Measuring Up to the TEKS Mathematics 2nd edition, Grade 6

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 6 materials include an Alignment Guide that outlines the TEKS, the ELPS, and the concepts that are covered. Educators can use the “Lesson correlation to the grade 6 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 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.

Additionally, 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 guide educators in supporting all students. The “Critical Thinking” section 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 6 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 pages direct educators to practice tests (diagnostic assessments) and student tracking charts in the Appendix that, when paired with the tables in the front matter, 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 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. Lesson planners show how each lesson builds on prior learning and connects to future concepts, explain how students can engage with the lesson, and provide prompts to assess understanding. The “Instructional Planning” section provides further guidance on using chapter overviews and lesson planners to plan lessons effectively, ensuring readiness and maximized instructional impact.

Chapter overviews provide clear protocols for internalization within each chapter. Educators preview key standards, objectives, vocabulary, and assessments to prepare for instruction. They also 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 in the grade 6 front matter includes 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 and Assessment” section provides guidance for working with striving learners (SLs) and emergent bilingual learners (EBLs).

Each lesson in the grade 6 Teacher Edition includes a lesson planner that clearly outlines learning objectives that are aligned to the TEKS and the ELPS. Also included are 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 these family letters. Both English and Spanish versions are included in the Student Edition to support home-to-school communication and family engagement.

Chapter 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. It 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 for 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 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. This section also describes the instructional purpose of each assessment type within the lesson 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—including administration and 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 in the front matter of each chapter of the Teacher Edition guides educators to ensure the 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 assessments. Summative assessments, including 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 time frames 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 the 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 included 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 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 assessments. The Practice assessment for each lesson clearly indicates the 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 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 the DOK levels. For example, the lesson 1 assessment includes DOK 1-, 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.

“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 platform provides detailed scoring reports for each student.

The Practice assessment and lesson assessment in each lesson include scoring information and guidance for interpreting students’ performance in the Teacher Edition. The sidebar for the Practice assessment includes common errors and hints for educators to interpret students’ 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.

In the Teacher Edition, exit tickets provided at the end of each lesson include guidance on interpreting student performance on the task and on using patterns in student responses, to guide instruction in the following lesson. For example, the lesson 1 exit ticket suggests, “If many students confuse where negative numbers or decimals belong in the diagram, begin the next lesson with a brief whole-group review using number lines and set diagrams.”

The “Instructional Formats and Use” section details how educators 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. This includes educator-facing progress-monitoring tools through the “Measuring Up Live” Insight platform. The “Teacher Tools for Monitoring Progress” section provides an analysis of assessment items and proficiency reports by standard. Educators use these reports to monitor students’ performance by the TEKS standards; by individual student, small group, or whole class; and by question type, item difficulty, and DOK level.

The “Critical Thinking” section in each lesson includes a “How Am I Doing?” section for students 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.

In the Teacher Edition, each lesson 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, “Why doesn’t zero have an opposite?” Then, the educator can use a sample response to assess students’ responses.

Beyond the lesson introduction, the “How Am I Doing?” sidebar 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 determined whether an integer is positive, negative, or zero. The note specifically prompts educators to listen for misconceptions related to the sign of zero, absolute value, or opposites.

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 the 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, helping 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, aligns with the specific standard addressed in each lesson, and includes an “Extension” activity to help students reach proficiency. For example, chapter 1 targeted supports include using Venn diagrams, number cards, counters, number lines, benchmark numbers, 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 preteaching and embedded language supports for developing academic vocabulary throughout. 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. It prompts students to describe the relationship between subsets of rational numbers 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, providing ongoing opportunities to develop and apply academic vocabulary in context. While the materials include explicit educator guidance throughout each lesson for preteaching 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 that are 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 on supporting students who demonstrated proficiency in grade-level content and skills. For example, the “Extension” activity in lesson 1 prompts students to work in small groups to research real-world contexts in which different number types are used. Additionally, the “Above-Level Extension Bank” section of the Appendix includes one “Extension” activity per lesson that extends learning beyond the current grade level. For example, the “Extension” activity for lesson 2 in the “Above-Level Extension Bank” section of the Appendix asks students to explore numbers that are not rational. This work introduces the concept of irrational numbers and provides an opportunity for 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” activity included with 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 create, represent, and explain their understanding of fractions as division, using a variety of strategies. Students 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 for educators to 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” sections provide specific prompts and guidance for educators to activate knowledge of positive rational numbers in grade 5, leading to visual classification of rational numbers in grade 6. This guidance helps educators activate prior knowledge of grade 5 concepts and connect these concepts to the grade 6 learning progression. Additionally, the wraparound provides guidance and questions throughout the first lesson to help the educator guide students in using visual models to relate rational 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 guides 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 8 includes a “Learn Together” activity that engages the entire class by having small groups model and solve an integer multiplication and division word problem for an integer operations gallery walk. The “Differentiation” activity guides educators in prompting striving students and/or emergent bilingual students to sort integer problems into positive or negative product or quotient categories. Additionally, students work independently through “Critical Thinking” assessment questions to develop a model that shows the rate of descent of an airplane from a given altitude.

