Measuring Up to the TEKS Mathematics 2nd edition, Grade 7

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 7 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 7 TEKS” chart to locate lessons that address specific TEKS. The “ELPS alignment” chart shows how recurring components align with the ELPS. The “Horizontal and vertical progression” table includes a rationale for how concepts and skills connect across grade levels (vertical alignment) and within the same grade level (horizontal alignment), as designed in the materials.

Chapter overviews outline specific examples of how the TEKS and the ELPS are integrated into each chapter’s lessons, clearly linking the standards and instructional content within the grade level. 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’s structure plus suggested lesson pacing, assessment timing, and tips for use, including differentiation and maximizing instructional time.


Each lesson planner includes instructional supports that are aligned to students’ needs, such as tips for adjusting instruction for whole-group (tier 1), small-group (tier 2), or individual instruction (tier 3); ELPS language and discourse supports; and detailed instructional design strategies to guide educators in supporting all students. The “Critical Thinking” 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 7 TEKS,” “ELPS alignment,” and “Horizontal and vertical progression” tables together act as a TEKS correlation guide that includes recommended skill entry points. The “What’s Inside the Teacher Edition: Full-Length Practice Tests” and “Tracking and Pacing Charts” front matter sections direct educators to practice tests (diagnostic assessments) and student tracking charts in the Appendix that, when paired with the tables in the front matter, can guide educators to skill entry points based on diagnostic assessment results.

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

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

The “What’s Inside the Teacher Edition: Chapter Overview” and “Teacher Lesson Sequence” sections outline protocols and guidance on how to read the chapter overviews at the beginning of each chapter and the lesson planners at the beginning of each lesson. The outline indicates that chapter overviews summarize the mathematical focus and progression of learning across the chapter. Additionally, lesson planners show how each lesson builds on prior learning, connects to future concepts, explains how students can engage in the lesson, and provides prompts to assess understanding. The “Instructional Planning” section provides further guidance on using chapter overviews and lesson planners to plan lessons effectively, ensuring readiness and maximizing 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 7 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 that instructional leaders can 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 the 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 educator materials to guide educators. Lessons also include various assessment tools that are aligned with the TEKS and the ELPS. Educator wraparounds for the “Guided Instruction” section and the “Assessment” section provide guidance for working with striving learners (SLs) and emergent bilingual learners (EBLs).

Each lesson in the grade 7 Teacher Edition includes a lesson planner that clearly outlines learning objectives that are aligned to the TEKS and the ELPS plus 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 structure and provides suggested time frames for each lesson component.

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

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

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

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


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

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

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

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

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

The “Assessment Types, Purposes, and Administration” section outlines each assessment, including administration and guidance, to ensure consistent, accurate administration. For example, the table indicates that students should 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. Summative assessments, such as each lesson’s assessment and the “Building Stamina” chapter test, are used to monitor student mastery and inform instructional decisions. Additionally, the “Pacing” section provides recommended instructional timeframes for lesson and chapter assessments.

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

The “What’s Inside the Teacher Edition: Full-Length Practice Tests” section indicates that two printable full-length practice tests are available in the Appendix. The “Digital Only Supports” section highlights text-to-speech features that educators can toggle on and 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, or Depth of Knowledge (DOK) level. This section outlines varying levels of complexity and question types for chapter tests and diagnostic assessments. Chapter tests and diagnostic assessments include DOK 1-, DOK 2-, and DOK 3-level questions.

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

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

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

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

Each lesson assessment clearly indicates DOK levels. For example, the lesson 1 assessment includes DOK 1- and DOK 3-level questions, and question types include multiple-choice, inline choice, and drag-and-drop.

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

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

The “Practice” and “Assessment” activities in each lesson include scoring information and guidance for interpreting students’ performance in the Teacher Edition. The sidebar for the “Practice” activity includes common errors and hints so educators can interpret students’ responses. The sidebar for the “Assessment” activity 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 at the end of each lesson include guidance on interpreting students’ 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 share a misconception, begin the next lesson with a brief whole-group review of set relationships.”

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

Evaluation for 2.2c
Materials include tools for teachers to track student progress and growth, and tools for students to track their own progress and growth.

The materials include tools for both educators and students to track progress and growth. They include educator-facing progress-monitoring tools through the “Measuring Up Live” Insight digital platform. The “Teacher Tools for Monitoring Progress” section provides an analysis of assessment items and proficiency reports by standard. Educators can use these reports to monitor students’ performance by 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 is it helpful to change subtraction to addition when working with rational numbers?” Then, the educator can use the 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 chose the operation and determined the sign of their answer. The note specifically prompts educators to listen for misconceptions related to sign reasoning, absolute value, and/or representation choice.

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

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

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

The “What’s Inside the Teacher Edition: Wraparound Student Edition Lesson Support” section describes scaffolded supports that are available for students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. Before each lesson, an “Activating Prior Knowledge” section provides educators with guidance to gauge students’ understanding and prepare them for the lesson’s focus. Additionally, the wraparound provides targeted supports for striving students and emergent bilingual students through visual models, language scaffolds, and guided practice, which helps 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 that is addressed in each lesson, and includes an extension activity to help students reach proficiency. For example, chapter 1 targeted supports include using Venn diagrams, number lines, and sentence frames to reinforce students’ understanding of rational numbers throughout each lesson.

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

The materials include preteaching and embedded language supports for developing academic vocabulary throughout the lessons. 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 compare 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, which provide 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 with a partner to define two sets of numbers and create a Venn diagram to show their relationship. 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 adding and subtracting variable terms with rational coefficients. This work introduces the concept of combining like terms and provides an opportunity for students to learn above-grade-level content and skills.

