias and randomization matter, reinforcing randomization and control protocols, reminding students to consider other explanations for the data, and reviewing the components of a reliable study. The lesson also includes an intervention activity for struggling students using a grade 7 video on interpreting data in bar graphs, dot plots, and circle graphs.

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 “Engage” section of each lesson uses the Accessing Prior Knowledge (APK) strategy, which provides grouping strategies, question prompts to probe student thinking, directions for students working in groups, and linguistic accommodations in the form of sentence starters based on language proficiency levels. For example, in lesson 5 “Models and Variability,” the APK strategy is a think-pair-share in which students examine the meaning of variability by determining the statement that best models the definition.

The High School Math Implementation Guide provides explicit educator guidance on the available embedded language support activities, such as “Vocabulary Scavenger Hunt” and tiered vocabulary scaffolds. For example, the “Vocabulary Scavenger Hunt” instructs educators to give students the vocabulary list and have students explore words on their own. Then, educators ask students to identify the words as students encounter the words. Finally, educators place those words on the word wall. However, the materials do not include explicit educator guidance on pre-teaching academic vocabulary or unfamiliar references in text.

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 High School Math Implementation Guide includes 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 guide states that each lesson includes videos with two or three questions for students to work through to reinforce key concepts and promote discussion. Educators may organize students into small groups based on their needs to complete the appropriate enrichment activities. Additionally, the enrichment videos often draw from above-grade-level resources.

In the lesson “Analyzing Statistical Studies,” the “Additional Activities for Intervention and Enrichment” section provides an advanced student activity using an AP statistics video titled “Compare Two Distributions.” The lesson also includes educator prompts that extend students’ reasoning by asking them to explain their problem-solving process, consider alternate approaches, justify their conclusions, and share multiple methods.

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 How-To Guides article “What accommodations are available in Progress Learning?” describes the included text-to-speech functionality and calculator accessibility, which educators can enable or disable for individual students during assessments. Educators can select one of three types of calculators (four-function, scientific, and graphing) that are powered by Desmos to include with an assessment.

The Accommodations Guide shows that educators can set individual student language supports to English Default, Spanish Default, or English Only. The materials also provide Spanish translation options, Spanish video transcripts, and accessibility tools, such as color contrast, font size, zoom, highlighting, response masking, drawing tools, sticky notes, and line reader. However, the materials do not provide the ability to turn on content and language supports for students.

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 High School Math Implementation Guide provides educator guidance on various types of exploration activities that require students to demonstrate understanding of mathematical concepts in various ways. For example, some activities instruct students to engage in academic discourse in “Discuss and Do” activities, to show their problem-solving strategies step-by-step in “Show What You Know!” activities, and to make comparisons using diagrams in “Alike and Different” activities. Each activity type includes support for educator guidance. For example, in an “Alike and Different” activity, the educator guidance says, “Place students into cooperative pairs. Project two items for students to compare. Verify correct answers and clarify questions as a whole class.”

The lesson plans provide educators guidance on offering students multiple options for demonstrating understanding of statistical concepts in written, visual, oral, and multimedia formats. In lesson 4, the objective directly states that students communicate methods used, analyses conducted, and conclusions drawn for a data-analysis project through “a written report, a visual display, an oral report, or a multi-media presentation.” The lesson also includes opportunities for students to demonstrate understanding through writing in quick write, “Rally Coach & Player,” and “Brain Dump” activities; visual displays, such as histograms and box plots; captions; oral report revisions; and critical analysis paragraphs. For example, students design a visual display for a multimedia presentation, write a caption explaining variability, and rewrite a study conclusion for an oral report using appropriate statistics language.

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 High School Math Implementation Guide includes explicit prompts and guidance for educators to build knowledge by activating prior knowledge and anchoring big ideas. The guide explains that the “Engage” phase is when educators activate and understand students’ prior knowledge and includes questions vertically aligned with prior-grade-level standards. The “Vertical Alignment” section helps educators understand what students were previously taught and what they will learn later, which frames the context for current learning. In Lesson 8, the “Engage” section specifically directs educators to “Activate prior knowledge of 6.12(C)” using a think-pair-share activity. The educator guidance includes questions, such as “How do we find the measures asked for?” and “How can we tell what best represents the data?” and suggested feedback to refresh students’ understanding of mean, median, and mode and to connect those ideas to selecting a measure that represents the data.

The lesson plan for lesson 8 includes explicit educator guidance to highlight and connect key patterns, features, and relationships through multiple representations. In the “Compare and Contrast Data” lesson, the Teacher Guide includes guiding questions, such as “How do we pick the best representation for a set of data?” and “What meaningful data can we get from data representations?” The “Explore” section directs educators to facilitate “Alike and Different” and “Discuss and Do” activities in which students compare histograms, box plots, dot plots, stem-and-leaf plots, and summary statistics. Educator prompts ask students how displays are alike and different, what measures can be clearly identified from the displays, how a coach might use the data, which representation is best, which data value is most useful, and which statistic is most impacted by outliers. The materials directly guide educators to help students connect visual representations, numerical summaries, data context, patterns, features, and relationships.

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

The “Explain” section of the High School Math Implementation Guide provides educators guidance on effective lesson delivery and facilitation using various instructional approaches. The guide instructs educators to “use the links provided to watch the videos and use a cooperative learning strategy, such as THINK-PAIR-SHARE, to discuss and answer the questions that accompany the video.” Additionally, the “Evaluate” section of the guide advises educators to use “the optional Snapshot Reflection Tool” that “offers valuable opportunities for students to think critically about their own learning and performance.”

