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

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

The materials include an Alignment Guide that outlines the TEKS, the ELPS, and the concepts that are covered. Educators can use the “Lesson correlation to the grade 2 TEKS” chart to locate lessons that address specific TEKS. The “English Language Proficiency Standards (ELPS) Alignment” chart shows how recurring components align with the ELPS. The “Horizontal and vertical progression” table includes a rationale for how concepts and skills connect across grade levels (vertical alignment) and within the same grade level (horizontal alignment), as designed in the materials.

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

Evaluation for 1.1b
Materials include an implementation guide with usage recommendations and strategies for effective educator use in various contexts, 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 five core components of the lesson structure, suggested lesson pacing, assessment timing, and tips for use, including differentiation and maximizing instructional time.

Additionally, each lesson planner includes instructional supports that are aligned to students’ needs, such as tips for adjusting instruction for whole-group (tier 1), small-group (tier 2), or individual instruction (tier 3); ELPS language and discourse supports; and detailed instructional design strategies. These tools are designed 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 2 TEKS,” “ELPS alignment,” and “Horizontal and vertical alignment” tables together act as a TEKS correlation guide that includes recommended skill entry points. The “What’s Inside the Teacher Edition: Full-Length Practice Tests” and “Tracking and Pacing Charts” front matter pages direct educators to practice tests (diagnostic assessments) and student tracking charts in the appendix that, when paired with the tables in the front matter, 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. This platform automatically scores these tests, and educators can use detailed reports to identify strengths, address gaps, and target instruction accordingly.

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

The “What’s Inside the Teacher Edition: Chapter Overviews” and “Teacher Lesson Sequence” sections outline protocols and guidance on how educators should read the chapter overviews at the beginning of each chapter and read the lesson planners at the beginning of each lesson. The outline indicates that chapter overviews summarize the mathematical focus and progression of learning across the chapter. Additionally, lesson planners show how each lesson builds on prior learning, connects to future concepts, explains how students engage in the lesson, and provides prompts to assess understanding. The “Instructional Planning” section provides further guidance on using chapter overviews and lesson planners to plan lessons effectively, ensuring 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 2 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” is a quick-reference checklist with look-fors to guide observations. The “Instructional Leader Strategies Guide” section provides targeted actions for addressing pacing, differentiation, extension, assessment use, and data-driven instruction.

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

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

Each lesson in the Teacher Edition for grade 2 includes a lesson planner that clearly outlines learning objectives that are aligned to the TEKS and the ELPS plus embedded educator and student resources. Also provided are instructional components that are aligned to the 5E instructional model and assessment resources that support and measure mastery of the TEKS and the ELPS. The “Core Lesson Design and Pacing” section outlines the lesson’s structure and provides suggested time frames for each lesson component.

Evaluation for 1.2b
If designed to be adaptive, materials include responsive 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 provided family letters. It includes both English and Spanish versions 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 representing, comparing, and analyzing whole numbers. The family letter also includes “Questions to Ask Your Child,” “Practice Together at Home,” “Math Words to Know (Lesson),” and “How You Will Know Your Child is Making Progress?” sections.

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

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

Each chapter overview includes an “Assessment” section that identifies assessments as formative or summative. This section also describes the instructional purpose of each assessment type within the lesson’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 guidance to ensure consistent, accurate administration. For example, the table indicates that students must complete assessments independently in quiet or timed settings, and print and online administration options are available. The “Suggested Assessment Timing” section provides further guidance on timing for chapter and practice tests.

The “Assessment” section in the front matter of each chapter of the Teacher Edition prompts 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 time frames for lesson and chapter assessments.

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

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

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

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

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

The “Assessment types, purposes, and administration” table indicates that each lesson assessment, exit ticket, and “Building Stamina” chapter test is a formative or summative assessment. However, the “Assessment” section 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 3 assessment includes DOK 2- and DOK 3-level questions, and question types include multiple-choice, inline choice, and drag-and-drop.

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

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

“Practice” and “Assessment” sections in each lesson include scoring information and guidance for interpreting students’ performance in the Teacher Edition. The sidebar for the “Practice” section includes common errors and hints so educators can interpret students’ responses. The sidebar for the “Assessment” section gives tips for striving students and emergent 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 using patterns in students’ responses to guide instruction in the following lesson. For example, the lesson 1 exit ticket suggests, “If many students struggle with regrouping hundreds into tens or accurately recording digits in the place-value chart, begin the next lesson with a brief whole-group review using base 10 models to demonstrate equivalent representations.”

