Measuring Up to the TEKS Mathematics 2nd edition, Grade 8

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.

Grade 8 materials include an Alignment Guide that outlines the TEKS, the ELPS, and the concepts that are covered in the course. Educators can use the “Lesson correlation to the grade 8 TEKS” chart to locate lessons that address specific TEKS. The “ELPS alignment” chart shows how recurring components align with the ELPS. The “Horizontal and vertical progression” table includes a rationale for how concepts and skills connect across grade levels (vertical alignment) and within the same grade level (horizontal alignment), as designed in the materials.

Chapter overviews outline specific examples of how the TEKS and the ELPS are integrated into each chapter’s lessons, clearly linking the standards and instructional content within the grade. Each chapter overview includes a “Horizontal/Vertical Progression Summary” section that explains how the chapter’s content builds within the grade level and connects to previous and future grade-level skills.

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 use in various contexts. The “Getting Started” section offers two ways to implement the materials based on either scope and sequence or students’ needs. The “Core Lesson Design and Pacing” section explains the five core components of the lesson structure plus suggested lesson pacing, assessment timing, and tips for use, including differentiation and maximizing instructional time.


Each lesson planner includes instructional supports that are aligned to students’ needs, such as tips for adjusting instruction for whole-group (tier 1), small-group (tier 2), or individual instruction (tier 3); ELPS language and discourse supports; and detailed instructional design strategies to guide educators in supporting all students. The “Critical Thinking” activity that is included in each lesson provides challenge questions for students who demonstrated proficiency in grade-level materials.

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

The “Lesson correlation to the grade 8 TEKS,” “ELPS alignment,” and “Horizontal and vertical progression” tables together act as a TEKS correlation guide that includes recommended skill entry points. The “What’s Inside the Teacher Edition: Full-Length Practice Tests” and “Tracking and Pacing Charts” front matter sections direct educators to practice tests (diagnostic assessments) and student tracking charts in the Appendix. When paired with the tables in the front matter, these tests can guide educators to skill entry points, based on diagnostic assessment results.

Full-length practice tests are available digitally through the “Measuring Up Live” Insight digital platform. The platform automatically scores these tests, and educators can use detailed reports to identify strengths, address gaps, and target instruction accordingly.

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

The “What’s Inside the Teacher Edition: Chapter Overviews” and “Teacher Lesson Sequence” sections outline protocols and guidance for how to read the chapter overviews at the beginning of each chapter and the lesson planners at the beginning of each lesson. The outline indicates that chapter overviews summarize the mathematical focus and progression of learning across the chapter. Additionally, lesson planners show how each lesson builds on prior learning, connects to future concepts, explains how students engage in the lesson, and provides prompts to assess understanding. The “Instructional Planning” section provides further guidance on using chapter overviews and lesson planners to plan lessons effectively, ensuring that students are ready and instructional impact is maximized.

Chapter overviews provide clear protocols for internalization within each chapter. Educators can preview key standards, objectives, vocabulary, and assessments to prepare for instruction. They also can examine the learning sequence and identify places within the chapter for differentiation, scaffolding, and formative assessment review.

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

The “Guidance for Instructional Leaders” section that is included in the grade 8 front matter provides resources and guidance to support educators in implementing the materials as designed. This guidance includes a table that outlines key features and look-fors for various instructional focuses.

The materials provide resources for instructional leaders to use when supporting educators in implementation. For example, the “Implementation Checklist for Instructional Leaders” section provides a quick-reference checklist with look-fors to guide observations. The “Instructional Leader Strategies Guide” section provides targeted actions for addressing pacing, differentiation, extension, assessment use, and data-driven instruction.

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 “What’s Inside the Teacher Edition: Teacher Lesson Sequence” section outlines components of each lesson, beginning with detailed lesson plans that include learning objectives that are aligned with the TEKS and the ELPS. Each lesson includes student insert pages with wraparound materials to guide educators. Lessons also include various assessment tools that are aligned with the TEKS and the ELPS. The educator wraparound for the “Guided Instruction” section and assessment provides guidance for working with striving learners (SLs) and emergent bilingual learners (EBLs).

Each lesson in the grade 8 Teacher Edition includes a lesson planner that clearly outlines learning objectives that are aligned to the TEKS and the ELPS. The lesson planner also includes embedded educator and student resources, instructional components that are aligned to the 5E instructional model, and assessment resources that support and measure mastery of the TEKS and the ELPS. The “Core Lesson Design and Pacing” section outlines the lesson’s structure and provides suggested time frames for each lesson component.

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. The “Program and Chapter Family Letters” section in the Teacher Edition explains the purpose of the family letters. Both English and Spanish versions are included in the Student Edition to support home-to-school communication and family engagement.


Family letters are available at the beginning of each chapter in both English and Spanish. For example, the chapter 1 family letter explains what students will learn about real numbers and includes sections such as “Questions to Ask Your Child,” “Practice Together at Home,” “Math Words to Know (Lesson),” and “How You Will Know Your Child is Making Progress.”

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

The materials include definitions and the intended purpose of various types of instructional assessments. The “Assessment Types, Purposes, and Administration” section identifies assessment categories, including lesson practice, lesson assessment, exit tickets, chapter tests, and full-length practice tests. This section also includes a chart that explains the program’s formative, summative, and diagnostic purposes.

Each chapter overview includes an “Assessment” section that identifies assessments as formative or summative. The section also describes the instructional purpose of each assessment type within the lesson’s sequence.

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

The “Assessment Types, Purposes, and Administration” section outlines each assessment and includes guidance to ensure consistent, accurate administration. For example, the table indicates that students must complete assessments independently in quiet or timed settings, and print and online administration options are available. The “Suggested Assessment Timing” section provides further guidance on timing for chapter and practice tests.

The “Assessment” section that is included in the front matter of each chapter in the Teacher Edition prompts educators to ensure consistent and accurate administration of each type of instructional assessment. This section describes formative assessments within each lesson, such as “Guided Instruction,” “Learn Together,” and “Practice” activities. Summative assessments, such as each lesson’s assessment and the “Building Stamina” chapter test, are used to monitor students’ mastery and inform instructional decisions. Additionally, the “Pacing” section provides recommended instructional timeframes for lesson and chapter assessments.

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 “What’s Inside the Teacher Edition: Full-Length Practice Tests” section indicates that two printable full-length practice tests are available in the Appendix. The “Digital Only Supports” section highlights text-to-speech features that educators can toggle on or off for individual students, along with outlined content and language support options.

“Measuring Up Live” Insight digital assessments include accessibility options that are assigned to individual students. These options include text-to-speech, line reading, a magnifier, font size, and color contrast. The “Digital Only Supports” section indicates that the platform provides word and text translations plus a dictionary for individual student’s needs.

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

The “Teacher Tools for Monitoring Progress” section indicates that the “Measuring Up Live” Insight digital platform provides progress monitoring for TEKS-aligned practice tests by question type, item difficulty, and/or Depth of Knowledge (DOK) level. This section outlines varying levels of complexity and question types for chapter tests and diagnostic assessments. Chapter tests and diagnostic assessments include DOK 1-, DOK 2-, and DOK 3-level questions.

Two practice tests in the Appendix include TEKS-aligned questions with varying levels of complexity and more than two interactive item types, including multiple-choice, multiselect, fill-in, inline choice, and drag-and-drop questions. While item difficulty and DOK levels are not labeled in the print version, the “Measuring Up Live” Insight platform provides this information digitally.

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 “Assessment” section that is included at the beginning of each chapter in the Teacher Edition describes TEKS-aligned formative assessments within each lesson, including “Guided Instruction,” “Learn Together,” and “Practice” activities. The “Practice” section for each lesson clearly indicates DOK levels. Other lesson activities vary in complexity but do not indicate DOK levels.