Lesson 12 “Calculate and Interpret Confidence Intervals” includes explicit guidance for more than two instructional approaches. The Teacher Guide directs educators to use “Alike and Different,” think-pair-share, “Sage & Scribe,” “IQ Slapdown,” and “Finger Vote” activities. The lesson also includes educator modeling, whole-class discussion, student justification, video-based instruction, independent digital practice, formative assessment, and self-assessment reflection. The cooperative learning appendices provide detailed guidance for facilitation, including suggestions for grouping, educator scripting, discussion prompts, student directions, and linguistic accommodations. For example, “Sage & Scribe” supports paired explanation and recording of solution steps, “IQ Slapdown” guides students through analyzing incorrect and correct answer choices, and “Finger Vote” provides immediate formative assessment data while requiring students to justify their reasoning.

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 High School Math Implementation Guide provides intervention methods for multiple practice types. Students can receive support through intervention videos with accompanying questions, Study Plan practice, educator-created assignments, Learning Snapshot reflection, and reteach opportunities based on item rationales. The guide states that intervention videos may come from below-grade or on-grade-level resources and include questions for students to work through. The guide also notes that educators can gather and analyze student data as students engage with the content.

The “Additional Activities for Intervention and Enrichment” section of lesson 14 identifies a specific intervention video for struggling students: “Statistics Video: Hypothesis Testing: Structuring.” The lesson also includes Study Plan practice, educator-selected assignments, a Learning Snapshot assessment, Snapshot Rationales, and an optional reflection tool to help students identify areas needing more practice.

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 High School Math Implementation Guide provides guidance on implementing enrichment and extension methods effectively. The lesson-specific Teacher Guides provide structured and flexible strategies, such as hands-on activities, visual supports, collaborative discussions, and differentiated questioning, to ensure that all students can access and extend their understanding. Additionally, the Teacher Guides offer clear, actionable guidance to help educators effectively integrate these supports into instruction, including opportunities for student choice and independent application.

The Teacher Guide for lesson 14 “Interpreting a Hypothesis Test” provides directions for several cooperative learning strategies to support on-level and advanced students. For example, educators can group students and use the SPARK strategy in the third section of the lesson to help students process and practice that section’s content before moving on. SPARK stands for Solve-Pass-Agree-Repeat-Keep Going. These components provide opportunities for individual reflection and work, analysis of other students’ solution steps and answers, possible error identification, and explanations or justifications using informal and academic language.

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

The High School Math Implementation Guide includes prompts and guidance to help educators provide timely feedback during lesson delivery. The guide explains that when students miss items in their Study Plans, the platform provides immediate text-based feedback to guide students through the problem-solving process.

The lesson plans provide lesson-specific prompts and guidance to help educators give timely feedback during lesson delivery. For example, lesson 4 “Analyzing Statistical Studies” provides educators potential student questions and feedback responses, such as remembering the steps of conducting a study and the potential errors in a study. In the “Explore” and “Elaborate” sections, the lesson directs educators to ask students questions, such as “What is a response bias?” and “How can you correct potential study errors?” The lesson also directs educators to identify common mistakes, project a problem students are struggling with, model a mistake, and have students identify and correct it.

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 Cooperative Learning Strategy Guide with Embedded Support for ELLs outlines all the cooperative learning strategies used in the program, explains their purposes, offers grouping suggestions for different math proficiency and emergent bilingual (EB) levels, and provides instructions and guidance for educators. The guide also includes directions for students and linguistic accommodations for the five EB proficiency levels as defined by the ELPS. The “Linguistic Accommodations for Language Proficiency Levels” section gives guidance and prompts for Pre-Production, Beginning, Intermediate, High Intermediate, and Advanced students. For example, at the Pre-Production level, students use visual representations of related key words to add facts, and their partners record all facts for the pair. Students at the Beginning level use a word bank of key words to add facts, and their partners record all facts for the pair. At the Intermediate level, students use a word bank of key words and a sentence frame, such as “. . . is related to . . .,” to record their facts. Students at the High Intermediate level use a word bank of key words and a sentence frame, such as “. . . is related to . . . because . . .” to record their facts. At the Advanced level, students use a sentence frame, such as “I know that . . . is related to . . . because . . .” to record their facts.

Additionally, lesson 12 includes educator guidance on providing and incorporating linguistic accommodations across ELPS proficiency levels. The plan includes ELPS-aligned language objectives that require students to speak using content-area vocabulary and to narrate, describe, explain, justify, discuss, elaborate, or evaluate orally with increasing specificity and detail. The lesson directs educators to use embedded cooperative learning strategies, including “Alike and Different,” think-pair-share, “Sage & Scribe,” “IQ Slapdown,” and “Finger Vote.” For example, the guidance says, “Have the student point to images or models to indicate how the two items are alike or different, then have their partner verbalize and record these comparisons, and add their own input.”

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 Cooperative Learning Strategy Guide with Embedded Support for ELLs outlines all cooperative learning strategies included in the materials. Each strategy description featured in the guide includes the strategy’s purpose, grouping suggestions for different mathematics proficiency and EB levels, educator and student directions, and linguistic accommodations aligned with the five EB proficiency levels. For example, the “IQ Slapdown” activity suggests grouping a Pre-Production level student with a High Intermediate level buddy and then pairing that pair with non-EB students. The linguistic accommodations for this activity include allowing Pre-Production level students to point to the answer in each round as their partner explains the answer. The materials provide increasingly more-complex sentence stems for Beginning, Intermediate, High Intermediate, and Advanced level students.