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, helping educators create a more coherent, purposeful approach.

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

The materials include tools for both educators and students to track progress and growth. Educator-facing progress-monitoring tools are provided 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 student performance by the TEKS standards; by individual student, small-group, or whole-class settings; and by question type, item difficulty, and DOK level.

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

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

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 “Understand the TEKS” in the lesson 2 introduction, the educator can ask, “How does place value help you write numbers in expanded form?” Then, the educator can use the sample response to assess student 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 ask students to explain how they represented numbers in expanded and word form. The note directs educators to listen for misconceptions about place value and the sequencing of the word form.

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, a wraparound provides targeted supports for striving students and emergent bilingual students through visual models, language scaffolds, and guided practice, helping students access, process, and explain their learning.

“Common Misconceptions and Targeted Supports” sections in the Teacher Edition, located before each chapter, break down the TEKS by lesson. These sections include scaffolded educator guidance that targets students who have not yet reached proficiency in prerequisite or grade-level concepts and skills. This 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 place-value charts, base 10 models, number lines, counters, ten frames, and sentence frames to reinforce representing, comparing, and analyzing whole 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 course. The “ELPS Language and Discourse Support” section before each lesson provides educators with guidance on supporting mathematical discourse and language development for emergent bilingual students. This section supports academic language development through proficiency-level scaffolds that help students listen, speak, read, and write about their mathematical reasoning. For example, lesson 1 provides educator guidance on facilitating oral explanations of mathematical concepts and prompts students to describe place-value changes using academic language.

The materials also include home-language supports, Spanish cognates, and a “Words to Know” feature that helps students clarify meaning and connect familiar language to mathematical terminology. Additionally, the materials guide students from oral reasoning to written justification during “Critical Thinking” and “Exit Ticket” activities, providing ongoing opportunities to develop and apply academic vocabulary in context. While the materials include explicit educator guidance throughout each lesson for preteaching and embedded supports for developing academic language, they do not include language supports for unfamiliar references in text.

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

The “Supports for All Learners” section in the Teacher Edition outlines challenge and extension opportunities that are available for challenge-ready students. The table identifies extension prompts, “Critical Thinking” activities, and “Extension” activities as resources for these 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 for lesson 1 prompts students to determine which numbers in expanded form are equivalent and requires them to prove their thinking. 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 5 in the “Above-Level Extension Bank” section prompts students to explore the concept of “What is 10 less than 4?” This question introduces the concept of negative numbers and provides an opportunity for students to engage with above-grade-level content and skills.

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

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

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

The “Student Lesson Sequence” section describes the “Critical Thinking” component of each lesson, which provides students with options to demonstrate understanding through multistep and real-world problems. For example, the lesson 1 “Critical Thinking” activity requires students to explain, compare, solve, and justify using a variety of strategies to compose and decompose whole numbers. 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’s sidebar guides educators to support students by listening for accurate concept development and correcting misconceptions as students explain their thinking for each question.

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

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

Lesson materials in the Teacher Edition include explicit (direct) prompts and guidance so educators can help students build knowledge by activating prior knowledge and anchoring big ideas, using the front matter and wraparound for each lesson. For example, the “Lesson 1 Planner” and “Activating Prior Knowledge” sections provide specific prompts and guidance for educators to activate knowledge of building and breaking apart numbers through 120 in grade 1 and moving toward composing and decomposing numbers up to 1,200 in grade 2. This guidance helps educators activate prior knowledge of grade 1 concepts and connect these concepts to the grade 2 learning progression. Additionally, the wraparound provides guidance and questions throughout the first lesson to help the educator guide students in making connections between place-value representations, place-value chart entries, and written explanations.

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

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

Each lesson in the Teacher Edition includes educator guidance for effective lesson delivery and facilitation. Lessons include whole-group discussion, small-group differentiation, and independent practice, among other approaches. For example, lesson 3 includes a “Learn Together” activity that engages the whole class by asking student pairs to demonstrate how to compare numbers and explain their thinking to the class using place-value language. The “Differentiation” activity guides educators to ask striving students to compare numbers in a place-value chart, moving one place at a time until the digits differ. Additionally, students work independently through “Critical Thinking” questions to create a place-value chart and use it to order three numbers from greatest to least.