The “Assessment types, purposes, and administration” table indicates that each lesson assessment, exit ticket, and “Building Stamina” chapter test is a formative or summative assessment. However, the “Assessment” section that is included at the beginning of each chapter describes these assessments as summative. Each “Building Stamina” chapter test includes more than two interactive item types and DOK 1-, DOK 2-, and DOK 3-level questions.

Each lesson assessment clearly indicates DOK levels. For example, the lesson 6 assessment includes DOK 2- and DOK 3-level questions, and question types include multiple-choice, inline choice, and drag-and-drop.

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

The “Building Stamina” chapter tests provide scoring and guidance for interpreting students’ performance by identifying correct responses, the TEKS, and the DOK for each question in the Teacher Edition. The sidebar for the “Building Stamina” section includes rationales for correct and incorrect responses. When educators give the test digitally, the “Measuring Up Live” Insight digital platform provides detailed scoring reports for each student.

The “Practice” activity and assessment that are included in each lesson in the Teacher Edition include scoring information and guidance for interpreting students’ performance. The sidebar for the “Practice” section includes common errors and hints so educators can interpret student responses. The sidebar for the assessment gives tips for striving students and emerging bilingual students to assist educators in assessing students’ needs.

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

Exit tickets that are included at the end of each lesson in the Teacher Edition include guidance on interpreting students’ performance on a specific task and using patterns in students’ responses to guide instruction in the following lesson. For example, the lesson 1 exit ticket suggests, “If many students struggle with real number classification, begin the next lesson with a brief whole-group review of the definitions.”

The “Instructional Formats and Use” section details how educators can address student performance during whole-class instruction, targeted small-group instruction, tutoring and enrichment sessions, and test prep. Built-in questions and assessments guide each chapter, helping educators create a more coherent, purposeful approach.

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 both educators and students to track progress and growth. They include educator-facing progress-monitoring tools through the “Measuring Up Live” Insight digital platform. The “Teacher Tools for Monitoring Progress” section provides an analysis of assessment items and proficiency reports by standard. Educators can use these reports to monitor students’ performance by the TEKS; by individual student, small group, or whole class; and by question type, item difficulty, and/or DOK level.

The “Critical Thinking” section that is included in each lesson includes a “How Am I Doing?” section for the student at the bottom of the page and for the educator in the Teacher Edition. Students can use this section to record questions and self-assess their progress with a specific skill. The Teacher Edition provides look-fors and common misconceptions to guide educators in monitoring students’ responses.

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.

Each lesson in the Teacher Edition includes “Introduction” and “Guided Instruction” sections that provide prompts and guidance to support educators in conducting frequent “Checks for Understanding” at key points in the lesson. For example, while guiding students through the “Understand the TEKS” section in the lesson 2 introduction, the educator can ask, “What does it mean for a number to be a non-terminating, non-repeating decimal?” Then, the educator can use sample responses to assess students’ responses.

Beyond the lesson introduction, the “How Am I Doing?” sidebar that is included in the Teacher Edition guides educators in monitoring students as they complete the “Critical Thinking” section. For example, the sidebar in lesson 2 directs educators to prompt students to explain how they approximate square roots. The note specifically prompts educators to listen for misconceptions in using a ratio to approximate the tenths place.

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 “What’s Inside the Teacher Edition: Wraparound Student Edition Lesson Support” section describes scaffolded supports that are available for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. Before each lesson, an “Activating Prior Knowledge” section provides educators with guidance to gauge students’ understanding and prepare them for the lesson’s focus. Additionally, the wraparound provides targeted supports for striving students and emergent bilingual students through visual models, language scaffolds, and guided practice, which help students access, process, and explain their learning.


The “Common Misconceptions and Targeted Supports” section in the Teacher Edition, which is located before each chapter, breaks down the TEKS by lesson. This section includes scaffolded educator guidance that targets students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. The support directly targets striving students and emergent bilingual students. It also aligns with the specific standard that is addressed in each lesson and includes an extension activity to help students reach proficiency. For example, chapter 1 targeted supports include using Venn diagrams, foldables, sorting cards, number lines, and sentence frames to reinforce students’ understanding of rational numbers throughout each lesson.

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 materials include pre-teaching and embedded language supports for developing academic vocabulary throughout the course. The “ELPS Language and Discourse Support” section that is included before each lesson provides educators with guidance on supporting mathematical discourse and language development for emergent bilingual students. This section supports academic language development through proficiency-level scaffolds that help students listen, speak, read, and write about their mathematical reasoning. For example, lesson 1 provides educator guidance on facilitating oral explanations of mathematical concepts and prompts students to compare rational and irrational number sets using academic language.

The materials also include home-language supports, Spanish cognates, and a “Words to Know” feature that helps students clarify meaning and connect familiar language to mathematical terminology. Additionally, the materials guide students from oral reasoning to written justification during “Critical Thinking” and “Exit Ticket” activities, which provide ongoing opportunities to develop and apply academic vocabulary in context. While the materials include explicit educator guidance throughout each lesson for pre-teaching and embedded supports for developing academic language, they do not include language supports for 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 “Supports for All Learners” section in the Teacher Edition outlines challenge and extension opportunities available for “challenge-ready learners.” The table identifies extension prompts, “Critical Thinking” activities, and “Extension” activities as resources for challenge-ready students.

“Critical Thinking” and “Extension” activities in the Teacher Edition provide educators with explicit guidance for supporting students who demonstrated proficiency in grade-level content and skills. For example, the “Extension” activity in lesson 1 prompts students to create their own list of 20 distinct real numbers and draw a visual that shows how the real-number sets relate to each other. Additionally, the “Above-Level Extension Bank” section in the Appendix includes one extension activity per lesson that extends the learning beyond the current grade level. For example, the “Extension” activity for lesson 5 in the “Above-Level Extension Bank” section in the Appendix prompts students to explore the intersection of linear inequalities. This work introduces the concept of systems of linear inequalities and provides an opportunity for students to learn above-grade-level content and skills.

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.

Digital materials provide text-to-speech, content, and language supports. The Student eBook provides an immersive reader, real-time translation, and an academic vocabulary picture dictionary. Educators can control which language and dialect students use to move through the materials. However, the materials do not explicitly state whether text-to-speech or dictionary options can be assigned to individual students for the Student eBook. Additionally, “Measuring Up Live” Insight online assessments allow educators to set accommodations for individual students such as text-to-speech, translation, and dictionary options. Digital materials do not provide calculator support.

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 “Student Lesson Sequence” section describes the “Critical Thinking” component of each lesson, which provides students with options to demonstrate understanding through multistep and real-world problems. For example, the lesson 3 “Critical Thinking” activity requires students to estimate, compare, and explain real number values using a variety of strategies. Students must demonstrate understanding by explaining their reasoning, comparing approaches, and representing their thinking in multiple ways. Additionally, the “How Am I Doing?” section in the Teacher Edition sidebar guides educators to support students by listening for accurate concept development and correcting misconceptions as students explain their thinking for each question.

The “Math Tools” section in the Appendix of both the Student Edition and the Teacher Edition provides reference tools such as number lines, fraction models, coordinate planes, and geometric nets. These tools help students model mathematical ideas, organize their thinking, and represent relationships when solving problems. The Teacher Edition guides educators on incorporating these tools to support students in modeling and representing mathematical ideas during lessons.

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.

Lesson materials in the Teacher Edition include explicit (direct) prompts and guidance so educators can build knowledge by activating prior knowledge and anchoring big ideas, using the front matter and wraparound for each lesson. For example, the lesson 1 planner and “Activating Prior Knowledge” section provide specific prompts and guidance for educators to activate knowledge of describing relationships between rational number sets in grade 7, which leads to the description of relationships between real number sets in grade 8. This guidance helps educators activate prior knowledge of grade 7 concepts and connect these concepts to the grade 8 learning progression. Additionally, the wraparound provides guidance and questions throughout the first lesson to help the educator guide students in creating visual models to relate real number sets.