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 of 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 student performance and assessment data. Additionally, the materials include recommendations for reteaching, intervention, progress monitoring, and enrichment to address diverse learning needs.

In the Teacher Edition, the lesson planner pages that are included before each lesson include 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” and independent “Practice” pages. Additionally, “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 can ask, “How can you decide whether a sharing situation will have a whole-number answer or a fraction?”

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 student thinking in lesson 2, they “listen for misconceptions such as confusing opposites with absolute value, thinking absolute value can be negative, misleading left/right order, or assuming larger negative numbers have a greater value.” Additionally, tiered support helps educators adjust instruction based on students’ understanding of integers and absolute value.

The sidebar in the Teacher Edition includes embedded prompts and guidance to help educators provide timely feedback throughout each lesson. Sidebar notes prompt 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 classifying rational numbers using a Venn diagram. 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.

The Teacher Edition wraparound for each lesson includes an "Emergent Bilingual Learners” tip box for guided instruction and a "Striving Learners/Emergent Bilingual Learners” tip box for lesson assessment. These boxes include sentence stems and discussion guidance for the teacher at all levels of language proficiency, so they can engage students in using increasingly more academic language.

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 so educators can 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 number relationships and rational-number reasoning 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 includes 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.” The lessons’ front matter, in conjunction with activities and EBL tips in the educator wraparound, embeds guidance throughout each lesson to support emergent bilingual students in developing academic vocabulary and increasing comprehension through oral and written discourse. The lessons also guide educators in building background knowledge and making crosslinguistic connections through oral discourse. The materials do not include embedded guidance to support emergent bilingual students in building background knowledge or making crosslinguistic connections through written discourse.

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

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

Evaluation for 4.1a
Practice opportunities throughout learning pathways (including instructional assessments) require students to demonstrate depth of understanding aligned to the TEKS.

In chapter 3, “Ratios and Proportions,” students develop an understanding of how multiplicative patterns relate to ratios, rates, and proportional thinking. They engage in a progression of tasks that move beyond procedural computation to representing ratios in multiple forms, determining and applying unit rates, solving real-world ratio and rate problems, analyzing equivalent ratios, and using proportions to solve multistep problems. Throughout the chapter, students are expected to justify solutions, interpret relationships among quantities, make predictions, and apply proportional reasoning in authentic contexts. Practice and assessment opportunities throughout the chapter, including “Guided Instruction,” “Extension,” and “Exit Ticket” activities, require students to demonstrate their knowledge and skills to solve problems.

“Guided Instruction,” “Critical Thinking,” “Learn Together,” and “Practice” activities for chapter 5, lesson 27, “Represent Situations Using Verbal Descriptions, Tables, Graphs, and Equations,” give students opportunities to create and connect linear relationships (e.g., y = kx or y = x + b) with various representations, including verbal descriptions, tables, graphs, and equations. Various practice activities require students to demonstrate depth of understanding that is aligned with the TEKS. For example, question 1 in the “Critical Thinking” activity requires students to “write a real-world verbal description that could relate to this table of values.” In addition, the assessment and exit ticket for lesson 27 provide students with further opportunities to create and connect linear relationships (e.g., y = kx or y = x + b) across various representations. For example, the “Exit Ticket” activity assesses whether students can connect a real-world situation—saving money for a family game night—to the four different representations they practiced throughout the lesson. Together, these practice opportunities and assessments require students to represent situations in more than one way, showing depth of understanding of linear relationships.

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 for chapter 1, lesson 2, “Compare Integers, Opposites, and Absolute Value,” provide students with questions and tasks that increase in rigor and complexity, leading to grade-level proficiency in comparing and ordering integers and rational numbers. For example, the “Differentiation” activities provide scaffolded support for identifying opposites, comparing integers using absolute value, and ordering integers on a number line. The “Critical Thinking” activity prompts students to compare and order integers, opposites, and absolute values using number-line models. The “Learn Together” activities prompt students to match and play games with integers, rational numbers, opposites, and absolute values. Questions and tasks in this lesson focus on grade-level proficiency and do not include comparing and ordering different forms of rational numbers.

In lesson 2, “Compare Integers, Opposites, and Absolute Value,” the “Critical Thinking” sidebar challenge questions and “Extension” activities in the Teacher Edition increase in rigor and complexity, leading to grade-level proficiency in composing and decomposing numbers. For example, the first “Extension” activity asks students to find real-world examples of integers, opposites, and absolute value and explain “how order or absolute value is important in different situations.” The second “Extension” activity asks students to create artwork with integers, opposites, absolute value, and/or the ordering of integers or rational numbers. While extensions increase in rigor and complexity within grade-level TEKS, they do not lead to above-grade-level proficiency in the mathematics TEKS.