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

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

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

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

The “Instructional Formats and Use” section indicates that educators can use enrichment sessions, multistep “Extension” activities, real-world application problems, and “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 before each lesson guides educators in extending students’ thinking by asking extension questions. For example, in lesson 3, the educator can ask, “How would you decide which number is greater if the hundreds digits were the same?” or “Why can you stop comparing once you find the first place where the digits are different?”

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 misconceptions such as switching tens and ones, omitting a place, using digit names instead of place-value amounts, or writing word form in the wrong order.” Additionally, tiered support helps educators adjust instruction based on students’ understanding of place value.

The sidebar in the Teacher Edition includes embedded prompts and guidance to help educators provide timely feedback throughout each lesson. Sidebar notes prompt educators to monitor students’ understanding through questioning, discussion, and observation of student responses. This guidance helps educators elicit 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 composing and decomposing whole numbers using place-value models. 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. For example, preproduction students receive visual cues and sentence frames, while advanced high students receive open-ended questions that require detailed justification.

The Teacher Edition wraparound for each lesson includes an "EBL Tip" box for guided instruction and an "SL/EBL Tip" box for the lesson assessment. These boxes include sentence stems and discussion guidance for the teacher at all levels of language proficiency to engage students in using increasingly more academic language.

Evaluation for 3.3b
If designed to be adaptive, materials include embedded linguistic accommodations for all levels of language proficiency [as defined by the English Language Proficiency Standards (ELPS)], which are designed to engage students in using increasingly more academic language.

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

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

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

The “ELPS Language and Discourse Support” section 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 “ELPS Support” section in the chapter 1 overview outlines supports that are embedded throughout the chapter. These supports are designed to make place-value reasoning and number relationships accessible to emergent bilingual students. This section outlines visual representations, language frames, vocabulary reinforcements, and collaborative talk routines that help educators implement guided mathematical discourse to develop academic vocabulary and increase comprehension through oral and written discourse.

The “ELPS Language and Discourse Support” section that is included before each lesson in the Teacher Edition includes guidance to facilitate mathematical discourse, with specific focus on “During Learn Together and Guided Instruction,” “Home Language and Cognates as a Bridge,” and “From Oral Reasoning to Written Justification” sections. This lesson’s front matter, in conjunction with activities and emergent bilingual student tips 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 cross-linguistic 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 4, “Multi-Step Addition and Subtraction,” students develop an understanding of how addition and subtraction can be used to represent, solve, and generate problem situations using whole numbers within 1,000. Throughout the chapter, students practice adding and subtracting within 1,000. When adding and subtracting numbers, students work in real-world problem-solving contexts throughout the chapter, with varied activities. Students use a variety of strategies, including place-value charts, number lines, and algorithms. Practice and assessment opportunities throughout the chapter, including “Guided Instruction” activities, “Extension” activities, and “Exit Ticket” assessments, require students to demonstrate their knowledge and skills to solve problems.

“Guided Instruction,” “Critical Thinking,” “Learn Together,” and “Practice” activities for lesson 1, “Compose and Decompose Numbers,” give students opportunities throughout the lesson to compose and decompose numbers in both standard and nonstandard ways. Various practice activities require students to demonstrate depth of understanding aligned with the TEKS. For example, question 1 in the “Critical Thinking” activity requires students to “Show the number 698 in two different ways.” In addition, the lesson 1 assessment and exit ticket provide students with further opportunities to compose and decompose numbers in both standard and nonstandard ways. For example, the exit ticket assesses whether students can show “1,176 using place-value groups in more than one way.” Together, these practice opportunities and assessments require students to represent the same quantity in more than one way, showing depth of understanding of place value and number representations.

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.

“Differentiation,” “Critical Thinking,” and “Learn Together” activities for lesson 1, “Compose and Decompose Numbers,” provide students with questions and tasks that increase in rigor and complexity, leading to grade-level proficiency in composing and decomposing numbers. For example, “Differentiation” activities provide scaffolded support to model regrouping and use a place-value chart. The “Critical Thinking” activity prompts students to compose and decompose numbers in pictorial form and with a place-value chart. “Learn Together” activities prompt students to compose and decompose numbers using multiple representations. Questions and tasks in this lesson focus on grade-level proficiency and do not include composing and decomposing numbers above 1,200.