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

Digital materials provide text-to-speech, content, and language supports. The Student eBook provides an immersive reader, real-time translation, and an academic vocabulary picture dictionary. Educators can control which language and dialect students use to move through the materials. However, the materials do not explicitly state whether text-to-speech and 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 each lesson’s “Critical Thinking” section, which provides students with options to demonstrate understanding through multistep and real-world problems. For example, the “Critical Thinking” activity for lesson 3 requires students to classify, create, represent, and explain rational number relationships using a variety of strategies. Students must demonstrate understanding by explaining their reasoning, comparing approaches, and representing their thinking in multiple ways. Additionally, the “How Am I Doing?” section in the Teacher Edition sidebar guides educators to support students by listening for accurate concept development and correcting misconceptions as students explain their thinking for each question.

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

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

Lesson materials in the Teacher Edition include explicit (direct) prompts and guidance so educators can build knowledge by activating prior knowledge and anchoring big ideas, utilizing the front matter and wraparound for each lesson. For example, the lesson 1 planner and “Activating Prior Knowledge” section provide specific prompts and guidance for educators to activate knowledge of classifying rational number sets in grade 6, which leads to the description of relationships between sets and subsets of rational numbers in grade 7. This guidance helps educators activate prior knowledge of grade 6 concepts and connect these concepts to the grade 7 learning progression. Additionally, the wraparound provides guidance and questions throughout the first lesson to help the educator guide students in creating visual models to relate 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 discussions, small-group differentiation, and independent practice, among other approaches. For example, lesson 10 includes a “Learn Together” activity that engages the whole class. It prompts student pairs to create a cityscape and draw new buildings that are similar to those already drawn on a poster in which each building is a different polygon. The “Differentiation” activity guides educators to ask striving students and emergent bilingual students to color-code corresponding angles and sides of similar figures. Additionally, students can work independently through “Critical Thinking” activity questions to draw similar quadrilaterals, identify corresponding angles, and write ratios with corresponding sides.

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

The “Instructional Formats and Use” section in the Teacher Edition outlines multitiered intervention methods and educator guidance for effective implementation across varying levels of students’ needs. The materials define structures for whole-group instruction, targeted small-group intervention, and intensive individual support. Provided 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.

The lesson planner pages that are included before each lesson in the Teacher Edition provide educator guidance to support effective implementation of multitiered intervention methods. The wraparound for each lesson guides educators through multitiered intervention methods for different types of practice, such as “Guided Instruction” and independent “Practice” sections. 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 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, “Why do sign rules work for all rational number multiplication and division?” or “How would you explain division by a fraction to someone else?”

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

The “Monitoring Understanding and Feedback” and “Instructional Support for Student Needs” sections that are included before each lesson in the Teacher Edition provide prompts and guidance to help educators deliver timely feedback during lessons. For example, as educators monitor students’ thinking in lesson 2, they “listen for common misconceptions such as determining the sign based on keywords instead of absolute value, forgetting to change subtraction to addition, or adding fractions or decimals without first rewriting them in the same form.” Additionally, tiered support helps educators adjust instruction based on students’ understanding of adding and subtracting rational numbers.

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 students’ 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.

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. Students can access content for dual-language programs 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 provides embedded guidance throughout the chapter. This guidance is designed to make rational-number concepts accessible to EB students. It outlines visual representations, language frames, vocabulary reinforcements, and collaborative talk routines that help educators implement guided mathematical discourse so students can 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 sections such as “During Learn Together and Guided Instruction,” “Home Language and Cognates as a Bridge,” and “From Oral Reasoning to Written Justification.” This lesson’s front matter, in conjunction with activities and tips regarding emergent bilingual students in the educator wraparound, embeds guidance throughout each lesson to support EB students in developing academic vocabulary and increasing comprehension through oral and written discourse. The lesson also guides educators in building background knowledge and making crosslinguistic connections through oral discourse.

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

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

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

In chapter 7, “Personal Finance,” students apply percent reasoning and numerical relationships to personal finance situations. They engage in a progression of tasks that move beyond procedural computation to analyzing financial situations, calculating and interpreting taxes, creating and evaluating budgets, determining net worth, comparing purchasing incentives, and calculating simple and compound interest. Throughout the chapter, students apply mathematical reasoning to authentic financial contexts, justify decisions, analyze relationships among financial concepts, and solve increasingly complex real-world problems. Practice and assessment opportunities throughout the chapter, including “Guided Instruction” and “Extension” activities and “Exit Ticket” assessments, require students to demonstrate their knowledge and skills to solve problems.

The “Guided Instruction,” “Critical Thinking,” “Learn Together,” and “Practice” activities that appear in chapter 1, lesson 4, “Solve Problems Involving Rational Numbers,” give students opportunities throughout the lesson to write expressions with rational numbers to solve one- to two-step problems. Various practice activities require students to demonstrate depth of understanding that is aligned to the TEKS. For example, question 2 in the “Critical Thinking” activity requires students to “write and simplify an expression to find how many yards of ribbon Glenn has.” In addition, the “Exit Ticket” assessments provide students with further opportunities to organize the information that is provided in a problem and choose the correct order of operations to find a solution. For example, the exit ticket assesses whether students correctly represent how prize money will be split between math classes. Students are expected to write a complete expression and simplify the expression accurately. Together, these practice opportunities and assessments require students to write expressions and find solutions, showing their depth of understanding for solving problems involving rational numbers.