Furthermore, each lesson begins with an APK activity. The materials include an appendix that explains each APK activity, each activity’s intended purpose, grouping suggestions for different mathematics proficiency and EB levels, educator and student directions, and linguistic accommodations aligned with the five EB proficiency levels. For example, lesson 3 “Steps in a Statistical Study” uses the APK structure for a “Quick Write/Draw” activity. The appendix also suggests grouping a Pre-Production level student with a High Intermediate level student or a non-EB student who speaks the EB student’s native language. The linguistic accommodations for this activity include allowing Pre-Production level students to use visual representations of related keywords to add facts and having their partner record all facts for the pair. The materials suggest Intermediate through Advanced level students use a word bank and increasingly more-complex sentence frames to record their facts.

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.

Each lesson in the materials includes language objectives requiring students to use content-area vocabulary and to explain, justify, discuss, elaborate, respond orally, and write with supporting details and evidence. Each lesson also identifies academic vocabulary terms, such as box plots, histograms, interquartile range, quartiles, and standard deviation. The lessons also embed activities, such as think-pair-share, “Alike and Different,” “Discuss and Do,” and a “5-10 Summary” reflection, that give students opportunities to discuss, compare, justify, and write about data representations and summary statistics. The cooperative structures include EB supports, such as visual cues, word banks, sentence starters, sentence frames, partner verbalization, and written recording on the handout.

The materials include embedded guidance to support EB students in developing academic vocabulary, increasing comprehension, and building background knowledge through oral and written discourse. Each lesson provides multiple opportunities to talk with a partner and write about the math through various cooperative learning strategies. For example, in lesson 2 “Observational Studies, Surveys, and Experiments,” students participate in a think-pair-share where they distinguish between observational studies, surveys, and experiments; complete a “Finger Vote” activity; and write explanations of why they picked what they did. During the think-pair-share, students are given a question to answer. Then, they "think about the answer and share with your partner" to explain their problem-solving process and verify their answer.

In addition, each lesson opens with an “Accessing Prior Knowledge (APK)” activity designed to activate students' prior knowledge relevant to the new math they are about to engage in. For example, lesson 10 “Probability and Random Values” opens with an APK activity called "Think/Pair/Share" in which students activate background knowledge from grade 7 probability and determine the experimental and theoretical probabilities in a dice-rolling activity. Students answer the questions independently and then share with a partner and finally with the whole class. Students justify their answers verbally and through writing. However, the materials do not include guidance for cross-linguistic connections through oral or written discourse.

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.

As outlined in the High School Math Implementation Guide, the materials structure each lesson around the 5E Instructional Model, which provides opportunities for students to practice throughout the lesson and demonstrate their understanding. For example, in the “Explore” section, students complete correlating activities aligned with the instructional slides that require them to “Show What You Know,” which are open-ended tasks requiring students to show their work. In lesson 14, one of the TEKS requires students to “Describe the potential impact of Type I and Type II Errors” (S.6J). Section IV of the corresponding student handouts is about Type I and Type II Errors. Question #16 asks, “What is the potential impact of the error in the situation?” and is followed by two real-world scenarios (factory quality control and wildfire alarm system), in which students must analyze the type of error and describe its potential impact.

The materials contain instructional assessments throughout the learning pathway that require students to demonstrate depth of understanding aligned with the TEKS. For example, the “Interpreting a Hypothesis Test” lesson includes an “Evaluate” section with an “Interpreting a Hypothesis Test Learning Snapshot,” which is available as a printable or digital assessment, and an optional Learning Snapshot Reflection. These assessments support the instructional assessment part of the guidance because the assessments are tied to the same TEKS-aligned lesson objectives and require students to interpret hypothesis test results, explain p-values, and evaluate error types in context.

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 include questions and tasks that increase in rigor and complexity, leading to grade-level proficiency in the mathematics TEKS. For example, unit 14 “Interpreting a Hypothesis Test” requires students to explain the meaning of the p-value in relation to the significance level, interpret technology-generated hypothesis test results, and describe the impact of Type I and Type II errors. The lesson moves students from “Engage” and “Explore” activities to TEKS-aligned practice and reflection, in which students explain problem-solving processes, consider alternative approaches, justify their thinking, and identify common mistakes.

In lesson 6, students begin the lesson by analyzing graphs and representations of categorical and numerical data. They then use this foundational knowledge to determine when to use each type of representation in the same lesson. However, in lesson 7, the learning increases in rigor and complexity as students analyze distribution characteristics of quantitative data, which is above-grade-level content and a skill for AP statistics.

The enrichment activity in lesson 7 “Analyzing Quantitative Distributions” provides an opportunity for students to explore AP-level content above grade level. This “Compare Two Distributions” activity includes an instructional video and check-for-understanding questions that provide students immediate feedback.

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

In the Statistics Scope and Sequence, the “Statistics Sequence Rationale” section provides coherence across concepts horizontally within the grade level by connecting patterns, big ideas, and relationships. Lesson 1 begins with “distinguishing between sample statistics and population parameters.” Then, lesson 2 builds on lesson 1 as students distinguish between different types of study designs. By lesson 3, students formulate their own meaningful questions and gather data by applying their knowledge of sampling and study design.