In the Teacher Edition, the “Above-Level Extension Bank” section in the Appendix includes one “Extension” activity per lesson that provides students with an opportunity to explore above-grade-level content. For example, the “Extension” activity for lesson 3 gives students an opportunity to explore terminating and repeating decimals. While this activity introduces students to grade 7 content, it 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 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 “Horizontal/Vertical Progression Summary” in the chapter 5, “Expressions and Equations,” overview states, “Students begin by generating and comparing equivalent numerical expressions with order of operations, exponents, and prime factorization, then extend that understanding to the distributive property, combining like terms, and rewriting algebraic expressions in equivalent forms.”

Additionally, the materials demonstrate coherence horizontally across concepts in chapter 3, “Ratios and Proportions,” by connecting the big ideas of multiplicative reasoning, ratios, rates, proportions, and measurement conversions throughout the chapter. Students begin by distinguishing multiplicative relationships and representing ratios in multiple forms before progressing to equivalent ratios, unit rates, proportional reasoning, and real-world problem solving. As the chapter progresses, students apply these interconnected concepts to compare quantities, solve problems involving proportions, analyze scale factors, and complete conversions between customary and metric units. These experiences help students recognize patterns and relationships among mathematical concepts while deepening their understanding of proportional reasoning.

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 5 and grade 7, 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” section in lesson planners throughout the Teacher Edition shows the progression from grade 5 to grade 7 TEKS, demonstrating vertical alignment.

Additionally, in chapter 7, “Equations and Inequalities,” students build on their prior understanding of variables, numerical operations, and mathematical relationships, extending it to one-step equations and inequalities. The chapter overview describes a progression from solving one-step equations and representing exact solutions to interpreting and solving inequalities and analyzing solution sets. Students apply inverse operations, represent solutions on number lines, and interpret solutions in mathematical, real-world, and geometric contexts. These experiences reinforce foundational algebraic reasoning that was developed in earlier grades, while establishing the conceptual understanding that is necessary for future work with two-step equations, inequalities, and more advanced algebraic representations.

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. This section outlines routines to bridge from the previous lesson, activate prior knowledge, and integrate previously learned skills. For example, in chapter 1, lesson 2, “Order Real Numbers,” this section prompts educators to use what students learned in lesson 1 “about rational and irrational numbers to justify why irrational numbers such as pi and square roots can still be approximated and placed on a number line.” 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, “Ratios and Proportions,” demonstrates coherence across lessons and activities by intentionally connecting students’ prior understanding of multiplicative relationships with concepts involving ratios, rates, proportions, and measurement conversions. This chapter builds on previously learned concepts as students represent and compare ratios, determine unit rates, and apply proportional reasoning in real-world contexts. They extend this knowledge by writing and solving proportions to compare quantities and solve real-world ratio and rate problems. For example, the “Activate Prior Knowledge” section that is included before lesson 12, “Explore Rates,” in the Teacher Edition builds a bridge to describing and comparing different kinds of rates, such as distance and time or cost and amount. Students start with a hands-on activity using counters to build division equations. Then, they write division and fraction expressions and share how fractions help compare amounts. 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, 3, 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 1 prompt states, “This is a Chapter 1 skill—how did you find the opposite and the absolute value of a number there?” Additionally, “Fluency Lab” activities provide spaced retrieval opportunities with previously learned skills for nine 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 2 skill for question 1, use a chapter 3 skill for question 2, and combine skills from chapters 1 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 14, “Solve Ratio and Rate Problems Using Proportions,” provides students with an opportunity to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations to solve ratio and rate problems. For example, as students set up a proportion in the “Guided Instruction” section to solve for the number of protein bars in 54 minutes, the educator asks, “Why is it helpful to start Problem 2 by writing 12/18 as a ratio before setting up the proportion?” When using models to find the perimeter of rectangular plots with proportional side lengths, the educator asks, “How can using the scale factor between 6 and 8 help you find the missing side length in the smaller rectangle?” Additionally, the “Critical Thinking” activity prompts students to write and solve a proportion to solve for the number of chairs, given the cost. Students must also set up two solutions, given salt-to-water ratios, and determine how the solutions compare to each other.

The overview section for chapter 3, “Ratios and Proportions,” outlines opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations. In the “Purpose of the Chapter” section, students are expected to identify additive and multiplicative patterns using words, tables, graphs, and equations. Then, they represent proportional relationships using multiple forms. In lesson 10, “Identify Additive and Multiplicative Patterns,” students interpret, analyze, and evaluate mathematical concepts and real-world situations throughout the lesson. In the “Guided Instruction” section, students interpret patterns represented in tables, graphs, and equations and evaluate whether each representation demonstrates an additive or multiplicative relationship. Problem 2 requires students to analyze a table and a graph that show the number of miles run over several weeks and determine whether both representations show the same pattern. Additionally, “Critical Thinking,” “Learn Together,” and “Extension” activities require students to evaluate real-world scenarios to justify conclusions about the mathematical relationships they show.

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

In lesson 7, “Add and Subtract Integers,” questions and tasks provide opportunities for students to create concrete models and representations for adding and subtracting integers. For example, the “Learn Together: Number Line Journey Game” activity prompts students to use a number line to make jumps using integer sums. Additionally, the “Learn Together: Integer Swap” activity provides students with an opportunity to use integer and operation cards to write and solve equations. Student pairs swap one card to write and solve a new equation; then, “partners compare how the swapped cards changed the answers.”