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, “Add and Subtract Rational Numbers,” provide students with questions and tasks that increase in rigor and complexity, leading to grade-level proficiency in adding and subtracting rational numbers. For example, the “Differentiation” activities provide scaffolded support for adding and subtracting rational numbers using number lines and real-world scenarios. The “Critical Thinking” activity prompts students to evaluate and model the addition and subtraction of integers. The “Learn Together” activities prompt students to play a game involving integer addition and subtraction and match rational number addition and subtraction cards to real-world scenarios. Questions and tasks in this lesson focus on grade-level proficiency but do not include adding and subtracting like terms.

The “Critical Thinking” sidebar challenge questions and “Extension” activities in the Teacher Edition for lesson 2, “Add and Subtract Rational Numbers,” increase in rigor and complexity, leading to grade-level proficiency in adding and subtracting rational numbers. For example, the first “Extension” activity asks students to write their own real-world scenarios with positive and negative rational numbers. Then, students trade scenarios to “write and simplify an expression to represent the scenario.” The second “Extension” activity asks students to create four-panel storyboards that illustrate real-world scenarios involving the addition and subtraction of rational numbers. While extensions increase in rigor and complexity within the grade-level TEKS, they do not lead to above-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. This activity provides students with an opportunity to explore above-grade-level content. For example, the “Extension” activity for lesson 18 gives students an opportunity to explore how the circumference of a circle changes versus how the area changes when doubling the radius. While this activity introduces students to quadratic versus linear growth, this exploration does not lead to above-grade-level proficiency in the mathematics TEKS.

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

The “Horizontal and vertical progression” chart that is included in the Teacher Edition demonstrates coherence horizontally across concepts within the grade level by connecting big ideas. Additionally, chapter overviews and lesson planners further detail horizontal alignment by connecting big ideas across the curriculum. For example, the overview for the “Horizontal/Vertical Progression Summary” section in chapter 1, “Rational Numbers,” states, “Students begin by classifying numbers and describing set relationships, then extend that understanding to opposites, absolute value, fractions as division, and comparison of rational numbers in multiple forms.”

The materials demonstrate coherence horizontally across concepts in chapter 2, “Proportional Relationships,” by connecting the big ideas of proportional reasoning, proportional relationships, percent applications, measurement conversions, and geometric reasoning throughout the chapter. Students progress from determining and representing unit rates and constants of proportionality to solving percent increase and decrease problems, converting measurements, and applying proportional relationships to similar figures and scale drawings. Throughout the chapter, students use multiple representations—including tables, graphs, equations, and verbal descriptions—to analyze and model proportional situations. These interconnected experiences help students recognize patterns and relationships among mathematical concepts while they develop a cohesive understanding of proportional reasoning and its applications across the grade 7 mathematics TEKS.

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

The “Horizontal and vertical progression” chart that is included in the Teacher Edition demonstrates coherence vertically across concepts and grade bands, including connections to grade 6, grade 8, Algebra, and Geometry, by linking big ideas. Chapter overviews and lesson planners further detail vertical alignment by connecting big ideas across the curriculum. For example, “Learning Progression” sections in the lesson planners throughout the Teacher Edition show the progression from grade 6 to grade 8 Algebra and/or Geometry TEKS, demonstrating vertical alignment.

Additionally, in chapter 7, “Personal Finance,” students build on their prior understanding of percent reasoning, numerical operations, proportional relationships, and financial contexts that were developed in earlier grade levels and extend that knowledge to more sophisticated personal finance applications. The chapter progresses from calculating sales tax and income tax to creating budgets, determining net worth, comparing purchasing incentives, and calculating simple and compound interest. These experiences reinforce foundational concepts involving percents, ratios, decimals, and problem solving while helping students apply mathematical reasoning to authentic financial situations. The materials also prepare students for future learning by deepening their understanding of personal finance and mathematical decision-making.

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 in the current grade level. Routines are outlined that build on the previous lesson, activate prior knowledge, and integrate previously learned skills. For example, this section in chapter 1, lesson 2, “Add and Subtract Rational Numbers,” prompts educators to “recall how integers are added using a number line.” Additionally, this section states that it “supports upcoming work with multi-step expressions and real-world situations involving rational numbers,” 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 2, “Proportional Relationships,” demonstrates coherence across lessons and activities by intentionally connecting students’ prior understanding of ratios, rates, and proportional reasoning to current grade-level concepts that involve proportional relationships, percent problems, measurement conversions, similar figures, and scale drawings. The chapter builds upon previously learned concepts as students represent proportional relationships using tables, graphs, equations, and verbal descriptions; determine unit rates and constants of proportionality; and apply proportional reasoning in real-world and geometric contexts. For example, the “Activate Prior Knowledge” section that is included before lesson 5, “Represent Constant Rates of Change Given Tables and Graphs,” in the Teacher Edition builds a bridge to using data in tables or graphs to represent constant rates of change. Students start with a hands-on activity using counters or blocks to represent bags of marbles. Then, they create a table to identify patterns and write a rule for the number of marbles in each bag. Next, students create a graph from the table. Throughout the chapter, lessons progressively increase in complexity, which helps 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” section in chapter 5 provides three problems in which students utilize skills from chapters 1, 2, and 3. The Teacher Edition wraparound provides prompts so educators can identify a specific skill and ask conceptual questions while students are working. For example, the question 2 prompt states, “This is a Chapter 2 skill; what does it mean to find a rate?” Additionally, “Fluency Lab” activities provide spaced retrieval opportunities with previously learned skills for 11 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” section in chapter 4 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 within 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 5, “Represent Constant Rates of Change Given Tables and Graphs,” provides students with an opportunity to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations to find the constant of proportionality. For example, as students use a table to find the speed of a remote-control car in the “Guided Instruction” section, the educator asks, “How do you know the table represents a proportional relationship?” When using a graph to find the rate of temperature change, the educator asks, “What does the constant of proportionality tell you in this experiment?” Additionally, the “Critical Thinking” activity prompts students to use a graph to determine the unit rate of earnings per hour and write an equation to predict earnings. Students also compare inches of snow and water to find the constant of proportionality.