The materials include educator guidance within each lesson that anchors learning around major mathematical concepts and instructs educators to highlight and connect patterns, features, and relationships through multiple representations. Across all lessons, the “Introduction,” “Guided Instruction,” and “Critical Thinking” sections engage students through visuals, mathematical symbols, models, vocabulary, and real-world applications. The sidebar in the Teacher Edition instructs educators to make connections between representations to deepen conceptual understanding as students progress through the lesson.

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

Each lesson in the Teacher Edition includes educator guidance for effective lesson delivery and facilitation. Lessons include whole-group discussion, small-group differentiation, and independent practice, among other approaches. For example, lesson 12 includes a “Learn Together” activity that engages the entire class by asking students to write an equation, create a table of values, draw a graph for a scenario, and discuss how the graph is not proportional. The “Differentiation” activity guides educators in asking striving students and emergent bilingual students to explain various linear relationships that are not proportional, using the provided sentence frames. Additionally, students can work independently through “Critical Thinking” activity questions to create a table and a graph from a linear equation.

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 “Instructional Formats and Use” section in the Teacher Edition outlines multitiered intervention methods and educator guidance for effective implementation across varying levels of student needs. The materials define structures for whole-group instruction, targeted small-group intervention, and intensive individual support. Guidance outlines when and how educators should use each intervention, based on students’ performance and assessment data. Additionally, the materials include recommendations for reteaching, intervention, progress monitoring, and enrichment to address diverse learning needs.

The lesson planner pages that are included before each lesson in the Teacher Edition provide educator guidance to support effective implementation of multitiered intervention methods. The wraparound for each lesson guides educators through multitiered intervention methods for different types of practice, such as “Guided Instruction” sections and independent “Practice” activity pages. Additionally, the “Learn Together,” “Differentiation,” and “Extension” activities in each lesson guide educators in multitiered intervention methods for whole-group, small-group, and individual structures.

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 “Instructional Formats and Use” section indicates that educators can use enrichment sessions, multistep “Extension” activities, real-world application problems, and/or “Building Stamina” chapter tests as challenge tasks. Embedded “Extension” activities support multiple forms of student engagement by challenging students to analyze, justify, and create mathematical ideas beyond core lesson expectations.

The Teacher Edition provides educator guidance for effective implementation, including required materials, activity directions, and facilitation prompts that support educators in extending learning and engaging students in deeper mathematical thinking. The “Extend Student Reasoning” section that is included before each lesson guides educators in extending students’ thinking by asking extension questions. For example, in lesson 3, the educator might ask, “Why does a positive exponent represent a large number and a negative exponent represent a small number in this context?” or “How is scientific notation useful when comparing real-world quantities of very different sizes?”

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

The “Monitoring Understanding and Feedback” and “Instructional Support for Student Needs” sections that are included before each lesson in the Teacher Edition provide prompts and guidance to help educators deliver timely feedback during lessons. For example, as educators monitor students’ thinking in lesson 2, they should “listen for common misconceptions such as using incorrect perfect squares, misplacing negative numbers, or comparing symbolic forms without first estimating their values.” Additionally, tiered support helps educators adjust instruction based on students’ understanding of comparing and ordering real numbers.

The sidebar in the Teacher Edition includes embedded prompts and guidance to help educators provide timely feedback throughout each lesson. Sidebar notes direct educators to monitor students’ understanding through questioning, discussion, and observation of student responses. This guidance helps educators elicit student reasoning, identify misconceptions, and provide immediate feedback to clarify understanding and adjust instruction as needed. For example, the sidebar for the “Exit Ticket” activity in lesson 1 includes embedded prompts so educators can review students’ work on describing whether a decimal is a rational or irrational number. The sidebar further guides reinforcement, follow-up questions, and next steps based on students’ responses.

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 “ELPS Language and Discourse Support” section that is included before each lesson in the Teacher Edition guides educators in facilitating mathematical discourse and supporting language development for emergent bilingual students. Additionally, this section includes guidance on providing and incorporating linguistic accommodations for all levels of language proficiency, including Preproduction, Beginning, Intermediate, Advanced, and Advanced High tiers. For example, Preproduction students receive visual cues and sentence frames, while Advanced High students receive open-ended questions that require detailed justification.

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 “Implementation Guidance for State-Approved Bilingual/ESL [English as a Second Language] Programs” section in the Teacher Edition outlines lesson-embedded ELPS supports. Lessons include implementation guidance to help educators effectively use the materials in ESL and dual-language programs. Both programs start with simplified speech and move toward more complex sentence structures and greater sophistication in academic mathematical language. For dual-language programs, students can access the content in over 120 languages and multiple dialects through the digital platform.

The “ELPS Language and Discourse Support” section that is included before each lesson provides ELPS language and discourse support to guide educators on mathematical discourse, the use of home language and cognates, oral-to-written responses, and other differentiated supports across all proficiency levels. This section provides ELPS-aligned support for educators who implement the materials within state-approved bilingual and ESL program models.

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 “English Language Proficiency Standards (ELPS) Support” section in the chapter 1 overview outlines supports that are embedded throughout the chapter. These supports are designed to make real number concepts accessible to emergent bilingual students. This section outlines visual representations, language frames, vocabulary reinforcements, and collaborative talk routines that help educators implement guided mathematical discourse to develop academic vocabulary and increase comprehension through oral and written discourse.

The “ELPS Language and Discourse Support” section that is included before each lesson in the Teacher Edition provides guidance to facilitate mathematical discourse, with a specific focus on sections such as “During Learn Together and Guided Instruction,” “Home Language and Cognates as a Bridge,” and “From Oral Reasoning to Written Justification.” This lesson’s front matter, in conjunction with activities and tips for emergent bilingual students in the educator wraparound, embeds guidance throughout each lesson to support EB students in developing academic vocabulary and increasing comprehension through oral and written discourse. The lesson also guides educators in building background knowledge and making crosslinguistic connections through oral 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.

In chapter 11, “Personal Finance,” students develop a connected understanding of personal finance. They engage in a progression of tasks that move beyond procedural calculations to analyzing and comparing simple and compound interest, evaluating borrowing options, determining the total cost of loans, developing college savings plans, and making informed financial decisions. Throughout the chapter, students interpret financial data, justify choices, compare alternatives, evaluate long-term financial outcomes, and apply mathematical reasoning in authentic personal finance contexts. Practice and assessment opportunities throughout the chapter, including “Guided Instruction” sections, “Extension” activities, and “Exit Ticket” assessments, require students to demonstrate their knowledge and skills to solve problems.

In chapter 4, lesson 11, “Solve Direct Variation Problems,” includes “Guided Instruction,” “Critical Thinking,” “Learn Together,” and “Practice” activities that give students opportunities throughout the lesson to connect the constant of variation with real-world scenarios. The various practice activities require students to demonstrate depth of understanding that is aligned with the TEKS. For example, question 2 in the “Critical Thinking” activity requires students to “explain how to find the length of a painting with a width of 135 inches.” In addition, the lesson 11 assessment and exit ticket provide students with further opportunities to connect the constant of variation to real-world applications. For example, the exit ticket assesses whether students can write a direct variation equation and find the distance between two cities on a map. Together, these practice opportunities and assessments require students to identify the constant of variation and write equations, demonstrating depth of understanding in solving direct variation problems.

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 “Differentiation,” “Critical Thinking,” and “Learn Together” activities in chapter 1, lesson 2, “Order Real Numbers,” provide students with questions and tasks that increase in rigor and complexity, leading to grade-level proficiency in ordering real numbers. For example, the “Differentiation” activities provide scaffolded support for estimating and ordering real numbers by listing perfect squares and using number lines. The “Critical Thinking” activity prompts students to approximate values and order rational and irrational numbers on a number line. The “Learn Together” activities prompt students to work more with organizing rational and irrational number cards from least to greatest. Questions and tasks in this lesson focus on grade-level proficiency and do not include further operations with real numbers such as simplifying radicals.