In lesson 28, “Apply Properties of Triangles,” the “Guided Instruction” section directs students to use the measures of two angles in a triangle to determine the third angle and identify the longest side. This work creates representations of the relationship between angle measurements and side lengths. In the “Differentiation: Angle-Sum Strip Strategy” activity, students use 10-inch paper strips to measure angles with corresponding sides. They create triangles by bending the strips so the endpoints meet. Additionally, a challenge question in the “Critical Thinking” activity asks students to “draw a new triangle that fits the same side length condition as Problem 3 but with different measurements.” Questions and tasks in this lesson provide multiple opportunities for students to create concrete models and representations to demonstrate angle-side relationships for triangles.

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

In lesson 21, “Find the Percent When Given the Whole and Part,” “Critical Thinking” questions provide students with opportunities to apply conceptual understanding to find the percent of a whole. Students explain their steps and create a bar diagram to solve real-world problems. Additionally, in the “Learn Together: Percent Story Problem Swap” activity, students create real-world percent problems that compare a part to a whole. They exchange problems to find each other’s percent using various strategies, then “discuss which strategy they chose and why it fits the problem.”

In lesson 32, “Solve One-Step Equations,” students apply conceptual understanding of equations and inverse operations to new situations and contexts. In the “Guided Instruction” activity, students apply their understanding of inverse operations to solve real-world problems involving measurements, distances, and financial situations. In the “Critical Thinking” section, they analyze multiple solution methods and justify conclusions. Additionally, the “Learn Together: Create and Swap Equation Stories” activity requires students to create original, real-world situations that one-step equations can represent, then exchange and solve their classmates’ problems. Together, these opportunities require students to transfer and apply their conceptual understanding of one-step equations 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 2A” prompts students to multiply fractions and compare which strategy choice is faster when solving each problem.

In lesson 10, “Identify Additive and Multiplicative Patterns,” students build automaticity and fluency through repeated practice identifying, representing, and analyzing additive and multiplicative relationships. In the “Activate Prior Knowledge” activity in the Teacher Edition, students examine tables of values and determine pattern rules by identifying consistent changes and relationships among terms. The “Develop Fluency” section guides educators in focusing on building accuracy in identifying additive and multiplicative patterns in tables, graphs, and equations. In the “Guided Instruction” section, students repeatedly analyze patterns, determine rules, write equations, and classify relationships as additive or multiplicative. Additionally, the “Practice” section provides additional opportunities for students to apply these skills across multiple representations. The “Exit Ticket” activity requires students to independently describe, represent, and compare additive and multiplicative patterns. Together, these experiences build the automaticity and fluency that are needed to identify additive and multiplicative patterns and complete grade-level tasks involving patterns, ratios, and proportional reasoning.

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

In grade 6, opportunities are provided throughout the lessons to practice applying efficient, flexible, and accurate mathematical procedures. For example, the “Critical Thinking” activity for lesson 6, “Divide Fractions,” prompts students to multiply by the reciprocal and divide by the equivalent decimal to show that the results are the same. The challenge question in the sidebar of the Teacher Edition asks students to compare 6 ÷ 1/4 and 6 ÷ 4 using words or diagrams. “Fluency Lab 2B” is paired with this lesson. Students divide fractions and evaluate which strategy helped in solving the problems more easily. They also conduct an error analysis and reflect on efficiency to further develop their accuracy and efficiency in dividing fractions.

In lesson 32, “Solve One-Step Equations,” students practice efficient, flexible, and accurate procedures while solving equations. In the “Guided Instruction” section, students identify the operation that acts on the variable, apply the appropriate inverse operation to isolate the variable, and determine the solution. The “Compare Strategies” section guides educators to require students to examine multiple approaches, including number-line models, inverse operations, and symbolic equations, to solve the same problem and compare the effectiveness of each method. Additionally, the “Differentiation: Build and Solve Simple Equations” activity provides students with opportunities to create and solve equations using inverse operations and explain the procedure that was used. Then, the “Differentiation: Equation Walk Number Line” activity provides opportunities for students to model inverse operations physically and connect those actions to symbolic procedures. Together, these experiences provide repeated opportunities for students to practice and refine 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.

In grade 6, 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 5, “Multiply Fractions,” asks students to evaluate whether the product of two mixed numbers is correct. The challenge question in the sidebar of the Teacher Edition asks students “to explain using diagrams why Andy’s method did not work for multiplying 6-2/3 x 5-1/4.” The “Learn Together” activity that follows prompts students to estimate whether products with fractions will increase, decrease, or stay the same. “Fluency Lab 2A: Multiplying Fractions” is paired with this lesson. Students are given the opportunity to choose strategies and evaluate solutions for efficiency and accuracy. In “Fluency Lab” activities, students are given 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 nine of the 46 lessons.