“Critical Thinking” sidebar challenge questions and “Extension” activities for lesson 1, “Compose and Decompose Numbers,” increase in rigor and complexity, leading to grade-level proficiency in composing and decomposing numbers. For example, the first “Extension” activity provides three expanded forms of numbers and asks students to identify two that are equivalent and explain their reasoning. Then, students are asked to “create their own set of three for a classmate.” The second “Extension” activity presents three statements and asks students to determine whether each statement is true or false. Next, students “justify using a model, equation, or explanation.” Finally, students write their own true-false statements about composing and decomposing numbers. While extensions increase in rigor and complexity within 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 of the Appendix includes one “Extension” activity per lesson that provides students with an opportunity to explore above grade-level content. For example, the “Extension” activity for lesson 9 gives students an opportunity to explore fractions beyond one whole. While this activity introduces students to grade 4 content, this exploration does not lead to above grade-level proficiency in the mathematics TEKS.

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

The “Horizontal and vertical progression” chart in the Teacher Edition for grade 2 demonstrates coherence horizontally across concepts within the grade level by connecting big ideas. Additionally, chapter overviews and lesson planners further detail horizontal alignment by connecting big ideas across the curriculum. For example, the “Horizontal/Vertical Progression Summary” section in chapter 1, “Represent, Compare, and Analyze Whole Numbers,” states, “Students begin by building and regrouping numbers with place-value units, then connect those quantities to standard, word, and expanded form.” Additionally, the materials demonstrate coherence horizontally across concepts in chapter 4, “Multi-Step Addition and Subtraction,” by connecting place-value understanding to addition and subtraction strategies through concrete and pictorial representations such as base 10 blocks. Guidance encourages educators to explain that regrouping is grounded in place-value principles, thereby reinforcing key mathematical relationships and conceptual understanding. These experiences help students recognize patterns and relationships among mathematical concepts while deepening their understanding of grade-level TEKS.

Evaluation for 4.2b
Materials demonstrate coherence vertically across concepts and grade bands, including connections from grade K–6, by connecting patterns, big ideas, and relationships.

Each chapter overview and lesson planner in the Teacher Edition demonstrates coherence vertically across concepts and grade bands by connecting patterns, big ideas, and relationships. For example, the chapter 8, “Data Analysis,” overview indicates that students must interpret and create pictographs and bar graphs, use data displays to solve one-step problems, and draw conclusions and make predictions based on data. This section explicitly describes a progression from basic graph reading and construction to more advanced data analysis and evidence-based reasoning. This progression builds on foundational data concepts that were introduced in earlier grades. It prepares students for future learning involving larger data sets, more complex graph scales, multistep data problems, and deeper analysis of patterns and relationships. In lesson 35, “Interpret Bar Graphs,” the “Learning Progression” section in the lesson planner demonstrates the progression from grade 1 to grade 3 TEKS (e.g., 1.8B to 2.10A and 2.10B to 3.8A) so educators can ensure a smoother transition between concepts across grade levels. Additionally, the “Horizontal and vertical progression” table in the front matter of the Teacher Edition shows how math concepts and skills connect across grade levels. The table indicates that lesson 35 “extends grade-1 data displays [and] prepares for grade 3 interpreting scaled bar graphs and solving one- and two-step data problems.”

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

The “Lesson Flow and Instructional Routines” section that is included before each lesson demonstrates coherence across lessons by connecting students’ prior knowledge of concepts and procedures to those that will be learned at the current grade level. This section outlines routines that educators can use to bridge from a previous lesson, activate prior knowledge, and integrate previously learned skills. For example, this section in chapter 1, lesson 2, “Represent Numbers,” prompts educators to “build on lesson 1 by using place-value relationships to connect digits to the values of hundreds, tens, and ones in each representation.” Additionally, this section states that it “supports grade-3 work extending number representations to 100,000,” 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 grades.

Chapter 4, “Multi-Step Addition and Subtraction,” demonstrates coherence across lessons and activities by intentionally connecting students’ prior understanding of addition and subtraction to increasingly complex problem-solving applications. This chapter builds on foundational concepts that were developed in earlier grades, including representing addition and subtraction situations, understanding unknown quantities, and using equations to model mathematical thinking. Students extend this knowledge by solving one-step and multistep problems involving unknowns in any position and generating problem situations from mathematical number sentences. For example, the “Activate Prior Knowledge” section before lesson 17, “Solve for the Unknown,” in the Teacher Edition creates a bridge to solve addition and subtraction word problems. Students start with a hands-on activity and use counting or connecting cubes to find the missing number that makes each number sentence true. Then, students write an equation to match a word problem and talk with a partner about what the unknown value represents. Throughout the chapter, lessons progressively increase in complexity, helping students connect previously learned concepts and procedures to new learning while they develop mathematical reasoning and problem-solving skills that are necessary for success in the current grade.