The lesson plan for "Compare and Contrast Data" reinforces coherence at the lesson level. The lesson connects students’ prior understanding of numerical summaries, including mean, median, range, and interquartile range, to the current work of comparing graphical representations and summary statistics. It also looks ahead to AP statistics and other fields where students compare representations and derive meaningful information from data.

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 lessons and other materials demonstrate coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. For example, lesson 6 “Categorical and Quantitative Data” ties the lesson’s learning to the TEKS 5.9(A) in grade 5 and to future learning in AP statistics or advanced science courses. Lesson 6 builds on students’ prior experiences in grade 5 (TEKS 5.9A) by helping students classify data and select appropriate methods to organize and represent information. This foundational understanding supports future learning in AP statistics, in which students must distinguish between categorical and quantitative variables when selecting statistical procedures, creating graphical displays, analyzing distributions, comparing groups, and drawing conclusions from data.

The lessons and other materials demonstrate coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. For example, lesson 7 “Analyzing Quantitative Data Distributions” ties the lesson’s learning to the TEKS 6.12(C) in grade 6 and to future learning in AP statistics or advanced science courses. Lesson 7 builds on the grade 6 TEKS 6.12(C), in which students summarize numerical data using measures, such as mean, median, mode, and range, and use graphical representations to describe data sets. In middle school, students begin to identify patterns, compare data sets, and interpret measures of center and variability. As students advance through the grade bands, they move from organizing and summarizing data to analyzing distributions, evaluating statistical models, and drawing inferences from data. These experiences prepare students for future learning in AP statistics, in which they analyze distributions in greater depth, conduct statistical investigations, interpret sampling distributions, and perform hypothesis testing using quantitative evidence.

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 materials demonstrate coherence by connecting prior procedures and concepts to current learning in hypothesis testing. In the “Interpreting a Hypothesis Test” lesson, the “Vertical Alignment” section identifies prior learning related to extraneous solutions and quadratic inequalities, and the “Engage” section activates prior knowledge by prompting students to consider how a mathematically correct solution may not make sense in context. This prior reasoning is then connected to the current lesson, in which students interpret p-values, hypothesis test results, and Type I and Type II errors in context.

The lesson plan objectives, “Explore” activities, and “Vertical Alignment” sections of the lesson plans demonstrate coherence in the lessons’ activities by connecting concepts and procedures at the current grade level to future grade levels. For example, in lesson 10, one objective is for students to construct a discrete random variable distribution. The concept is the understanding of discrete random variables, and the procedure is constructing distributions. The APK activity in the “Explore” section of the lesson requires students to analyze a table (distribution) of results when rolling a six-sided die. Then, the “Vertical Alignment” section connects these concepts to future research courses that compare sample means to theoretical sampling distributions.

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

The lesson plans provide repeated retrieval of previously learned skills through the “Engage,” “Explore,” “Explain,” “Elaborate,” and “Evaluate” structure. For example, lesson 8 “Compare and Contrast Data” activates prior grade 6 skills in representing numeric data graphically and summarizing it using measures of center and spread. Students then use those prior skills in the current lesson to compare graphical representations and summary statistics. The lesson continues with educator-guided activities, videos, practice problems, and a Learning Snapshot.

Lesson 15 “Analyzing Scatterplots and Line of Best Fit” reviews student expectation G8.5(D) using a trend line to make predictions and student expectation 8.11(A) construct a scatterplot to analyze data. Students need these prior skills to solve problems in current content. For example, solving problems analyzing scatterplots and line of best fit problems in statistics meet student expectations S.7(A) Analyze scatterplots for patterns, linearity, outliers, and influential points and S.7(B) Transform a linear parent function to determine a line of best fit.

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

The materials provide interleaved practice opportunities with previously learned skills and concepts across learning pathways in the main lesson plan guidance. For example, in the Assessments and Assignments feature on the educator’s digital dashboard, educators can create assessments and assignments on previously learned skills and concepts.

The lesson plans include APK activities, current lesson practice, Learning Snapshots, and reflection tools, which shows mixed practice that combines prior and current concepts across learning pathways. For example, in the “Explore” section of lesson 10 “Probability and Random Variables,” students practice determining probabilities, including using a two-way table learned in lesson 9 “Using Two-way Tables.” Additionally, in both lessons, students calculate the probability learned in geometry and middle school mathematics.

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

The questions and tasks provide opportunities for students to interpret models and representations for mathematical concepts and situations. In lesson 14 “Interpreting a Hypothesis Test,” students answer questions, such as “How do you interpret hypothesis test results?” and “A school principal tests if the average study time has increased from 5 hours a week. The test results in a P-value of 0.12. Using 𝛼 = 0.05, how should the principal interpret this in context?” Additionally, students interpret technology-generated hypothesis test results, including p-values, significance levels, null and alternative hypotheses, and test conclusions in context.

The questions and tasks provide opportunities to analyze models and representations for mathematical concepts and situations. In lesson 4 “Analyzing Statistical Studies,” students respond to prompts, such as “Write a critical analysis paragraph evaluating the sampling method, analysis, and conclusion,” and “Which of the following does NOT demonstrate communicating the analyses conducted for the project?” Additionally, students analyze study designs, published findings, variability, data distributions, scatterplots, lines of best fit, confidence intervals, and hypothesis test results.