In lesson 10, “Identify Additive and Multiplicative Patterns,” students evaluate representations, models, strategies, and solutions throughout the lesson. In the “Guided Instruction” section, students analyze tables, graphs, equations, and verbal descriptions to determine whether relationships are additive or multiplicative and justify their conclusions. In the second problem, students compare a table and a graph that represent the number of miles run over time and evaluate whether both representations convey the same mathematical relationship. Additionally, the “Critical Thinking” activity requires students to analyze solution strategies and justify conclusions about pattern rules. In contrast, the “Learn Together: Group Pattern Presentations” activity asks students to compare representations that were created by classmates and evaluate the accuracy and effectiveness of each model. Together, these opportunities require students to analyze and evaluate mathematical representations, models, strategies, and solutions for efficiency and accuracy throughout the lesson. However, the materials do not provide opportunities for students to evaluate mathematical representations, models, strategies, and solutions for flexibility throughout learning pathways.

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 2C” prompts students to consider more efficient strategies by asking, “How do sign rules help you solve integer problems more efficiently?” and “When is it helpful to use mental math instead of a number line?” Students actively reflect on when to use a model, sign rules, or mental math as a more helpful and efficient tool.

In lesson 32, “Solve One-Step Equations,” students receive explicit guidance for selecting efficient approaches to solving equations. In the “Guided Instruction” section, students learn to identify the operation that is acting on a variable and apply the corresponding inverse operation as an efficient method for isolating the variable and determining the solution. “Monitor Student Thinking” prompts in the Teacher Edition guide educators to help students evaluate whether their chosen strategy accurately represents the equation and leads to an efficient solution. In the “Compare Strategies” section, students examine number-line models, inverse operations, and symbolic equations to determine how each approach can be used to solve the same problem and discuss the advantages of each representation. Additionally, the “Differentiation: Equation Walk Number Line” activity helps students connect visual models to symbolic procedures, supporting a progression toward more efficient algebraic methods. Together, these supports help students select increasingly efficient approaches for solving one-step equations.

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

The “Purpose of the Chapter” section that is included in the overview before each chapter in the Teacher Edition outlines 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 build coherent understanding of real numbers by classifying number sets, reasoning about opposites and absolute value, interpreting fractions as division, and comparing and ordering rational numbers in mathematical and real-world contexts.” Additionally, this section indicates that students “use Venn diagrams, number lines, fraction notation, and contextual situations to connect concepts and explain their reasoning.”

The overview for chapter 7, “Equations and Inequalities,” 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 build a coherent understanding of one-variable, one-step equations and inequalities by writing algebraic statements, using inverse operations to solve them, representing solutions on numbers lines, and interpreting those solutions.” Additionally, this section indicates that the chapter “progresses from solving abstract one-step equations to writing, solving, and graphing one-step inequalities, then to applying both equations and inequalities in contextual and geometric situations.”

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.

The materials provide opportunities for students to use concrete models, pictorial representations, and abstract models, as required by the TEKS. In the overview for chapter 3, “Ratios and Proportions,” in the Teacher Edition, the “ELPS Support” section indicates that students will engage with a variety of representations, including ratio tables, tape diagrams, bar models, number lines, graphs, coordinate grids, conversion strips, and equations. These supports provide opportunities for students to move among concrete, pictorial, and abstract representations as they develop an understanding of additive and multiplicative relationships.

In lesson 10, “Identify Additive and Multiplicative Patterns,” students use concrete, pictorial, and abstract models throughout the lesson. In the “Activating Prior Knowledge” activity, students use two sets of number cards, created using either an addition or a multiplication rule, to organize and compare patterns and relationships. In the “Guided Instruction” section, students create and interpret pictorial representations such as tables and graphs to identify additive and multiplicative patterns. Then, students transition to abstract representations by writing equations and describing pattern rules using mathematical notation. Additionally, the “Differentiation: Describe the Pattern in Your Own Way” activity requires students to represent the same relationship using tables, graphs, equations, and verbal descriptions. Then, the “Learn Together: Group Pattern Presentations” activity asks students to create and explain multiple representations of assigned patterns. Together, these opportunities require students to use concrete, pictorial, and abstract representations in alignment with the grade 6 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 17, “Represent Percents,” asks students to create two models that represent 80%. Students make both a 10 x 10 grid and 10 squares. Additionally, the challenge question asks students to “represent 80% in two new ways: on a number line and as a fraction, and explain each.” Before the lesson, the Teacher Edition includes a hands-on task with fraction strips to activate students’ prior knowledge of dividing by unit fractions. Students also represent fractions by shading 10 x 10 grids. While the “Activating Prior Knowledge” activities help students activate their prior knowledge before each lesson begins, the material does not support students in connecting, creating, defining, 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 through it with the educator to connect representational models to abstract concepts. For example, in lesson 36, “Graph Points on a Coordinate Plane,” students use coordinate grids to plot and name points. Then, they transition to abstract representations by understanding the direction and location of points. “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 36 prompts students to connect three vertices and find the coordinates of the missing vertex to make an isosceles trapezoid. 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 specifically designed 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, in lesson 17, “Represent Percents,” this section asks students to explain how to represent percents by “prompting them to describe how a model shows parts out of 100.” As students understand how a hundredth grid connects to fractions and decimals, educators encourage them to “explain how they move between models, fractions, decimals, and percents orally, then revise explanations in writing.” Additionally, this section provides sentence stems and questions to guide educators in helping students develop academic mathematical language. For example, educators prompt justification by asking, “Why does this fraction simplify?” or “How do you know these forms are equivalent?” When asking these questions, educators are guided to require students to clearly connect models, fractions, decimals, and percents.