The “Critical Thinking” sidebar challenge questions and “Extension” activities in the Teacher Edition for lesson 2, “Order Real Numbers,” increase in rigor and complexity, leading to grade-level proficiency in comparing and ordering real numbers. For example, the first “Extension” activity asks students to create their own list of 20 real numbers, both rational and irrational. Then, students should “estimate the value of the numbers to the nearest tenth and order them from least to greatest.” The second “Extension” activity asks students to estimate the hypotenuse of a right triangle to the nearest tenth when given a right triangle. While extensions increase in rigor and complexity within the grade-level TEKS, they do not lead to above-level proficiency in the mathematics TEKS.

The “Above-Level Extension Bank” section in the Appendix in the Teacher Edition includes one “Extension” activity per lesson. This activity provides students with an opportunity to explore above-grade-level content. For example, the “Extension” activity for lesson 1 lets students explore numbers outside of the real number system (the complex number system). While this activity introduces students to Algebra 2 content, this exploration does not lead to above-grade-level proficiency in the mathematics TEKS.

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

The “Horizontal and vertical progression” chart that is included in the Teacher Edition demonstrates coherence horizontally across concepts within the grade level by connecting big ideas. Additionally, chapter overviews and lesson planners further detail horizontal alignment by connecting big ideas across the curriculum. For example, the overview for the “Horizontal/Vertical Progression Summary” section in chapter 4, “Proportional and Non-Proportional Relationships,” states, “Students first represent proportional relationships and identify the constant of proportionality as the same idea as slope and unit rate. They then solve direct variation problems using that proportional structure, extend the work to linear relationships with non-zero starting amounts, and finally classify relationships as proportional or non-proportional.” Additionally, the materials demonstrate coherence horizontally across concepts in chapter 3, “Slope and Y-Intercept,” by connecting the big ideas of proportional reasoning, similar triangles, slope, rate of change, and linear relationships throughout the chapter. Students progress from analyzing similar triangles and proportional relationships to determining slope from graphs, tables, and real-world situations. Then, they move to interpreting and applying the y-intercept in linear relationships. Throughout the chapter, students use multiple representations—including geometric models, tables, graphs, coordinate planes, and verbal descriptions—to analyze and represent mathematical relationships. These interconnected experiences help students recognize patterns and relationships among mathematical concepts and develop a cohesive understanding of linear relationships across the grade 8 mathematics TEKS.

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 “Horizontal and vertical progression” chart that is included in the Teacher Edition demonstrates coherence vertically across concepts and grade bands, including connections to grade 6, grade 7, Algebra 1, and Geometry, by linking big ideas. Chapter overviews and lesson planners further detail vertical alignment by connecting big ideas across the curriculum. For example, the “Learning Progression” sections in the lesson planners throughout the Teacher Edition show the progression from grade 6 or grade 7 to the Algebra or Geometry TEKS, demonstrating vertical alignment. Additionally, in chapter 11, “Personal Finance,” students build on their prior understanding of percentages, proportional reasoning, numerical operations, and financial literacy concepts that were developed in earlier grades. They extend that knowledge to more sophisticated personal finance applications. The chapter progresses from calculating and comparing simple and compound interest to evaluating loans and credit, analyzing investment growth, estimating college costs, and developing long-term savings plans. These experiences reinforce foundational concepts in percentages, rates, and financial decision-making while deepening students’ understanding of how mathematical reasoning applies to real-world financial situations. The materials also prepare students for future learning by introducing concepts related to exponential growth, financial modeling, and long-term financial planning.

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 “Lesson Flow and Instructional Routines” section that is included before each lesson demonstrates coherence across lessons by connecting students’ prior knowledge of concepts and procedures to those that will be learned at the current grade level. Routines are outlined to build on the previous lesson, activate prior knowledge, and integrate previously learned skills. For example, this section in chapter 1, lesson 2, “Order Real Numbers,” prompts educators to “recall how to locate and order rational numbers on a number line, including integers, fractions, and decimals.” Additionally, this section states that it “supports future reasoning with equations, formulas, and real-world situations that require estimating and comparing numerical values,” thereby connecting students’ prior knowledge to future grade-level work. However, the materials do not connect students’ prior knowledge of procedures to the mathematical concepts that will be learned in future grade levels.

Chapter 3, “Slope and Y-Intercept,” demonstrates coherence across lessons and activities by intentionally connecting students’ prior understanding of proportional relationships, rates, unit rates, and graphing concepts to current grade-level concepts involving slope and y-intercept. The chapter builds upon previously learned concepts as students analyze similar triangles, interpret proportional relationships, determine slope from tables and graphs, and connect rate of change to linear relationships. For example, the “Activate Prior Knowledge” section in the Teacher Edition before lesson 7, “Understand Slope Using Similar Triangles,” builds a bridge to understanding slope using similar triangles. Students start with a hands-on activity to measure the distance between start and finish lines. They walk from the start line to the finish line, count their steps, and calculate unit rates. Then, students represent unit rates on a graph to make the connection to slope. Throughout the chapter, lessons progressively increase in complexity, helping students connect previously learned concepts and procedures to new learning while developing mathematical reasoning and problem-solving skills that are necessary for success in the current grade level.

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

The “Cumulative Skills Review” section that follows each chapter provides spaced retrieval opportunities with previously learned skills and concepts across learning pathways. For example, the “Cumulative Skills Review: Chapter 5” section provides three problems in which students utilize skills from chapters 1, 2, and 4. The Teacher Edition wraparound provides prompts so educators can identify the skill and ask conceptual questions while students are working. For example, the question 2 prompt states, “This is a Chapter 4 skill; how did you find the constant of variation there?” Additionally, “Fluency Lab” activities provide spaced retrieval opportunities with previously learned skills for six of the lessons. These activities require students to revisit and apply previously taught mathematical concepts to reinforce current learning.

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

The “Cumulative Skills Review” section that follows each chapter provides interleaved practice opportunities with previously learned skills and concepts across learning pathways. For example, the “Cumulative Skills Review: Chapter 4” section provides three problems in which students utilize skills from chapters 1, 2, and 3. For this review, students use a chapter 1 skill for question 1, use a chapter 3 skill for question 2, and combine skills from chapters 2 and 4 for question 3. Skills and concepts are presented in varying orders with each chapter, so students must distinguish between multiple concepts within the review. The Teacher Edition wraparound provides a look-for and a prompt for each question so educators can monitor students’ progress with previously learned skills and concepts.

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

Lesson 13, “Distinguish Between Proportional and Non-Proportional Relationships,” provides students with an opportunity to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations to identify proportional and nonproportional relationships. For example, as students use various models to determine if five ride tickets for $20 is proportional in the “Guided Instruction” section, the educator asks, “How does finding the unit rate help you decide if the relationship is proportional?” Additionally, as students use various models to determine if a plumber’s fee of $100 or $40 per hour is proportional, the educator asks, “How do you know which cost, $100 or $40 per hour, is the constant and which is a factor in the variable term?” Additionally, the “Critical Thinking” activity prompts students to analyze a table that shows the relationship between the number of bulbs planted and the number of flowers to determine whether the relationship is proportional. Then, students represent the situation with an equation and explain how the equation verifies their conclusion. In this activity, students also must interpret the strategy an office uses to recycle paper, write an equation, and explain whether the relationship is proportional or non-proportional.