The overview section of chapter 2, “Proportional Relationships,” in the Teacher Edition outlines opportunities for students to interpret, analyze, and evaluate mathematical concepts and complex, real-world situations. In the “Purpose of the Chapter” section, students develop an understanding of proportional relationships by examining how ratios, rates, and unit rates can be represented in multiple forms. In lesson 5, “Represent Constant Rates of Change Given Tables and Graphs,” students interpret, analyze, and evaluate mathematical concepts and real-world situations throughout the lesson. In the “Guided Instruction” section, students analyze tables and graphs to determine constants of proportionality and explain how proportional relationships are represented across different models. Problem 1 requires students to evaluate a table that shows the time and distance traveled and determine whether the relationship is proportional by identifying the constant rate of change. Problem 2 requires students to analyze a graph that represents a temperature change over time and interpret how the constant of proportionality is represented in the graph. Additionally, “Critical Thinking,” “Learn Together,” and “Extension” activities require students to evaluate real-world scenarios to justify their 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 12, “Solve One-Variable Equations,” questions and tasks provide opportunities for students to create concrete models and representations for solving two-step equations with one variable. For example, the “Learn Together: Equation Charades” activity gives students an opportunity to act out solving one-variable, two-step equations using hand gestures. Additionally, the “Learn Together: Collaborative Equation Challenge” activity gives students an opportunity to “work in small groups to create their own one-variable, two-step equation and draw a model to represent it.” Then, students justify their steps and represent the solution on a number line.

In lesson 20, “Calculate Volume of Prisms and Pyramids,” the “Learn Together: Modeling the Relationship Between Pyramids and Prisms” activity prompts students to cut out, fold, and tape two-dimensional geometric nets. Students must physically manipulate and combine these three concrete models to form a single rectangular prism. They use this hands-on exploration to structurally explain the fractional relationship 1/3 between the volume formulas of matching pyramids and prisms. Additionally, the “Learn Together: Comparing Prisms and Pyramids” activity prompts students to transition to drawing a rectangular prism and a rectangular pyramid that share identical base and height dimensions on graph paper to calculate the volume. Questions and tasks in this lesson provide multiple opportunities for students to create concrete models and representations to calculate the volume of prisms and pyramids.

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

“Critical Thinking” questions for lesson 8, “Solve Percent Problems,” provide students with opportunities to apply conceptual understanding to finding percent increases and decreases. Students explain their thinking and draw a number line to model a discount problem. Additionally, in the “Learn Together: Percent Change Match” activity, student pairs receive a set of percent change problems. They create a chart with columns for the initial amount, change, new amount, and percent change and fill it in for each scenario.

In Lesson 30, “Solve Problems Using Data Displays,” students apply conceptual understanding of statistical representations to new situations and contexts. In the “Guided Instruction” section, students analyze graphs and make predictions to solve real-world problems. In the “Critical Thinking” activity, students analyze a monthly budget that is represented in a circle graph and determine missing values using proportional reasoning. Additionally, the “Learn Together” activity requires students to collect, represent, and analyze real-world survey data. Together, these opportunities require students to transfer and apply their conceptual understanding of statistical displays to new mathematical situations and real-world contexts.

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

“Fluency Lab” activities are designed to build students’ automaticity and fluency in numbers and operations. For example, “Fluency Lab 1A” prompts students to add and subtract rational numbers and compare which strategy choice is most efficient for solving each problem.

In lesson 5, “Represent Constant Rates of Change Given Tables and Graphs,” students build automaticity and fluency through repeated practice; they also determine unit rates and constants of proportionality from multiple representations. In the “Activate Prior Knowledge” activity that is included in the Teacher Edition, students calculate unit rates from proportional tables and identify patterns in the data. The “Develop Fluency” section guides educators to focus specifically on building procedural fluency by calculating unit rates and constants of proportionality from tables and graphs. They also focus on writing equations to represent proportional relationships. In the “Guided Instruction” section, students repeatedly divide corresponding values to determine constants of proportionality and explain how the constant appears in tables, graphs, and equations. Additionally, the “Practice” section provides multiple opportunities to apply these procedures across real-world contexts and mathematical representations. The “Exit Ticket” activity requires students to independently determine a unit rate, write an equation, and interpret a proportional relationship. Together, these experiences build the automaticity and fluency that are needed to successfully complete grade-level tasks involving proportional relationships, unit rates, and constants of proportionality.

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

Opportunities are provided throughout the lessons so students can practice applying efficient, flexible, and accurate mathematical procedures. For example, the “Critical Thinking” activity in lesson 2, “Add and Subtract Rational Numbers,” prompts students to add and subtract integers on a number line and use an expression to show that the results are the same. The challenge question in the sidebar of the Teacher Edition prompts students to “represent the expression -1.8 - 1/5 on a number line and simplify the expression.” “Fluency Lab 1A” is paired with this lesson. Students add and subtract rational numbers and evaluate which strategy helped them solve the problems most efficiently. Students also conduct an error analysis and reflection on efficiency to further develop their accuracy and efficiency in adding and subtracting rational numbers.