In lesson 33, “Solve One-Step Inequalities,” 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 solution sets, describe the meaning of inequality symbols, and justify whether boundary values are included. A table in the “Differentiated Language Support” section provides sentence stems and scaffolded academic language for students at varying proficiency levels, progressing from identifying symbols to explaining and justifying solutions using precise mathematical language. In the lesson, the “Understand the TEKS” section explains how inequalities represent sets of possible solutions rather than a single value. The “Guided Instruction” section uses number lines, open and closed circles, shading, and inequality symbols to help students describe solution sets and explain the meaning of inequalities using appropriate mathematical vocabulary. Additionally, “Differentiation” activities that are included in the Teacher Edition wraparound require students to connect visual models with academic vocabulary while communicating mathematical reasoning.

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 sidebar in the Teacher Edition includes 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 12, “Explore Rates,” provides sentence frames for students who demonstrate lower levels of language proficiency to help them explain unit rates. For students who demonstrate higher levels of language proficiency, educators are guided to ask them to use “precise terms such as unit rate and tape diagram.” 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. For students who demonstrate lower levels of language proficiency, this box directs educators to ask students to restate each ratio in words (e.g., “_____ to ” or “out of _____”). For students who demonstrate higher levels of language proficiency, this box directs educators to ask students to “explain why their division gives a unit rate and how that rate lets them compare speeds or write equivalent ‘_____ per 1 _____’ statements.”

In lesson 33, “Solve One-Step Inequalities,” 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 encourage students to explain how open and closed circles and shading on a number line show whether a boundary value is included and which values make the inequality true. The “Home Language and Cognates” section guides connecting familiar language to new mathematical vocabulary, while the “From Oral Reasoning to Written Justification” section encourages educators to move students from verbal explanations to written mathematical justifications using precise academic language. 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.

In lesson 4, “Compare and Order Rational Numbers,” the “Understand the TEKS” section in the student pages defines the vocabulary terms rational numbers, converted, and inequality. This section also includes examples of these terms plus some guidance on how they are related. An included chart shows an example of converting between fractions, decimals, and percents. The text states, “To compare rational numbers in different forms, it can be helpful to rewrite them in all decimals, all fractions, or all percents.”

Additionally, the Teacher Edition sidebar includes guiding questions to support students in developing academic language. One question asks, “How can benchmark numbers like 0, 1/2, and 1 help you compare rational numbers?” Following the “Guided Instruction” section, students are given opportunities throughout the lesson to work with their peers and discuss how to use a number line to compare and order rational numbers. For example, during the “Learn Together: Rational Number Sorting” activity, students work together to order a set of mixed rational number cards by using “discussion and consensus to create one ordered number line of all cards from least to greatest.” In the “Extension: Rational Number Relay” activity, students use a set of rational number cards in different forms in a race to arrange their cards in the correct order along a number line. They are directed to “discuss as a class whether the order is correct and ask how students decided which numbers were greater or smaller.”

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” activity 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 5, “Multiply Fractions,” students work in pairs for the first “Learn Together” activity. They “discuss how they knew to estimate whether their quantity increased, decreased, or stayed the same and if they were right.” The second “Learn Together” activity asks students to work in groups with a real-world context to write a multiplication problem and “present both the problem and the solution to the class.”