The overview section for chapter 11, “Personal Finance,” outlines opportunities for students to interpret, analyze, and evaluate models and representations for mathematical concepts and complex, real-world situations. In the “Purpose of the Chapter” section, students develop an understanding of personal finance by examining real-world contexts and making informed financial decisions. In lesson 37, “Calculate Simple Interest and Compound Interest,” students interpret, analyze, and evaluate mathematical concepts and real-world situations throughout the lesson. The “Introduction” and “Understand the TEKS” sections teach students to interpret financial situations and compare how simple and compound interest generate different results over time. Problems in the “Guided Instruction” section ask students to evaluate investment scenarios, identify relevant variables, analyze account growth, and compare simple-interest and compound-interest outcomes. Additionally, the “Critical Thinking,” “Learn Together,” and “Extension” activities require students to evaluate real-world scenarios to justify conclusions about the mathematical relationships they show. Together, these opportunities require students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations to compare investment scenarios and understand authentic personal finance contexts.

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

The questions and tasks in lesson 4, “Model and Solve One-Variable Equations,” provide opportunities for students to create concrete models and representations to solve one-variable equations. For example, the “Learn Together: Model and Solve Equations” activity gives students an opportunity to create bar models for a set of equation cards. Additionally, the “Extension: Multiple Methods Challenge” activity gives students an opportunity to solve equations using two different methods—algebra tiles and bar models. Then, students are asked to compare the two methods for solving an equation.

The “Activate Prior Knowledge” activity before lesson 29, “Apply the Pythagorean Theorem and Its Converse,” prompts students to use straws of various lengths to build triangles and use the Pythagorean theorem to determine if the triangles are right triangles. Additionally, the “Differentiation: Build Your Own Squares Model” activity prompts students to draw a right triangle with integer side lengths and construct a square on each side of the triangle. Students color the squares, calculate and label each area, and verify that the side lengths satisfy the Pythagorean theorem. Questions and tasks in this lesson provide multiple opportunities for students to create concrete models and representations to apply the Pythagorean theorem.

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

The “Critical Thinking” questions in lesson 11, “Solve Direct Variation Problems,” provide students with opportunities to apply conceptual understanding to finding the missing value when y varies directly with x. Students explain their thinking and use their knowledge of scale factors to design a playground as a scale drawing of an actual area. Additionally, in the “Learn Together: Direct Variation Application” activity, students use a direct variation scenario to determine the constant of variation, write an equation, and graph the relationship.

In lesson 37, “Calculate Simple Interest and Compound Interest,” students apply conceptual understanding of simple and compound interest to new situations and contexts. In the “Guided Instruction” section, students apply formulas to determine the interest that is earned, ending balances, and investment growth while interpreting the meaning of their calculations within realistic financial situations. Students move beyond procedural calculations by explaining why compound interest produces different results than simple interest and how changes in principal, rate, or time affect earnings. In the “Critical Thinking” activity, students compare investment options, analyze the effects of changing rates and time periods, and explain why compound interest often generates greater returns over long periods. Additionally, the “Learn Together: Interest Showdown” activity requires students to compare account growth across multiple years and use evidence from their calculations to explain differences between simple and compound interest. Together, these opportunities require students to transfer and apply their conceptual understanding of simple and compound interest to new mathematical situations and real-world contexts.

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

“Fluency Lab” activities are designed to build students’ automaticity and fluency in numbers and operations. For example, “Fluency Lab 1A” prompts students to solve linear equations and compare strategies to determine which is most efficient for each problem.

In lesson 21, “Perform Translations on the Coordinate Plane,” students build automaticity and fluency through repeated practice in determining and applying translation rules. In the “Activate Prior Knowledge” activity in the Teacher Edition, students build foundational fluency by plotting points in all four quadrants and determining new coordinate locations after specified movements. The “Guided Instruction” section provides repeated opportunities for students to apply translation rules to multiple vertices, identify coordinate patterns, and write algebraic representations of translations. The “Differentiation” activities provide repeated practice in applying translation rules and graphing images on coordinate planes. Additionally, “Practice” activity problems require students to efficiently determine image coordinates, identify translation rules, and verify transformations using multiple examples. The “Exit Ticket” activity further reinforces fluency by requiring students to apply horizontal and vertical shifts and represent the movement using algebraic notation. Together, these experiences build the automaticity and fluency that are needed to complete grade-level tasks involving transformational geometry tasks.

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

Opportunities are provided throughout the lessons so students can practice applying efficient, flexible, and accurate mathematical procedures. For example, the “Critical Thinking” activity in lesson 4, “Model and Solve One-Variable Equations,” prompts students to write an equation to model and solve for the number of candles that make the total cost the same for two different stores. The challenge question in the sidebar of the Teacher Edition prompts students to draw a balance scale to model the equation and explain the model they prefer. “Fluency Lab 2A” is paired with this lesson. Students solve linear equations and evaluate which strategy helped in solving the problems most efficiently. They also conduct an error analysis and reflection on efficiency to further develop their accuracy and efficiency in solving linear equations.

In lesson 37, “Calculate Simple Interest and Compound Interest,” students practice efficient, flexible, and accurate mathematical procedures to calculate the amount of interest that was earned, determine ending balances, and compare investment options. In the “Guided Instruction” section, students identify the appropriate formula, substitute values accurately, and solve for unknown quantities using both simple-interest and compound-interest models. Students apply procedures flexibly by working with variables such as principal, rate, time, interest earned, and ending balance. “Differentiation” activities support students in selecting and applying appropriate procedures while recognizing the role of each variable in the formulas. Additionally, the “Learn Together: Interest Showdown” activity requires students to apply both procedures to the same financial scenario and compare their results. Activities and assessments provide repeated opportunities to perform calculations accurately, evaluate results, and apply procedures across a range of financial situations. Together, these experiences support the development and application of efficient, flexible, and accurate mathematical procedures throughout the lesson.

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.

Opportunities are provided throughout the lessons to evaluate representations, models, strategies, and solutions for efficiency and accuracy. For example, the “Critical Thinking” activity in lesson 4, “Model and Solve One-Variable Equations,” prompts students to explain using different models to solve equations. The follow-up challenge question in the sidebar of the Teacher Edition prompts students to “solve the equation for x using operations and compare the solution to the one found using the model.” The “Learn Together” activity that follows prompts students to solve equations using bar models and check their solutions. “Fluency Lab 2A: Solve Linear Equations” is paired with this lesson. In “Fluency Lab activities,” students have the opportunity to choose strategies and evaluate solutions for efficiency and accuracy. While students have flexibility in the strategies they use, “Fluency Lab” activities are provided for only six of the 41 lessons.

In lesson 21, “Perform Translations on the Coordinate Plane,” students evaluate representations, models, strategies, and solutions throughout the lesson. In the “Guided Instruction” section, students compare pre-images and images to determine whether a translation was performed correctly and evaluate how coordinate changes correspond to a translation rule. Prompts in the “Monitoring Student Thinking” section in the Teacher Edition ask students to explain how they know a figure was translated, evaluate whether coordinate changes are consistent across all vertices, and justify whether a proposed solution is reasonable. Additionally, the “Differentiation” activities require students to compare strategies for identifying translation rules and evaluate the accuracy of graphical and algebraic representations. The “Learn Together: Graph the Move” activity requires students to analyze and discuss their classmates’ translations and determine whether the graphical model, coordinate changes, and translation rule are consistent. Together, these opportunities require students to analyze and evaluate mathematical representations, models, strategies, and solutions for efficiency and accuracy throughout the lesson. While students practice flexibility in modeling and solving problems, there is no consistent evaluation of that flexibility across lessons.

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

Each “Fluency Lab” activity provides guidance to help students select the most efficient approaches to operations with numbers. For example, “Fluency Lab 5A” prompts students to consider more efficient strategies by asking, “When is substitution an efficient way to solve a system?” and “Why is it important to check your solution in both equations?” Students actively reflect on when to use a substitution or mental math as a more helpful and efficient tool.