The questions and tasks provide opportunities to evaluate models and representations for mathematical concepts and situations. In lesson 8 “Compare and Contrast Data,” students respond to prompts, such as “How are the displays alike and different?” and “Determine the values of the mean, median, and mode of the data.” Additionally, students evaluate graphical and visual representations and summary statistics from the same data set and compare measures to determine which best represent the data and why.

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

The materials include questions and tasks that provide opportunities for students to create representations of mathematical situations. In lesson 10 “Probability and Random Variables,” students encounter scenarios, such as rolling dice, drawing marbles, and using a virtual spinner. Students calculate theoretical and empirical probabilities from given data summaries in each scenario. However, the materials do not provide opportunities for students to use concrete objects to collect data or to construct frequency distributions that model empirical and theoretical probabilities.

Additionally, in lesson 8 “Compare and Contrast Data,” students analyze real-world scenarios using statistical data organized into various graphical representations. The task requires students to compare the graphs and determine which is the more appropriate data display using a Venn diagram. Problems 1 and 3 in the “Explore” section refer to basketball shots and free throws. The task requires students to create dot plots and stem-and-leaf plots, which are graphical representations rather than concrete models.

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

In lesson 5 “Models and Variability,” students apply conceptual understanding to new problem situations as they graph and discuss findings from box plots and histograms of basic statistical data. Students then graph more variable data using dot plots and histograms and show their conceptual understanding when asked, “How can the results be described (mean, median, distribution, variability, shape)?”

In lesson 16 “Modeling and Interpreting Line of Best Fit,” students apply their knowledge of lines of best fit and the slope-intercept form of a line to new contexts by interpreting the slope and y-intercept to check for reasonableness within the problem. Students respond to questions, such as “What are some of the different methods that can be used to determine a line of best fit for data? What are some ways to check the reasonableness of a slope or y-intercept of a line of best fit?”

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 repeated grade-level practice opportunities through platform-based practice problems in the Study Plan feature. Students have unlimited access to their individualized Study Plans, which provide an unlimited opportunity to build automaticity and fluency by practicing skills until they have demonstrated mastery. In the Study Plans, Focus Areas identify which standards students need further practice on. From the Focus Areas identified, students practice on aligned problems until those standards are no longer Focus Areas. This process builds the grade-level fluency and automaticity necessary to complete grade-level tasks.

The “Think or Swim” activity provides opportunities for students to build automaticity and fluency with grade-level standards in a competitive setting. Educators select questions aligned with the TEKS, and students take turns answering the revealed questions in a timed setting. The timed format of “Think or Swim” builds automaticity by requiring students to retrieve facts quickly under time pressure, and the repeated Study Plan practice across lessons builds broader fluency with grade-level procedures.

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 provide opportunities for students to practice accurate statistical procedures through Study Plan practice and educator-selected assignments. In the “Interpreting a Hypothesis Test” lesson, the students begin by defining significance level, decision rule, and interpreting in context. Students practice calculating p-values, interpreting hypothesis tests, and understanding Type I and Type II errors. Then, they move on to practice identifying the correct decision and its explanation for each scenario. Finally, students practice formulating their own interpretations from the scenarios. This practice allows students to become more efficient at analyzing data before making their own interpretations.

Additionally, the materials provide opportunities for flexible procedural thinking during practice. Lesson 14 “Interpreting a Hypothesis Test” directs educators to ask students how they solved a problem, whether they can think of other ways to approach the problem, and what students could provide to convince the class that their approach is valid. Educators model a mistake, ask students to identify and correct it, and encourage students to share multiple approaches and justify their reasoning.

The materials provide opportunities for students to practice accurate statistical procedures through Study Plan practice and educator-selected assignments. In lesson 14 “Interpreting a Hypothesis Test,” students practice explaining the meaning of the p-value in relation to the significance level in providing evidence to reject or fail to reject the null hypothesis, describe the potential impact of Type I and Type II errors, and interpret the results of a hypothesis test using technology-generated results, such as large sample tests for proportion, mean, difference between two proportions, and difference between two independent means, including p-values, interpreting hypothesis tests, and Type I and Type II errors. The lesson also includes a Learning Snapshot and rationales that identify correct answers and explain likely misconceptions, which supports accuracy in statistical procedures.

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.

The materials provide opportunities for students to evaluate the accuracy of mathematical representations, models, strategies, and solutions throughout learning pathways. Students interpret hypothesis test results, compare the p-value to alpha, and identify common errors, such as comparing the null hypothesis population parameter to the sample parameter instead of using the decision rule. The materials also prompt students to identify and correct mistakes during practice.

The materials provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for flexibility throughout learning pathways. Students compare different graphical or visual representations of the same data set and compare information derived from summary statistics. The guiding question asks students how to choose the best representation for a data set, which helps students evaluate multiple representations and determine how different displays communicate information.

Lesson 16 “Modeling and Interpreting Line of Best Fit” provides an opportunity for students to evaluate mathematical representations, models, strategies, and solutions for efficiency throughout learning pathways. For instance, in the “Elaborate” section, students work in groups and discuss their problem-solving processes. With their group members, students answer the following questions: “How did you solve this problem? Can you think of any other ways to approach the problem? What is something you could say or provide to convince the class that your approach is valid?”