In lesson 30, “Solve Problems Using Data Displays,” students practice efficient, flexible, and accurate procedures for solving problems using statistical displays. In the “Guided Instruction” section, students calculate percentages from bar graphs, determine proportions represented in dot plots, and analyze part-to-whole relationships in circle graphs. The “Compare Strategies” section guides educators in encouraging students to examine multiple methods for determining percentages and making comparisons using graphical data. Additionally, the “Critical Thinking” activity requires students to apply percentage and proportional reasoning procedures to analyze a monthly budget that is represented in a circle graph. The assessment and “Exit Ticket” activity provide further opportunities for students to apply and refine efficient, flexible, and accurate mathematical procedures while interpreting and solving problems involving statistical displays. Together, these experiences support the development and application of efficient, flexible, and accurate mathematical procedures throughout the lesson.

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

Opportunities are provided throughout the lessons so students can evaluate representations, models, strategies, and solutions for efficiency and accuracy. For example, the “Critical Thinking” activity in lesson 3, “Multiply and Divide Rational Numbers,” prompts students to evaluate integer expressions to determine if the product is positive or negative. The follow-up challenge question in the sidebar of the Teacher Edition asks students to “explain why multiplying two negative numbers gives a positive product.” The “Learn Together” activity that follows prompts students to sort multiplication and division expressions into sets based on whether the results are positive or negative. Then, students discuss the rules for determining the sign and create a poster summarizing the rules for multiplying and dividing rational numbers. “Fluency Lab 1B: Multiply and Divide Rational Numbers” is paired with this lesson. In “Fluency Lab” activities, students receive an 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 11 of the 37 lessons.

In Lesson 5, “Represent Constant Rates of Change Given Tables and Graphs,” students evaluate representations, models, strategies, and solutions throughout the lesson. In the “Guided Instruction” section, students analyze tables and graphs to determine whether relationships are proportional and evaluate how the constant of proportionality is represented in each model. The “Compare Strategies” section in the Teacher Edition directs educators to ask students to evaluate multiple approaches to determining constants of proportionality and compare information presented in tables, graphs, and equations. Additionally, the “Critical Thinking” activity requires students to justify their conclusions about proportional relationships, using evidence from multiple representations. The “Learn Together: Proportional Relationship Gallery Walk” activity provides opportunities for students to evaluate representations created by their classmates and discuss the accuracy and effectiveness of each model. Together, these opportunities require students to evaluate mathematical representations, models, strategies, and solutions for efficiency and accuracy throughout the lesson. While students practice flexibility in modeling and solving problems, there is no consistent evaluation of that flexibility across lessons.

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

Each “Fluency Lab” activity provides guidance that helps students select the most efficient approaches to operations with numbers. For example, “Fluency Lab 1B” prompts students to consider more efficient strategies by asking, “When you multiply or divide rational numbers, when is it more efficient to use fractions instead of decimals?” and “How do sign rules help you work more efficiently without checking each step with a model or calculator?” Students actively reflect on when to use different number forms and sign rules to solve problems more efficiently.

In lesson 30, “Solve Problems Using Data Displays,” students receive explicit guidance for selecting efficient approaches when solving statistical problems. In the “Guided Instruction” section, students learn to identify the type of data display, determine the total that is represented, and use percentages and proportional reasoning to analyze information efficiently. The “Monitoring Student Thinking” section prompts in the Teacher Edition guide educators in helping students identify relevant information in graphs, focus on part-to-whole relationships, and evaluate whether their solution method is appropriate for the problem. Additionally, the “Critical Thinking” activity encourages students to select appropriate strategies to analyze a monthly budget and determine missing values in a circle graph. Together, these supports help students evaluate and select increasingly efficient approaches for solving problems involving data displays and statistical reasoning.

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, “Rational Numbers,” states, “Students develop a coherent understanding of rational numbers by examining how they are classified and how they behave under the four operations.” Additionally, this section indicates that students “use Venn Diagrams, number lines, models, and contextual problem situations to connect rational number representations and operations.”

In chapter 5, “Probability,” the “Overview” section includes statements for both conceptual and procedural elements of the TEKS that are included in the lessons for this chapter. The “Purpose of the Chapter” section states, “Students develop an understanding of probability by representing events, determining likelihood, and applying probability to make predictions.” Additionally, this section indicates that “as the chapter progresses, students determine experimental probability from data and trials and theoretical probability from sample spaces.”

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. The “ELPS Support” section in chapter 6, “Statistics,” in the Teacher Edition indicates that students will engage with a variety of representations, including bar graphs, dot plots, circle graphs, tables, visual models, and percentage representations. These supports provide opportunities for students to move among concrete, pictorial, and abstract representations while developing an understanding of statistical relationships and data analysis.

In lesson 30, “Solve Problems Using Data Displays,” students use concrete models, pictorial representations, and abstract models throughout the lesson. In the “Activate Prior Knowledge” activity, students use colored counters to organize and represent data before creating frequency tables and graphical displays. In the “Guided Instruction” section, students interpret pictorial representations such as dot plots, bar graphs, and circle graphs and connect those representations to abstract concepts, including proportions, percentages, and probability predictions. Additionally, the “Learn Together: Solving Bar Graph Problems” activity requires students to collect data, organize it in a graph, and use numerical reasoning to answer questions and make comparisons. The “Extension: Create Your Own Bar Graph” activity further requires students to create a graphical representation from a data set and analyze that information using percentages and proportional reasoning. Together, these opportunities require students to use concrete, pictorial, and abstract models, in alignment with the grade 7 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 for lesson 12, “Solve One-Variable Equations,” prompts students to solve an equation using a bar model, then represent the solution on a number line. Additionally, the challenge question asks students to “create a bar model for the equation they write in the problem 1 challenge.” In the previous challenge question, students “write their own one-variable, two-step equation and explain the steps to solve it.” Before the lesson, the Teacher Edition includes a hands-on task with counters to activate students’ prior knowledge of solving one-step equations. Then, students try to use this strategy with counters to solve a two-step equation. While the “Activating Prior Knowledge” activities help students activate prior knowledge before each lesson, they do not support students in connecting, creating, defining, and/or explaining concrete models to abstract concepts, as required by the TEKS.