In lesson 37, “Calculate Simple Interest and Compound Interest,” students receive explicit guidance for selecting efficient approaches when solving personal finance problems. In the “Guided Instruction” section, students learn to identify the known variables in a problem, select the appropriate simple-interest or compound-interest formula, and substitute values systematically to determine the amount of interest that was earned or ending balances. The lesson emphasizes using formulas as an efficient alternative to repeated calculations and demonstrates how organized substitution supports accuracy and efficiency. The “Differentiation: Equations for Calculating Simple Interest and Compound Interest” activity helps students recognize which formula is appropriate for a given situation and how each variable contributes to the solution process. Additionally, the “Learn Together: Interest Showdown” activity requires students to compare methods and determine the most effective approach for analyzing investment growth. Together, these supports help students evaluate and select increasingly efficient approaches for solving problems involving simple and compound interest.

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

The “Purpose of the Chapter” sections in the overview before each chapter in the Teacher Edition outline both conceptual and procedural elements of the TEKS that are embedded throughout the lessons. For example, this section in chapter 1, “Real Numbers,” states, “Students develop a connected understanding of the real number system by classifying real numbers, describing relationships among sets and subsets, approximating irrational numbers, ordering real numbers on a number line, and converting between standard notation and scientific notation.” Additionally, this section indicates that students “use Venn diagrams, number lines, decimal place-value reasoning, benchmark values, and powers of 10 to connect structure, magnitude, and representations within the real number system.”

In chapter 6, “Similar Figures and Dilations,” the overview includes statements for both conceptual and procedural elements of the TEKS that are included in the lessons for this chapter. The “Purpose of the Chapter” section states, “Students develop a connected understanding of similarity and dilation by generalizing proportional relationships between similar figures, comparing figures and their dilations on the coordinate plane, representing dilation rules algebraically, and modeling the effects of dilation on linear and area measurements.” Additionally, this section indicates that the lessons “move from proportional reasoning with similar figures to coordinate dilations, then to algebraic rules and measurement effects of dilations.”

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 the overview for chapter 7, “Transformations,” in the Teacher Edition, the “ELPS Support” section indicates that students should engage with a variety of representations, including coordinate grids, transformation diagrams, geometric figures, ordered pairs, and algebraic rules. These supports provide opportunities for students to move among visual, graphical, and symbolic representations as they develop an understanding of geometric transformations.

Students use concrete, pictorial, and abstract models throughout lesson 21, “Perform Translations on the Coordinate Plane.” In the “Activate Prior Knowledge” activity, students use coordinate grids and plotted points to model movement on the coordinate plane. In the “Guided Instruction” section, students use pictorial representations such as coordinate-plane diagrams, pre-images, and images to visualize translations and analyze how figures move. Then, students connect these visual models to abstract representations by writing and applying translation rules using algebraic notation. Additionally, in the “Differentiation” activities, students graph figures, perform translations, represent coordinate changes numerically, and write algebraic rules that describe the transformation. Together, these opportunities require students to use concrete, pictorial, and abstract representations in alignment with the grade 8 TEKS.

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

The materials include supports throughout the lessons for connecting, creating, defining, and explaining representational models to abstract concepts. For example, the “Critical Thinking” activity in lesson 29, “Apply the Pythagorean Theorem and its Converse,” prompts students to draw a model that shows the sum of the areas of Square A and Square B equals Square C. Additionally, the challenge question has “students explain how they can use Pythagorean triple 3, 4, 5 to verify their answer.” Before the lesson, the Teacher Edition includes a hands-on task with straws of various lengths to activate students’ prior knowledge of building triangles. Students also discuss how to use the Pythagorean theorem to determine if a triangle is a right triangle. While the “Activating Prior Knowledge” activities help students activate prior knowledge before each lesson, they do not support students in connecting, creating, defining, and/or explaining concrete models to abstract concepts, as required by the TEKS.

The “Guided Instruction” section for each lesson is designed so students can work with educators to connect representational models to abstract concepts. For example, in lesson 21, “Perform Translations on the Coordinate Plane,” students explain how translation rules affect each coordinate of a figure and connect graphical representations to symbolic rules of the form (x,y)→(x + a, y + b). The “Critical Thinking,” “Practice,” “Assessment,” and “Exit Ticket” activities in the student pages for each lesson provide further support for students to meaningfully connect, create, define, and explain representational models to abstract concepts. For example, the “Critical Thinking” activity in lesson 21 prompts students to draw and translate a parallelogram on a coordinate grid. In addition to the student pages, the Teacher Edition wraparound provides activities that include support in connecting concepts with representational models. While the materials include concrete activities that are designed specifically for struggling students, the tasks in the Teacher Edition wraparound are not structured to connect concepts for students using a concrete-pictorial-abstract progression.

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

The “ELPS Language and Discourse Support” section that is included before each lesson in the Teacher Edition provides guidance to help educators facilitate mathematical discourse and support language development. For example, this section in lesson 4, “Model and Solve One-Variable Equations,” prompts students to explain how to model and solve one-variable equations with variables on both sides by “prompting them to identify terms, combine like terms, isolate the variable, and describe how algebra tiles or a bar model show that the equation stays balanced.” As students understand the terms and operations on both sides, educators encourage them to “discuss how they solved the equation orally first, then revise explanations in writing using the lesson’s language.” Additionally, this section provides sentence stems and questions to guide educators in helping students develop academic mathematical language. For example, educators prompt students to justify by asking, “Why do you simplify expressions on both sides first?” When explaining, educators are guided to connect each step to the model and the meaning of the terms in the real-world situation.

In lesson 22, “Perform Reflections on the Coordinate Plane,” students develop academic mathematical language through multiple language-support strategies. The “ELPS Language and Discourse Support” section that is included before the lesson encourages students to explain how reflections affect coordinates, identify the line of reflection, describe which coordinates remain the same or change, and justify why reflected figures remain congruent to the original figure. The “Differentiated Language Support” section within the table provides scaffolded sentence stems and progressively more sophisticated language expectations that move students from identifying reflections to explaining reflection rules using precise mathematical vocabulary. The “Understand the TEKS” section in the lesson explains that reflections create mirror images across the x- and y-axes and preserve congruence. The “Guided Instruction” section uses coordinate graphs, reflection rules, labeled pre-images and images, and worked examples to help students describe reflections using appropriate mathematical vocabulary. Additionally, “Differentiation” activities in the Teacher Edition wraparound require students to use coordinate grids, visual models, and mathematical language to explain and justify transformations.

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 sidebars in the Teacher Edition include guidance for educators to scaffold, support, and extend students’ use of academic mathematical vocabulary in context. For example, the “Emergent Bilingual Learners” tip box in the “Guided Instruction” section of lesson 4, “Model and Solve One-Variable Equations,” provides sentence frames for students who demonstrate lower levels of language proficiency. This resource helps students explain how they determine which steps to take when solving an equation. For students who demonstrate higher levels of language proficiency, the educator guides them to “explain how a model helps them understand the process of solving.” The “Striving Learners/Emergent Bilingual Learners” tip box for the lesson assessment also provides sentence frames and guidance for educators to help students justify their answers using academic mathematical vocabulary. Students who demonstrate lower levels of language proficiency use sentence frames such as “You add/subtract _____ because _____” to explain sign and operation choice. Students who demonstrate higher levels of language proficiency justify their steps “using operations and relationships.”

In lesson 22, “Perform Reflections on the Coordinate Plane,” embedded educator guidance supports students in using academic mathematical vocabulary throughout instruction. The “ELPS Language and Discourse Support” section in the Teacher Edition explicitly directs educators to develop mathematical discourse by prompting students to explain how a reflection moves a figure on the coordinate plane. Students also must identify the line of reflection, determine which coordinates remain the same or become opposites, and justify why reflected figures remain congruent to the pre-image. The “Home Language and Cognates” section encourages educators to connect familiar language with lesson-specific vocabulary. The “From Oral Reasoning to Written Justification” section helps students transition from verbal explanations to written justifications, using precise mathematical terminology related to reflections and coordinate geometry. This progression from oral to written justification demonstrates how the materials extend students’ vocabulary beyond initial scaffolding. These embedded supports scaffold, reinforce, and extend students’ use of academic mathematical vocabulary during communication with both their peers and educators.