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

Lesson 16 “Modeling and Interpreting the Line of Best Fit” contains guidance to support students in selecting increasingly efficient approaches to solving mathematical problems. For instance, in the “Elaborate” section, educators identify and discuss common mistakes. Educators project one problem that students are struggling with and model a mistake in the problem-solving process. Students identify the mistake and how to correct it and share multiple ways to approach the problem and to justify their approach. By listening to how their peers solved the same problem, students analyze their own strategy and determine which method was the most efficient and why. In addition, students begin to compare lines of best fit and attributes of those lines. Students analyze various solution methods by discussing questions, such as ‘What are some of the different methods that can be used to determine a line of best fit for data?” and “What are some ways to check the reasonableness of a slope or y-intercept of a line of best fit?”

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

The materials explicitly state how the Teacher Guide for each lesson addresses the TEKS' conceptual emphases. For example, in lesson 3 “Steps in a Statistical Study,” students formulate meaningful questions, determine what is necessary to answer the question, and outline the steps to reach a final solution. The materials present students with scenarios in which they must brainstorm facts about how recycling frequency is affected by their awareness of pollution. Then, they come up with a question and collect the data for a two-way table. Using the data they collected, students create a stacked bar graph showing how frequency and awareness are related. All of these tasks help students understand the reasoning behind statistical studies.

The Statistics Scope and Sequence includes a rationale that explains how each lesson addresses the procedural emphasis of the TEKS. For example, in lesson 4 “Analyzing Statistical Studies,” students critically analyze published findings for the appropriateness of the study design implemented, the sampling methods used, and the statistics applied and then communicate their findings through reports or presentations. Students also learn to critically analyze published findings, which enables them to identify flaws in study designs or sampling methods. Students work with a partner to brainstorm answers for the scenarios before writing their findings.

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.

In lesson 8 “Compare and Contrast Data,” students compare graphical and visual representations of the same data set, including histograms, box plots, dot plots, and stem-and-leaf plots. The lesson asks students to determine what information can be gathered from each representation and which display best represents the data, which allows students to use pictorial representations to analyze and communicate statistical information.

Students use population and sampling distributions, summary statistics, two-way tables, probability models, confidence intervals, hypothesis statements, p-values, and lines of best fit. These tasks require students to use numerical, tabular, symbolic, and statistical models to represent and analyze data, which addresses the TEKS expectation for abstract models. However, the materials do not provide opportunities for students to use concrete models. Questions and tasks rely on graphical, numerical, and symbolic representations rather than physical or manipulative materials.

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.

In lesson 8 “Compare and Contrast Data,” the materials help students connect representational models to abstract statistics concepts. Students compare graphical and visual representations, use two-way tables to determine marginal and conditional probabilities, use simulations of random variables to compare simulated and theoretical measures, and analyze scatterplots and lines of best fit to connect visual patterns in the data to correlation, slope, intercepts, and prediction.

In lesson 15 “Analyzing Scatterplots and Lines of Best Fit,” the materials support students in creating representational models through visual displays of graphs of scatterplots and lines of best fit. Students use these visuals to identify patterns, linearity, outliers, and influential points.

Additionally, lesson 11 “Understanding Confidence Levels” supports students in defining and explaining representational models by showing how a sample statistic and a confidence level are used to construct a confidence interval. Students explain how changes in the sample size, confidence level, and standard deviation affect the margin of error of a confidence interval. Students answer questions, such as “what happens to the margin of error, and why?” and “What is the primary reason that statisticians prefer larger sample sizes when constructing confidence intervals?” However, the materials do not provide supports for connecting concrete models to abstract concepts, and the materials do not provide supports for creating, defining, and explaining concrete models.

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

Each 5E Instructional Model includes opportunities for students to develop academic language through visuals, other language-development activities, and cooperative learning strategies embedded in each lesson. For example in Lesson 1: Sampling Techniques and Sample vs. Population, students participate in a Think/Pair/Share activity to distinguish between a sample and a population using real-world scenarios. Students explain their reasoning to a partner using academic vocabulary such as population, sample, census, parameter, and statistic, while teacher-guided discussion reinforces precise mathematical language.Teacher guidance includes sentence stems and discussion prompts to reinforce precise mathematical communication.

The materials provide opportunities for students to develop academic mathematical language using visual representations and structured language routines. In lesson 8 “Compare and Contrast Data,” students compare graphs and summary statistics while using vocabulary terms, such as histogram, box plot, interquartile range, quartile, and standard deviation. Discussion routines and sentence stems support students in explaining how data representations are alike and different by using academic statistics language.

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 materials provide embedded educator guidance to scaffold and support students’ use of academic vocabulary in context when communicating with peers and educators. In the lesson “Analyzing Statistical Studies,” the materials guide educators to use “Rally Coach & Player” and “Brain Dump” activities to focus on methods, analysis, conclusions, and critical analysis. The lesson also includes educator guidance for student questions, such as asking what it means to analyze data and reminding students of measures of central tendency.

The “Explain” section of the same lesson directs educators to ask students to use think-pair-share to answer video questions and complete sentence stems, such as “A response bias means _____” and “We can correct potential study errors by _____,” which requires students to extend the use of academic statistical vocabulary in peer discussion and class review.

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

The materials include embedded guidance to support student application of appropriate mathematical language and academic vocabulary in discourse. In the “Interpreting a Hypothesis Test” lesson, students use think-pair-share, SPARK, and “Discuss and Do” routines while working with terms, such as p-value, hypothesis test, decision rule, Type I error, and Type II error. In the “Explain” section, the materials direct students to use think-pair-share to complete sentence stems, such as “The only results of the decision rule are _____” and “When interpreting a hypothesis test, the first thing to state is _____,” which supports the use of academic vocabulary during discussion.