The “Guided Instruction” section for each lesson is designed so students can work with educators to connect representational models to abstract concepts. For example, in lesson 5, “Represent Constant Rates of Change Given Tables and Graphs,” students explain how the constant of proportionality appears in tables, graphs, and equations. Then, they connect each representation to the same mathematical relationship. “Critical Thinking,” “Practice,” “Assessment,” and “Exit Ticket” activities in the student pages for each lesson provide further support so students can meaningfully connect, create, define, and explain representational models to abstract concepts. For example, the “Critical Thinking” activity for lesson 5 prompts students to find the unit rate for babysitting from a graph and write an equation to predict the amount that will be earned. In addition to the student pages, the Teacher Edition wraparound provides activities that support students in connecting concepts with representational models. While the materials include concrete activities that are specifically designed for struggling students, 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 3, “Multiply and Divide Rational Numbers,” this section prompts students explain how sign rules apply when multiplying and dividing by “prompting them to describe patterns and relationships between positive and negative factors and how they decide if a product or quotient is positive or negative.” As students understand how to determine whether numbers have the same or different signs, educators encourage them to “explain why the sign of the result makes sense orally, then revise [their] 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 students to “explain why the product is negative in this case.” When explaining, educators should require students to connect symbolic work to models or real-world contexts.

In lesson 32, “Make Inferences From Random Samples,” 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 what a sample represents, distinguish between a sample and a population, justify why a sample supports an inference, and describe how proportions are used to estimate results for a larger population using academic mathematical language. The “Differentiated Language Support” section within the table provides sentence stems and scaffolded academic language for students at varying proficiency levels, progressing from identifying samples and populations to explaining and defending statistical inferences using precise mathematical language. Within the lesson, the “Understand the TEKS” section explains the relationship between samples, populations, and inferences. The “Guided Instruction” section uses tables, bar graphs, proportions, and real-world survey data to help students explain statistical relationships using appropriate mathematical vocabulary. Additionally, the “Differentiation” activities in the Teacher Edition wraparound require students to connect visual models to academic vocabulary and communicate statistical 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 so educators can scaffold, support, and extend students’ use of academic mathematical vocabulary in context. For example, the “EBL Tip” box in the “Guided Instruction” section of lesson 2, “Add and Subtract Rational Numbers,” provides sentence frames for students who demonstrate lower levels of language proficiency, to explain how they determine the sign and combine values when adding and subtracting rational numbers. For students who demonstrate higher levels of language proficiency, educators should prompt students to “explain why the result is positive or negative using precise terms and complete explanations.” The “SL/EBL Tip” box for the lesson assessment also provides sentence frames and guidance so educators can help students justify their answers using academic mathematical vocabulary. Students who demonstrate lower levels of language proficiency can use sentence stems to explain sign and operation choices, while students who demonstrate higher levels of language proficiency can justify their solutions “using sign rules and relationships.”

In lesson 32, “Make Inferences From Random Samples,” 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 prompt students to explain what a sample represents, distinguish between a sample and a population, describe how proportions support an inference, and justify whether an inference is supported by the available data using precise academic vocabulary. The “Home Language and Cognates” section encourages educators to connect familiar language with lesson-specific statistical terminology, while the “From Oral Reasoning to Written Justification” section encourages educators to move students from verbal explanations to written mathematical justifications that use data evidence and correct mathematical vocabulary. 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 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 7, “Solve Ratio and Rate Problems,” the “Understand the TEKS” section in the student pages defines the vocabulary terms ratio, rate, unit rate, equivalent ratio, proportion, and cross multiply. This section includes examples of these terms plus guidance on how they are related. For example, the text states, “You can use proportions to solve problems involving rates and ratios.” The section includes an example of setting up a proportion, a description of using cross-multiplication to solve it, and a visual representation of the equivalent ratios. Additionally, the Teacher Edition sidebar includes guiding questions to support students in developing academic language. One question asks, “How does a unit rate help you compare two quantities?” Following the “Guided Instruction” section, students are given opportunities throughout the lesson to use appropriate mathematical language to compare rates and ratios and solve problems using proportions. For example, in the “Learn Together: Proportion Table” activity, students work in small groups to create a table of data for real-world scenarios involving proportions. Students discuss any mistakes or strategies they notice, and educators “encourage students to use multiplication, division, and reasoning when defending their answers.” In the “Extension: Proportional Reasoning” activity, students use the data set from the “Exit Ticket” activity to create a graph. They are challenged to “use their graph to make predictions for new values, find a unit rate, and describe how changing one value affects the other.”

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 3, “Multiply and Divide Rational Numbers, students work in small groups for the first “Learn Together” activity. Then, they “discuss the rules for determining the sign for each operation and explain their thinking to the group.” The second “Learn Together” activity prompts students to work with a partner to find errors in simplifying expressions and “explain the steps needed to correct the answers.”