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

The “Understand the TEKS” section in the student pages of lesson 13, “Distinguish Between Proportional and Non-Proportional Relationships,” defines the vocabulary terms proportional, constant of proportionality, unit rate, and nonproportional. This section includes examples of these terms plus guidance on how they are related. For example, the text states, “You can distinguish between proportional and nonproportional relationships using a verbal description, an equation, a table, or a graph that represents the relationship.” A provided table gives examples of different representational models for both proportional and nonproportional relationships. Additionally, the Teacher Edition sidebar includes guiding questions to support students in developing academic language. One question asks, “How do the two graphs show the difference between a proportional and nonproportional linear relationship?” Following the “Guided Instruction” section, students are given opportunities throughout the lesson to use appropriate mathematical language and various representations to explain whether a relationship is proportional or nonproportional. For example, in the “Learn Together: Compare and Contrast” activity, students work in pairs to analyze two sets of real-world data—one proportional and one nonproportional. They are expected to “graph each relationship, write an equation, and discuss the similarities and differences between the two relationships.” In the “Extension: Rewrite the Relationship” activity, students write a real-world description with an initial value, then revise it to remove the initial value. Students are expected to “explain how the change in the initial value affects the relationship, focusing on the role of the y-intercept and whether the ratio y/x remains constant.”

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

The “Activate Prior Knowledge” section that is included before each lesson in the Teacher Edition guides educators on including partner talk and “Think-Pair-Share” opportunities so students can hear and use math language with their peers. Lessons in the Teacher Edition wraparound include opportunities for educators to facilitate mathematical conversations through “Differentiation,” “Learn Together,” and “Extension” activities. For example, in lesson 4, “Model and Solve One-Variable Equations,” students form a circle and work together to solve equations with variables on both sides, either mentally or on paper. The educator facilitates the process by asking “one student to describe the first step, another student to state the next step, and continue around the circle until the equation is solved and checked.”

Embedded guidance in lesson 9, “Find Slope and y-Intercept from Tables and Graphs,” supports mathematical conversations through structured partner and whole-class discussions. In the “Activate Prior Knowledge” section that is included before the lesson in the Teacher Edition, students create a table starting with two points and discuss how additional points can be found using the rate of change. The “ELPS Language and Discourse Support” section directs educators to prompt students to explain how they identified the slope and y-intercept, describe what each represents within the context of a real-world situation, compare multiple representations of a linear relationship, and justify their reasoning using precise mathematical vocabulary. The “Differentiation,” “Learn Together,” and “Critical Thinking” activities require students to discuss mathematical ideas, compare interpretations, and explain their reasoning with their peers using academic mathematical language. Across both lesson 4 and lesson 9, the materials consistently support students in hearing and using math language with their peers, but do not guide them in refining that 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 “Monitoring Understanding and Feedback” section that is included before each lesson in the Teacher Edition guides educators in anticipating students’ responses. For example, this section in lesson 5, “Write One-Variable Equations and Inequalities,” states, “Listen for how students define the variable, describe the quantities being compared, and justify whether the relationship should be represented with an equation or an inequality.” This section also provides questions for when students demonstrate understanding, such as “What changes if one quantity or rate changes?” The “Bridge: Getting Ready for Hundred” activity, also included before the lesson, provides an expected answer to a “Think-Pair-Share” prompt in which students are tasked with writing a one-variable equation with variables on both sides. Additionally, educators are provided a response to each guiding question in the Teacher Edition sidebar. Student inset pages for “Critical Thinking” and “Exit Ticket” activities provide one exemplar response for each question.

The “Monitoring Understanding and Feedback” section guides educators in supporting and redirecting inaccurate student responses. This section in lesson 5 states, “Watch for misconceptions such as reversing the inequality symbol, combining unlike pieces of information into one expression, or writing an equation when the situation calls for an inequality.” This section also provides questions for when students make errors, such as “What does the variable represent in this situation?” Additionally, the Teacher Edition sidebar for the “Practice” activity provides a common error for each practice question plus a hint that educators can use to help guide struggling students.

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

The TEKS process standards are appropriately integrated into the materials. The lesson planner that is included before each lesson in the Teacher Edition describes how the lesson’s process standards are incorporated into the learning objectives. The sidebar for the “Guided Instruction” section includes these same process standard numbers for the lesson. For example, in lesson 2, “Order Real Numbers,” the sidebar indicates that “[TEKS] 8.1E: Organize and communicate ideas” and “[TEKS] 8.1G: Justify ideas using precise mathematical language” should guide students through each problem. Educators guide students in organizing the second problem to approximate real numbers so they can be compared in the same form. Additionally, the “Building Stamina” chapter assessments and “Practice” assessment activities indicate the process standard that is paired with the grade-level TEKS for each question in the answer key.

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

The lesson planner that is included before each lesson in the Teacher Edition describes how the TEKS process standards are incorporated into the lesson’s learning objectives. For example, lesson 5, “Write One-Variable Equations and Inequalities,” indicates that TEKS 8.1B and TEKS 8.1E represent the mathematical processes that are included in this lesson. This section states that students will “use verbal models to write equations or inequalities” and “use verbal representations to organize and communicate mathematical ideas.” While this section describes how the process standards are incorporated into the lesson, it does not explain how they are connected throughout the learning pathways.

The “Guided Instruction” section sidebar in the Teacher Edition includes the process standard numbers for the lesson. For example, this section in lesson 16, “Identify Functions,” indicates that “[TEKS] 8.1C: Select tools and strategies to solve problems” and “[TEKS[ 8.1D: Communicate reasoning with multiple representations” should be incorporated to guide students through each problem. The “Learn Together: Function or Not?” activity in lesson 16 prompts students to sort cards that show various relations in different forms to determine whether each relation is a function. Then, students explain their sorting criteria and “identify which representation makes it easiest to determine if a relation is a function.” While this activity requires students to communicate their reasoning with multiple representations, there is no description of how TEKs 8.1D is connected to this activity or throughout the learning pathways.

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

The “Lesson Correlation to the Grade 8 TEKS” section in the Teacher Edition provides an overview of where process standards are incorporated into the lessons. Each TEKS process standard is listed in a table with the corresponding lessons. Each lesson planner includes a section that identifies the process standards that are incorporated in the lesson. For example, lesson 2, “Order Real Numbers,” includes mathematical processes for TEKS 8.1E and TEKS 8.1G. These same process standards are indicated in the sidebar for the “Guided Instruction” section to “guide students through each problem using mathematical processes.”

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

Lessons provide opportunities for students to think mathematically, persevere through problem solving, and make sense of mathematics. In lesson 4, “Model and Solve One-Variable Equations,” sidebar questions for the “Understand the TEKS” and “Guided Instruction” sections in the Teacher Edition help students think about and make sense of mathematics. For example, the educator asks questions such as “What does it mean to model an equation, and how can a model help you understand the solution?” and “Why is it important to combine like terms on the left side of the equal sign before you perform operations on both sides?” Additionally, the “Critical Thinking” activity prompts students to use models and explain how to solve equations. Challenge questions for this activity challenge students to persevere and extend their thinking for each problem. For example, one challenge question in lesson 16 asks students to “solve the equation for x using operations and compare the solution to the one found using the model.” At the end of the lesson, the “Exit Ticket” activity provides an opportunity for students to independently draw a bar model and solve a one-variable equation with variables on both sides.