The “Interpreting a Hypothesis Test” lesson directs educators to circulate during practice and ask students, “How did you solve this problem?” “Can you think of any other ways to approach the problem?” and “What is something you could say or provide to convince the class that your approach is valid?” The materials also direct educators to model mistakes, ask students to identify and correct errors, and encourage students to share multiple approaches and justify their reasoning.

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

The materials include embedded guidance to facilitate mathematical conversations that allow students to hear mathematical language with peers. In the lesson “Interpreting a Hypothesis Test,” the “Engage,” “Explore,” and “Explain” sections complete think-pair-share, “Finger Vote,” SPARK, and “Discuss and Do” activities, which provide students structured opportunities to listen to peers discuss p-values, hypothesis test results, and Type I and Type II errors.

Lesson 16 “Modeling and Interpreting Lines of Best Fit” includes embedded guidance to facilitate mathematical conversations and allow students to refine and use mathematical language with peers. Cooperative learning strategies included in the lesson plans, such as “Discuss and Do,” include guidance to facilitate mathematical conversations that allow students to hear, refine, and use mathematical language with peers. For example, the “Discuss and Do” activity instructs students to “Read the problem and talk about the situation and different ways to solve the problem with your partner.” Students then solve the problems independently before sharing with their partner. Finally, the materials guide partners to “Compare answers and solution processes. Verify correct answers and clarify questions during the whole class discussion.”

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 Teacher Guide for each lesson includes a “Common Misconceptions and Suggestions of Teacher Responses” section that provide guidance for educators to anticipate and respond to a variety of student answers. For example, in lesson 16 “Modeling and Interpreting Lines of Best Fit,” the Teacher Guide cautions that “Students may think that linear regression is the only option for finding the line of best fit for a data set. Suggested Teacher Response: Remind students that a line of best fit can be found by transforming the linear parent function, f(x) = x, by performing a linear regression, by applying the median-median method, or by using the absolute value method.”

In lesson 5 “Models and Variability,” the Teacher Guide identifies the potential misconception that students may confuse mathematical and statistical models. The suggested educator response clarifies by directing educators to emphasize the deterministic nature of mathematical models and to provide a specific way to address the misconception during instruction.

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

The materials appropriately integrate the TEKS process standards using APK through Learning Snapshot activities. Students apply mathematics to everyday problems, which aligns with S.1(A); use representations to organize mathematical ideas, which aligns with S.1(D); and explain or justify arguments using mathematical language in written or oral communication, which aligns with S.1(G). For example, the Learning Snapshot Reflection activity for lesson 4 “Analyzing Statistical Studies” instructs students to “Choose one problem you solved correctly. Explain your problem-solving approach. How could you demonstrate that your solution is valid to someone who approached the problem in a different way?”

In addition, students apply mathematics to everyday problems, which aligns with S.1(A); use representations to organize mathematical ideas, which aligns with S.1(D); and explain or justify arguments using mathematical language in written or oral communication, which aligns with S.1(G). For example, in the student handout for Lesson 1 “Sampling Techniques and Sample vs. Population,” students use a Venn diagram to compare and contrast populations and samples.

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

The Teacher Guides describe how each lesson incorporates the process standards and connects the process standards to previous and future lessons. For example, in lesson 6 “Categorical and Quantitative Data,” two of the four process standards listed for the lesson are S.1(A) Apply mathematics to problems arising in everyday life, society, and the workplace; and S.1(B) Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. The guide also informs that “These topics are applied in sciences when analyzing data.”

The materials connect process standards throughout the pathway by explaining how each lesson builds toward later statistical reasoning. For example, the Statistics Scope and Sequence document states that students move from sampling methods to study design; then to conducting statistical studies, communicating findings, modeling variability, analyzing data distributions, probability, confidence intervals, hypothesis testing; and finally to bivariate data modeling. The document explicitly connects lesson 11 on confidence intervals to sampling distributions from lesson 5 and connects lesson 13 on null and alternative hypotheses to estimation and p-values as the next logical step after confidence intervals.

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, as outlined in the Statistics Scope and Sequence, which identifies the full progression of lessons and provides rationales that connect lesson goals to process-standard behaviors. For example, lesson 4 “Analyzing Statistical Studies” states that students communicate findings through reports or presentations and critically analyze published findings to identify flaws in study design or sampling methods. The materials also provide a course-level overview of the lesson sequence and include a standards-alignment table that identifies which process standards are incorporated across the lessons. This table helps educators see how the materials address the TEKS process standards.

In addition, each lesson plan includes a “Standards” section that lists the content, process, and language standards for the lesson separately. For example, the “Analyzing Statistical Studies” lesson lists process standards S.1(A), S.1(B), S.1(D), and S.1(G), including applying mathematics to real-world problems, using a problem-solving model, communicating mathematical ideas with multiple representations, and displaying, explaining, and justifying mathematical ideas using precise mathematical language.

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. For example, in lesson 7 “Analyzing Quantitative Data Distributions,” students analyze the distribution characteristics of quantitative data and determine the presence and impact of any outliers. The lesson includes think-pair-share, “Discuss and Do,” and “Finger Vote” tasks in which students analyze quantitative data and data distributions, the lesson also provides practice problems from categorical and quantitative data on the platform.