In lesson 7, “Solve Ratio and Rate Problems,” 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 use counters to write a ratio and discuss how to find equivalent ratios. The “ELPS Language and Discourse Support” section directs educators to prompt students to explain how ratios and rates compare quantities, justify why proportions or unit rates are appropriate for solving problems, describe relationships that are represented in ratio tables and visual models, and communicate their reasoning using precise mathematical vocabulary. The “Differentiation,” “Learn Together,” and “Critical Thinking” activities require students to discuss mathematical ideas, compare strategies, and explain proportional reasoning with their peers, using academic mathematical language. Across both lesson 3 and lesson 7, 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 the lesson in the Teacher Edition guides educators in anticipating students’ responses. For example, in lesson 2, “Add and Subtract Rational Numbers,” this section states, “Acknowledge correct reasoning using precise mathematical language and prompt students to justify their work using sign rules, absolute value, and rewriting subtraction as addition.” This section also provides questions for when students demonstrate understanding, such as “Why does rewriting subtraction as addition work for all rational numbers?” Also included before the lesson, the “Bridge: Getting Ready for Hundred” activity includes an expected answer to a “Think-Pair-Share” prompt in which students compare the rules for adding positive and negative integers, fractions, or decimals. Additionally, educators are given 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 common misconceptions such as determining the sign based on keywords instead of absolute value, forgetting to change subtraction to addition, or adding fractions and decimals without first writing them in the same form.” This section provides questions for when students make errors, such as “What changed when you wrote this subtraction expression as addition?” 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 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, “Add and Subtract Rational Numbers,” the sidebar indicates that “[TEKS] 7.1A: Apply math to real-world situations,” “[TEKS] 7.1B: Use a problem-solving model to find and justify solutions,” and “[TEKS] 7.1E: Organize and communicate ideas” should guide students through each problem. In the third problem, educators should prompt students to apply math to real-world situations by having them calculate the change in elevation for hikers descending a mountain. 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 planner that is included before each lesson in the Teacher Edition describes how the TEKS process standards are incorporated into the lesson’s learning objectives. For example, lesson 13, “Write One-Variable Equations,” indicates that TEKS 7.1A and TEKS 7.1E are the mathematical processes that are included in this lesson. This section states that students will “apply mathematics to real-world situations” and “create verbal models and equations to represent real-world situations.” While this section describes how the process standards are incorporated into the lesson, it does not explain how they are connected throughout the learning pathways.

The “Guided Instruction” section in the Teacher Edition includes the process standard numbers for each lesson. For example, in lesson 18, “Calculate Circumference and Area of Circles,” the section indicates that “[TEKS} 7.1F: Analyze relationships” and “[TEKS] 7.1G: Justify ideas using precise mathematical language” should be incorporated to guide students through each problem. The “Learn Together: Exploring Circumference” activity in lesson 18 prompts students to use a piece of string and a ruler to measure the circumference and the diameter of three circular objects. Then, students should analyze the relationship between the circumference and the diameter of each circle to connect their models to the circumference formula. While this activity requires students to analyze relationships, there is no description of how TEKS 7.1F 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 7 TEKS” section in the Teacher Edition provides an overview of where process standards are incorporated into the lessons. Each TEKS process standard is listed in a table with the corresponding lessons. Each lesson planner includes a section that identifies the process standards that are incorporated in the lesson. For example, lesson 2, “Add and Subtract Rational Numbers,” includes mathematical processes for TEKS 7.1A, TEKS 7.1B, and TEKs 7.1E. These same process standards are indicated in the sidebar for the “Guided Instruction” section to “guide students through each problem using mathematical processes.”

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

Lessons provide opportunities for students to think mathematically, persevere through problem solving, and make sense of mathematics. In lesson 2, “Add and Subtract Rational Numbers,” the “Understand the TEKS” and “Guided Instruction” section sidebar questions in the Teacher Edition help students think about and make sense of mathematics. For example, the educator can ask questions such as “Why is it helpful to change subtraction to addition when working with rational numbers?” and “How does writing each mixed number as an improper fraction make subtraction or addition easier?” Additionally, the “Critical Thinking” activity prompts students to add and subtract integers using expressions and number lines. Challenge questions for this activity prompt students to persevere and extend their thinking for each problem. For example, one challenge question in lesson 2 asks students to “represent the expression -1.8 - 1/5 on a number line and simplify the expression.” At the end of the lesson, the “Exit Ticket” activity provides an opportunity to independently write and simplify an expression to solve for how much the temperature dropped overnight.

In lesson 32, “Make Inferences from Random Samples,” students engage in problem-solving that promotes perseverance and statistical reasoning. In the “Activate Prior Knowledge” section in the Teacher Edition, students analyze sample data and discuss how a random sample can be used to make predictions about a larger population. The “Understand the TEKS” and “Guided Instruction” sections require students to interpret tables, graphs, and proportions; distinguish between samples and populations; evaluate whether samples are representative; and make evidence-based inferences. Rather than applying a single procedure, students must analyze the context of the data, determine whether conclusions are reasonable, and justify their reasoning using statistical evidence. Additionally, the “Monitoring Understanding and Feedback” section encourages educators to ask probing questions that help students reconsider misconceptions, justify statistical conclusions, and persevere when analyzing unfamiliar data sets. “Critical Thinking,” “Practice,” “Assessment,” and “Exit Ticket” activities require students to analyze statistical situations, justify conclusions, and verify the reasonableness of their inferences.

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

Lesson materials support students in understanding, explaining, and justifying that there can be multiple ways to solve problems and complete tasks. In lesson 14, “Solve One-Variable Inequalities,” students are encouraged to solve one-variable inequalities using models or the algorithm and graph the solution on a number line. For example, the “Critical Thinking” activity and the challenge questions prompt students to explain and justify their steps when finding a solution. Two challenge questions ask students to write and solve their own two-step inequality, then create a bar model for the same inequality. Additionally, “Learn Together” activities for lesson 14 support students by helping them solve inequalities with bar models and the algorithm, represent solution sets on number lines, and identify different values that make the inequality true. Students are expected to discuss their approach to finding their solutions.