In lesson 11, “Represent Ratios,” embedded guidance supports mathematical conversations through structured partner and whole-class discussions. In the “Activate Prior Knowledge” activity that is included before the lesson in the Teacher Edition, students compare equivalent fractions using fraction strips or fraction circles and discuss how those relationships connect to ratios. The “ELPS Language and Discourse Support” section encourages students to describe the quantities being compared; explain whether ratios are part-to-part, part-to-whole, or whole-to-whole; and justify how the order of the terms affects the meaning of the ratio using precise mathematical vocabulary. “Differentiation,” “Learn Together,” and “Critical Thinking” activities require students to discuss ratio relationships, compare representations, explain solution strategies, and justify conclusions with their classmates using academic mathematical vocabulary. Across both lesson 5 and lesson 11, 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, in lesson 2, “Compare Integers, Opposites, and Absolute Value,” this section states, “Acknowledge correct reasoning and prompt students to justify how they know values are opposites, how absolute value represents distance from zero, and which numbers are greater or less.” This section also provides questions for when students demonstrate understanding, such as “Why can a number have a large absolute value but still be ‘less’ than another number on the number line?” The “Bridge: Getting Ready for Hundred” activity, also included before the lesson starts, includes a set of three expected answers to a “Think-Pair-Share” prompt in which students put different forms of numbers on a number line. Additionally, educators are provided with 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 also guides educators in supporting and redirecting inaccurate student responses. In lesson 2, this section states, “Listen for misconceptions such as confusing opposites with absolute value, thinking absolute value can be negative, misreading left/right order, or assuming larger negative numbers have greater value.” This section also provides questions for when students make errors, such as “How does the position of each number on the number line show which value is greater or represents a greater debt or depth?” 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, “Compare Integers, Opposites, and Absolute Value,” the sidebar indicates that “[TEKS] 6.1D: Communicate math ideas with words and symbols” and “[TEKs} 6.1E: Use representations to show and explain math” should guide students through each problem. In the second problem, educators are guided to ask students to use representations to compare integers by prompting them to “compare the numbers to determine which integers represent the greatest debt.” Additionally, the “Building Stamina” chapter assessments and Practice assessments 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 planners that are included before each lesson in the Teacher Edition describe how the TEKS process standards are incorporated into the lesson’s learning objectives. For example, lesson 3, “Understand Fractions as Division,” indicates that TEKS 6.1A, TEKS 6.1D, and TEKS 6.1E are the mathematical processes that are included in this lesson. This section states that students will “apply mathematics to everyday problems by solving division situations involving fractions,” “communicate mathematical ideas using words, symbols, and fraction notation to show understanding of division with fractions,” and “use representations, such as visual models and expressions, to explain and justify how division and fraction notation are connected.” While this section describes how process standards are incorporated into the lesson, it does not explain how they are connected throughout learning pathways.

The “Guided Instruction” sidebar in the Teacher Edition includes process standard numbers for the lesson. For example, lesson 11, “Represent Ratios,” states that “[TEKS] 6.1B: Use a problem-solving model,” “[TEKS] 6.1E: Organize and communicate ideas,” and “[TEKs] 6.1G: Use precise mathematical language” should be incorporated to guide students through each problem. The “Learn Together: Create and Critique Ratio Stories” activity in lesson 11 asks students to write new real-world stories to match the “Critical Thinking” activity. Then, students discuss with their group “how they identified the parts and the whole in each story and how they used ratio language to justify whether each story matched the given ratio.” While this activity requires students to use precise mathematical language, there is no description of how TEKS 6.1G 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 6 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 to identify the process standards that are incorporated in the lesson. For example, lesson 11, “Represent Ratios,” includes mathematical processes for TEKS 6.1B, TEKS 6.1E, and TEKS 6.1G. 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.

In lesson 16, “Convert Metric Measurements,” the “Understand the TEKS” and “Guided Instruction” sections sidebar questions in the Teacher Edition help students think about and make sense of mathematics. For example, the educator asks questions such as “Why are you more likely to use a proportion with customary measurements than metric measurements?” and “How could you solve this problem if you converted 400 grams to 0.4 kilogram right away?” Additionally, the “Critical Thinking” activity prompts students to convert from kilograms to milligrams in two different ways. Challenge questions for this activity prompt students to persevere and extend their thinking for each problem. For example, one challenge question in lesson 16 asks students to “explain aloud a third way to use a unit rate to convert three kilograms to milligrams and justify why it works.” At the end of the lesson, the “Exit Ticket” activity provides students with an opportunity to independently convert metric measurements in a recipe and demonstrate their understanding of the lesson.

In lesson 33, “Solve One-Step Inequalities,” students engage in problem-solving that promotes perseverance and mathematical reasoning. In the “Activate Prior Knowledge” section in the Teacher Edition, students use concrete models to connect real-world situations to symbolic inequalities before extending their understanding to solving and graphing one-step inequalities. The “Understand the TEKS” and “Guided Instruction” sections require students to analyze contextual problems, determine the appropriate inequality, solve using inverse operations, and interpret solution sets on number lines. Rather than simply following a procedure, students must make sense of the context, determine whether the inequality symbol changes, and justify why their solution is reasonable. Additionally, the “Monitoring Understanding and Feedback” section encourages educators to ask probing questions that help students reconsider misconceptions, justify their reasoning, and persevere when solving unfamiliar inequality problems. “Critical Thinking,” “Practice,” “Assessment,” and “Exit Ticket” activities require students to analyze mathematical 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.

In lesson 7, “Add and Subtract Integers,” students are encouraged to add and subtract integers using various models or the algorithm. For example, the “Critical Thinking” activity, along with challenge questions, expects students to explain and justify multiple ways to add and subtract integers, including zero pairs and number lines, to demonstrate their understanding. One challenge question asks students to “explain in their own words and provide an example of what happens to the answer when both numbers in an addition problem are negative.” Additionally, “Differentiation” activities for lesson 7 support students by helping them understand different real-life ways to represent integer values, explain the addition and subtraction of integers using number lines and counters, and create a chart to illustrate and explain the algorithm for integer addition rules.