In lesson 22, “Perform Reflections on the Coordinate Plane,” students engage in meaningful problem-solving that promotes perseverance and mathematical reasoning. In the “Activate Prior Knowledge” section in the Teacher Edition, students analyze coordinate patterns and explore how reflections affect ordered pairs before formalizing reflection rules. The “Understand the TEKS” and “Guided Instruction” sections require students to determine the images of figures reflected across the x- and y-axes, identify lines of reflection, analyze changes in coordinates, and justify why reflections preserve congruence. Rather than simply applying a memorized rule, students must interpret coordinate relationships, recognize patterns, and explain why reflection rules produce the resulting image. Additionally, the “Monitoring Understanding and Feedback” section in the Teacher Edition encourages educators to ask probing questions that help students reconsider misconceptions, justify their reasoning, and persevere when solving unfamiliar reflection problems. “Differentiation” activities engage students in analyzing reflections through multiple representations and geometric contexts. The “Critical Thinking,” “Practice,” “Assessment,” and “Exit Ticket” activities require students to analyze geometric situations, justify conclusions, and verify the reasonableness of their solutions.

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 solve problems and complete tasks. In lesson 4, “Model and Solve One-Variable Equations,” students are encouraged to solve one-variable equations with various models and equations. For example, the “Critical Thinking” activity and challenge questions prompt students to explain multiple ways to solve equations with variables on both sides of the equation to demonstrate their understanding. One challenge question asks students to follow up on a problem in which they use a bar model to solve an equation by drawing a balance scale, and to explain which model they prefer. Additionally, the “Differentiation” activities for lesson 4 support students in understanding how to solve equations using algebra tiles, color-coded variable and constant terms, and representational models.

In lesson 9, “Find Slope and y-Intercept from Tables and Graphs,” students are encouraged to recognize and justify multiple approaches for analyzing linear relationships. In the “Guided Instruction” section, students determine the slope and y-intercept from tables, graphs, and contextual situations and explain why each representation communicates the same linear relationship. Educator questions in the Teacher Edition sidebar prompt students to justify their choice of strategy, compare methods for identifying slope and y-intercept, and explain how different representations lead to equivalent conclusions. Additionally, the “Differentiation” activities require students to analyze and compare linear relationships using different representations while discussing their reasoning with their peers. “Critical Thinking” tasks ask students to justify their conclusions and defend their reasoning using mathematical evidence. The “Practice,” “Assessment,” and “Exit Ticket” activities reinforce flexible thinking by allowing students to analyze, interpret, and justify slope and y-intercept using multiple representations.

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 “Critical Thinking” activity in lesson 7, “Understand Slope Using Similar Triangles,” involves explaining how to use similar triangles to determine whether slopes are the same or whether lines are parallel. The “Learn Together” activities in this lesson involve verifying when triangles are similar and how this relates to slopes being the same. Additionally, “Extension” activities prompt students to explore how using different points on the same right triangle incline can be used to find the same slope. In the second “Extension” activity, students are expected to “write a reflection explaining why having a constant slope is important in the real-world context shown in the photo.”

In lesson 21, “Perform Translations on the Coordinate Plane,” students make sense of mathematics by performing, analyzing, and discussing translations throughout the instructional sequence. In the “Activate Prior Knowledge” section in the Teacher Edition, students examine coordinate patterns and discuss how translations affect ordered pairs before formalizing translation rules. The “Understand the TEKS” and “Guided Instruction” sections require students to translate figures in the coordinate plane, compare pre-images and images, explain how coordinates change, and justify why translations preserve congruence. Additionally, the “Differentiation” activities require students to create representations, record mathematical reasoning, compare approaches, and communicate their thinking. “Critical Thinking” tasks prompt students to analyze geometric situations, justify conclusions, and explain how to find the translation rule. The “Practice,” “Assessment,” and “Exit Ticket activities”require students to solve problems, write mathematical explanations, and discuss solutions with their peers and educators.

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 “ELPS Language and Discourse Support” section that is included before each lesson in the Teacher Edition helps educators guide students to share and reflect on their problem-solving approaches. For example, in lesson 4, “Model and Solve One-Variable Equations,” students are expected to explain how to model and solve one-variable equations with variables on both sides of the equal sign. Educators prompt them to “identify terms, combine like terms, isolate the variable, and describe how algebra tiles or a bar model show that the equation stays balanced.” Educators should also prompt students to present an argument with multiple entry points by explaining “which terms are variable terms or constant terms, what operation they used on both sides of the equal sign, and how the model matches the equation before writing the final answer.” Prompts for justification include, “Why do you simplify the expressions on both sides first?” and “How does the model show that the equation stays balanced?” Additionally, “How Am I Doing?” boxes in both the student pages and the sidebar of the Teacher Edition guide educators and students to reflect on the lesson. The educator is instructed to “circulate and have them explain how they isolate the variable.”

In lesson 11, “Solve Direct Variation Problems,” educators are provided with embedded guidance to facilitate student explanations, arguments, justifications, and multiple points of entry during problem solving. In the “Guided Instruction” section, prompts in the Teacher Edition sidebar encourage students to explain how they determined x and y variables to match the problem situation, justify how those values should be used to write a linear equation, and compare multiple representations to find the constant of variation. The “Monitoring Understanding and Feedback” section that is included before the lesson provides questioning strategies that prompt students to defend their reasoning, reflect on the appropriateness of their solution methods, and explain why their conclusions are mathematically valid. Students are encouraged to approach the lesson concepts using multiple entry points, including models, equations, ratios, proportional relationships, rate of change, and constant of variation. The “From Oral Reasoning to Written Justification” section further guides educators in helping students transition from verbal explanations to written mathematical justifications. Additionally, the “Learn Together” activities require students to collaborate with their peers, find the constant of variation, write real-world scenarios to match a constant of variation, and explain how the constant of variation controls the relationship. “Critical Thinking” tasks require students to defend their reasoning and explain how ratios, slopes, and scale factors show the same mathematical relationship. The “Practice,” “Assessment,” and “Exit Ticket” activities provide opportunities for students to explain, justify, and reflect on their problem-solving approaches.

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

The “Monitoring Understanding and Feedback” section that is included before each lesson in the Teacher Edition provides prompts and guidance to support educators in providing explanatory feedback based on students’ responses and anticipated misconceptions. For example, this section in lesson 13, “Distinguish Between Proportional and Non-Proportional Relationships,” guides educators to listen to students’ explanations and “prompt them to explain how the starting value, equation structure, table ratios, and graph location all support the same conclusion.” Additionally, this section provides questions based on whether students make errors or demonstrate understanding. For errors, educators can ask questions such as “What is the value of b?,” “Does the graph pass through (0,0)?,” and/or “Is the ratio y/x the same in every row?” To extend student thinking, educators can ask, “How can you use the equation, table, and graph to prove that one plan is proportional and the other is nonproportional?” and “How do the rate of change and the starting value help you decide whether a relationship is proportional?”

In lesson 33, “Construct and Interpret Scatterplots,” embedded educator guidance supports explanatory feedback through the “Monitoring Understanding and Feedback” section in the Teacher Edition. Educators are prompted to listen to students’ explanations as they write ordered pairs, plot bivariate data on a scatterplot, and describe the relationship between variables. The materials identify misconceptions, such as mixing up x- and y-values or confusing positive and negative association. Educators are instructed to ask probing questions that encourage students to explain their reasoning, reconsider their strategies, and justify their solutions rather than simply correcting errors. Additionally, the “Instructional Support for Student Needs” section provides tier 1, tier 2, and tier 3 guidance on addressing errors with assigning x- and y-values and identifying positive versus negative association. The “Differentiated Language Support” section provides sentence stems, guided questions, and language scaffolds to help educators reinforce correct mathematical reasoning and address misunderstandings. Lesson activities provide opportunities for educators to monitor responses, identify misunderstandings, and guide students toward accurate reasoning through questioning and discussion.