In lesson 7, “Solve Ratio and Rate Problems,” students are encouraged to recognize and justify multiple approaches for solving proportional reasoning problems. In the “Guided Instruction” section, students solve problems using unit rates, proportions, ratio tables, equations, and visual models while explaining why each strategy produces the same solution. Educator questioning in the Teacher Edition sidebar prompts students to justify their choice of method, compare the efficiency of different approaches, and explain how multiple representations communicate the same proportional relationship. The “Monitoring Understanding and Feedback” section in the Teacher Edition prompts educators to ask students how they solved a problem, whether another strategy could also be used, and why different methods are mathematically valid. Additionally, the “Learn Together” activity encourages students to compare multiple solution strategies and explain the advantages of each approach. “Critical Thinking” tasks prompt 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 solve, represent, interpret, and justify ratio and rate problems 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.

Lessons are designed to require students to make sense of mathematics through multiple opportunities for students to do, write about, and discuss math with their peers and/or educators. For example, the “Critical Thinking” activity in lesson 3, “Multiply and Divide Rational Numbers,” involves explaining how to simplify multiplication expressions and create models to find a quotient. “Learn Together” activities in this lesson prompt students to create a poster that summarizes sign rules, identifies errors, and explains the steps for simplifying multiplication and division expressions. Additionally, “Extension” activities prompt students to write an assessment and questions on real-world scenarios involving rational numbers. In the first “Extension” activity, students are expected to “present and defend their assessment questions and answers to the class.”

In lesson 30, “Solve Problems Using Data Displays,” students make sense of mathematics by analyzing data, drawing inferences, and discussing data representations throughout the instructional sequence. In the “Activate Prior Knowledge” section in the Teacher Edition, students create a percent bar graph and discuss comparisons of data. The “Understand the TEKS” and “Guided Instruction” sections require students to interpret various types of graphs, compare data using ratios, and explain how ratios can be used to make predictions. Additionally, “Learn Together” activities require students to collaborate with their peers to analyze sample data, compare data to determine ratios or percentages, and make predictions about the data. “Critical Thinking” tasks prompt students to evaluate data representations, justify conclusions, and explain how to use a graph to find raw data. “Practice,” “Assessment,” and “Exit Ticket” activities \require students to solve problems, write mathematical explanations, and discuss solutions with their peers and educators.

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

The “ELPS Language and Discourse Support” section that is included before each lesson in the Teacher Edition helps educators guide students to share and reflect on their problem-solving approaches. For example, in lesson 2, “Add and Subtract Rational Numbers,” students are expected to explain how signs and operations affect a result by “prompting them to reference number line movement and the rules for adding rational numbers.” Educators should also prompt students to present an argument with multiple entry points by explaining “whether ‘the signs are the same’ or ‘different’ and how they used absolute value or changed subtraction to addition.” The prompt for justification asks students to “explain why subtraction becomes addition in this problem.” Additionally, “How Am I Doing?” boxes in both the student pages and the sidebar of the Teacher Edition guide educators and students to reflect on the lesson. The educator is instructed to “circulate and have them explain how they chose the operation and determined the sign of their answer.”

In lesson 16, “Represent Linear Relationships Using Verbal Models and Equations,” educators are provided with embedded guidance to facilitate student explanations, arguments, justifications, and multiple points of entry during problem solving. In the “Guided Instruction” section, educator prompts encourage students to explain the different parts of linear equations, justify why a particular representation is appropriate, and compare the efficiency of different solution methods. The “Monitoring Understanding and Feedback” section that is included before the lesson provides questioning strategies that prompt students to defend their reasoning, reflect on the appropriateness of their solution methods, and explain why their mathematical conclusions are valid. Students are encouraged to approach linear relationships using multiple entry points, including graphs, tables, equations, and real-world contexts. The “From Oral Reasoning to Written Justification” section further guides educators in helping students transition from verbal explanations to written mathematical justifications. Additionally, the “Learn Together” activities require students to collaborate with their peers; write linear equations; and explain the meaning of slope, y-intercepts, and variables in context. “Critical Thinking” tasks require students to defend their reasoning and explain how to write an equation to represent a table. “Practice,” “Assessment,” and “Exit Ticket” activities provide opportunities for students to explain, justify, and reflect on their problem-solving approaches while communicating with their peers and educators.

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 3, “Multiply and Divide Rational Numbers,” this section instructs educators to listen to students’ explanations. They should also “acknowledge correct reasoning using precise mathematical language and prompt students to justify how they determined the sign of a product or quotient.” Additionally, this section provides questions based on whether or not students make errors and/or demonstrate understanding. For errors, educators can ask questions such as “How did you determine the sign of the product or quotient?,” “What step tells you when to use the reciprocal?,” and “Why did you rewrite this mixed number before multiplying and dividing?” To extend student thinking, educators can ask, “Why do the sign rules work for all rational number multiplication and division?” and “How would you explain dividing by a fraction to someone else?”

In lesson 27, “Determine Probability Related to Compound Events,” embedded educator guidance provides explanatory feedback through the “Monitoring Understanding and Feedback” section in the Teacher Edition. Educators are prompted to listen to students’ explanations as they identify whether events are independent or dependent, organize outcomes in a list or tree diagram, and find the probability of a compound event. The materials identify misconceptions such as failing to adjust the second probability, miscounting outcomes, or using the wrong operations. Educators should 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 students’ reasoning as they connect events to sample spaces. 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.