In lesson 11, “Represent Ratios,” students are encouraged to recognize and justify multiple approaches for representing and analyzing ratios. In the “Guided Instruction” section, students represent the same ratio using words, fractions, colon notation, tables, diagrams, and visual models while explaining why each representation communicates the same relationship. Educator questions in the Teacher Edition sidebar prompt students to justify why the order of the terms is important and explain how different representations support the same mathematical idea. The “Monitoring Understanding and Feedback” section in the Teacher Edition prompts educators to ask students how they represented a specific ratio, whether another representation could also be used, and why each representation is mathematically valid. Additionally, the “Learn Together” activity encourages students to compare multiple representations of the same ratio and explain the advantages of each approach. “Critical Thinking” tasks ask students to justify their choice of representation and defend their reasoning using mathematical evidence. “Practice,” “Assessment,” and “Exit Ticket” activities reinforce flexible thinking by allowing students to represent, interpret, and justify ratios in multiple ways.

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 for lesson 3, “Understand Fractions as Division,” involves writing fractions to represent real-world division problems and, with a partner, writing real-world division problems that a given fraction can represent. “Learn Together” activities in this lesson ask students to match division expressions to fractions, create real-world division scenarios, then write matching division and fraction expressions. Additionally, “Extension” activities prompt students to write division stories to represent fractions and division equations. In the second “Extension” activity, students are expected to “present their object and fraction division problems to the class and explain why each is a valid fraction division story.”

In lesson 34, “Write and Solve Equations for Real-World Problems,” students make sense of mathematics by solving, representing, and discussing equations throughout the instructional sequence. In the “Activate Prior Knowledge” section in the Teacher Edition, students use concrete models to connect real-world situations to symbolic equations before discussing their observations with their classmates. The “Understand the TEKS” and “Guided Instruction” sections require students to write and solve equations and explain how equations can represent real-world situations and measurements involving different polygons. Additionally, “Learn Together” activities require students to collaborate with their peers to create real-world stories, write one-step equations, identify the unknown, and explain what the solution means in the context of the problem. “Critical Thinking” tasks prompt students to analyze real-world problems, justify conclusions, and explain how to write an equation to find the solution. “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 in sharing and reflecting on their problem-solving approaches. For example, in lesson 10, “Identify Additive and Multiplicative Patterns,” students are expected to explain how to identify additive and multiplicative patterns orally. Educators prompt them to “describe how consecutive terms change, how tables and graphs show a constant difference or constant ratio, and how equations in the forms y = ax and y = x + a match the pattern.” Educators are guided to ask students to present an argument with multiple entry points by explaining “whether the values change by adding the same amount or multiplying by the same factor and how the table, graph, or equation shows that rule.” Prompts for justification include, “Why does this equation match the pattern?” and “How do consecutive terms show the rule?” 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 prompted to “circulate and have them explain how they identified and represented additive and multiplicative patterns using equations, tables, and graphs.”

In lesson 14, “Solve Ratio and Rate Problems Using Proportions,” educators are provided with embedded guidance to facilitate student explanations, arguments, justifications, and multiple points of entry during problem solving. Educator prompts in the “Guided Instruction” section of the Teacher Edition sidebar encourage students to explain why it is helpful to write a rate as a ratio before setting up a proportion, justify the order of the quantities being compared, and explain why making predictions prior to solving helps determine if a solution is reasonable. The “Monitoring Understanding and Feedback” section that is included before the lesson provides questioning strategies that prompt students to defend their reasoning, reflect on their problem-solving approach, and explain why their solutions are mathematically valid. Students are encouraged to approach ratio problems using multiple entry points, including unit rates, scale factors, equivalent ratios, and proportions. 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” activity requires students to collaborate with their peers, compare different models and real-world representations of ratios, and explain why different representations show constant rates or scale factors. “Critical Thinking” tasks require students to defend their reasoning and explain how to set up and solve a proportion, and “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 includes prompts and guidance to support educators in providing explanatory feedback based on students’ responses and anticipated misconceptions. For example, in lesson 10, “Identify Additive and Multiplicative Patterns,” this section guides educators to listen to students’ explanations and “acknowledge correct reasoning and prompt students to explain whether the relationship shows a constant difference or a constant ratio, and why multiplicative patterns pass through (0, 0) while additive patterns do not.” Additionally, this section provides questions based on whether students make errors or demonstrate understanding. For errors, educators can ask questions such as, “How do the values change from one term to the next?,” “Are you adding the same amount each time or multiplying by the same factor?,” and/or “What does each part of the equation represent?” To extend student thinking, educators can ask, “How do the table, graph, and equation all show the same pattern type?” and “How can checking a term not shown in the original table help confirm that the rule is correct?”

In lesson 38, “Construct and Interpret Box Plots,” 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 order data; find the minimum, lower quartile, median, upper quartile, and maximum; and use those values to construct and interpret box plots. The materials identify misconceptions such as confusing the maximum with the range, incorrectly finding quartiles, and focusing on individual data points rather than on what the sections of the box plot show about the data. Educators are guided 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 in finding quartiles, confusing measurements, and misreading sections that show greater consistency. 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 observe students’ reasoning, identify misconceptions, and guide students through accurate reasoning through questioning and discussion.