As students move through the 5E Instructional Model lesson structure, they have multiple opportunities to persevere while solving problems and working with partners and groups in various cooperative learning structures. For example, in lesson 3 “Analyzing Statistical Studies,” students complete a “Brain Dump” activity by partnering up and taking turns stating facts about the given scenario. This activity helps students recall information they know, make connections to new information with the help of their partner, and build confidence to continue working on the problems.


In lesson 12 “Calculate and Interpret Confidence Intervals,” students make sense of mathematics by interpreting confidence intervals in context, including statements from news- or media-style reports. For example, students must choose the correct interpretation of a 90-percent confidence interval for local drivers’ commute time, distinguishing the correct interpretation from common misconceptions. The Statistics Scope and Sequence also explains that students learn to interpret confidence intervals in the context of media or statistical reports, which makes the mathematics relevant to real-world information.

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 materials support students in understanding, explaining, and justifying that there can be multiple ways to complete a mathematical task. In lesson 8 “Compare and Contrast Data,” students compare different graphical or visual representations of the same data set and compare information derived from summary statistics. The student handout asks students to determine the mean, median, and mode, then decide which value best represents the data and to justify their choice. Students also compare a histogram with a box plot and determine which representation is better for identifying a percentage range. These tasks support students in understanding that data can be analyzed and represented in multiple ways, explaining the differences between those approaches, and justifying which representation or statistic is most appropriate for the situation.

The materials support students in explaining and justifying multiple approaches through recurring educator guidance in the “Elaborate” sections. For example, lesson 8 “Compare and Contrast Data” directs educators to circulate as students work and ask, “How did you solve this problem?” “Can you think of any other ways to approach the problem?” and “What is something you could say or provide to convince the class that your approach is valid?” The guidance also directs educators to encourage students to share multiple ways to approach a problem and justify their approach.

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.

The “Explore” section of each lesson is designed to engage students in collaborative activities while doing, writing, and discussing mathematics. For example, lesson 1 “Sampling Techniques and Sample vs. Population” gives students a question on their student handout to answer with a partner or their group about the parameter of a study’s population and asks students to discuss and write their answers to the following prompts over three rounds: “Round 1: Indicate with your fingers (one to four) which answer you think is the worst and why; Round 2: Indicate which answer is the ‘trickiest’ answer and why; Round 3: Indicate which answer is the correct answer and support your answer.” Additionally, the “IQ Slapdown” activity is designed for students to do, write, and discuss mathematics with their peers first, then as a whole group.

The materials provide a variety of cooperative learning strategies incorporated into each lesson. The strategies are designed to require students to discuss, do, and write about mathematics with their peers and educators. Strategies, such as think-pair-share and “Discuss and Do,” allow students to work independently and share their problem-solving process with another student using academic mathematical language. The “Sage & Scribe” activity begins with the “sage” explaining (discussing and doing) the mathematics necessary for the problem and the “scribe” recording (writing) the mathematics, then the partners switch roles. Partners provide feedback throughout the problem, then partners share the processes with the whole group.

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 materials support educators in guiding students to share their problem-solving approaches through explanations, arguments, justifications, and multiple points of entry. The Cooperative Learning Strategy Guide with Embedded Support for ELLs includes routines, such as think-pair-share, “Discuss and Do,” “Rally Round,” and “Finger Vote,” in which students explain their process, compare approaches with partners, provide arguments when they disagree, and justify answers during whole-class discussion. In lesson 5 “Models and Variability,” the educator guidance includes prompts, such as “How did you solve this problem?” “Can you think of any other ways to approach the problem?” and “What is something you could say or provide to convince the class that your approach is valid?” The students construct a statistical model to describe variability around the structure of a mathematical model for a given situation, such as tables, scenarios, histograms, bar graphs, and/or scatterplots.

In addition, the lessons direct educators to circulate during practice and ask students to reflect on how they solved a problem, whether there are other ways to approach it, and what they could say or provide to convince the class that their approach is valid. Lesson 14 also directs educators to model common mistakes and to ask students to identify, correct, and share multiple approaches and to justify their reasoning. For instance, if students confuse the types of errors, students could review their think-pair-share activity. The pair of students has the opportunity to reflect on the two errors, their vibe, and the penalty they may incur.

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

The materials include prompts and guidance to support educators in providing explanatory feedback based on student responses. The Teacher Guides direct educators to display questions and possible responses, verify correct answers, and clarify student questions during instruction. For example, in lesson 14 “Interpreting a Hypothesis Test,” the Learning Snapshot provides feedback for all answers, correct or not. Question 3 gives some data and asks, “What is the potential impact of a Type I error?” The guide gives the following response feedback: “A is incorrect. Students might pick this because it sounds correct, but it describes a correct decision, not an error.” and “C is correct. A Type I error occurs when we reject a true null hypothesis. Here, it would mean concluding the battery lasts less than 10 hours when it actually meets the claim, potentially causing the company to reject a perfectly good product.”

The materials include prompts and guidance to support educators in providing explanatory feedback based on anticipated misconceptions. The Teacher Guides prompt educators to use guiding questions and clarify misunderstandings, such as distinguishing observations, surveys, and experiments and identifying what is required for valid conclusions. In addition, the Teacher Guide for each lesson directs educators to identify and discuss common mistakes as students work, project a problem students are struggling with, model a mistake in the problem-solving process, and ask students to identify and correct the mistake.