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

The “Cumulative Skills Review” section that follows each chapter provides spaced retrieval opportunities with previously learned skills and concepts across learning pathways. For example, the “Cumulative Skills Review: Chapter 5” section provides three problems in which students utilize skills from chapters 2, 3, and 4. 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 1 prompt states, “This is a chapter 2 skill; how did you count fractions beyond one whole there?” Additionally, “Fluency Lab” activities provide spaced retrieval opportunities with previously learned skills for six lessons. These activities require students to revisit and apply previously taught mathematical concepts to reinforce current learning.

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

The “Cumulative Skills Review” section that follows each chapter provides interleaved practice opportunities with previously learned skills and concepts across learning pathways. For example, the “Cumulative Skills Review: Chapter 4” section provides three problems in which students use 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 models and representations for mathematical concepts and situations.

The “Guided Instruction” section in lesson 1, “Compose and Decompose Numbers,” provides students with an opportunity to interpret, analyze, and evaluate models and representations for composing and decomposing numbers. For example, as students decompose the number 157 in more than one way, the educator asks, “When you build 157 with base 10 blocks, what does each part represent, and how do you know the blocks match the number 157?” Additionally, when using models to compose the number 1,134, the educator asks, “After composing 10 hundreds into one thousand, how can you figure out what is left without counting the blocks one by one? How can you use what you know about hundreds and thousands to reason it out?”

The overview for chapter 4, “Multi-Step Addition and Subtraction,” outlines opportunities for students to interpret, analyze, and evaluate models and representations of mathematical concepts. The “Purpose of the Chapter” section states that students are expected to connect story contexts, equations, and representations while solving multistep problems involving whole numbers within 1,000. In lesson 16, “Solve Multi-Step Problems,” students interpret and analyze multiple representations throughout the lesson. In the “Bridge: During Guided Instruction” section, students analyze multistep problems by connecting story events to equations and evaluating how the solution to one equation becomes the starting value for the next. In the second problem, students use a table to organize information about muffins that were baked, purchased, and donated. Then, students analyze the representation to determine the remaining quantity that is needed. Additionally, the “Differentiation: Use a Step Table to Organize Information” activity prompts students to interpret and create a step table representation, then convert each row into an equation. Together, these opportunities require students to interpret, analyze, and evaluate mathematical models and representations to solve multistep addition and subtraction situations.

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

In lesson 1, “Compose and Decompose Numbers,” questions and tasks provide opportunities for students to create concrete and pictorial representations to compose and decompose numbers. For example, the “Learn Together: Draw and Decompose” activity allows students to draw base 10 pictorial models to represent a number between 300 and 1,200. After they draw the number in a standard way, students then “redraw it in a different way by decomposing one place value.” Additionally, the “Learn Together: Compose and Compare” activity provides students with an opportunity to build numbers using base 10 blocks. Then, students suggest ways to decompose one part of the number “until the class has generated at least three different ways to compose and decompose the same number.”

The “Guided Instruction” section in In lesson 1, “Compose and Decompose Numbers,” prompts students to divide a flatbread into four equal parts, divide a shape into eight equal parts, and identify and name the fractional parts of each whole. In the “Differentiation: Create Halves, Fourths, and Eighths” activity, the educator directs students to use paper circles or rectangles and fold them into halves, fourths, and eighths. Additionally, the “Critical Thinking” activity prompts students to divide real-world shapes into equal parts by drawing a model and naming the parts. Questions and tasks in this lesson provide multiple opportunities for students to create concrete and pictorial models to understand that fractional pieces are equal parts of a whole.

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

The “Critical Thinking” activity questions for lesson 16, “Solve Multistep Problems,” provide students with opportunities to apply conceptual understanding to solving multistep problems. Students explain and justify the steps that are used to solve multistep problems. Additionally, in the “Learn Together: Solve and Compare Paths” activity, students solve a problem using both the standard algorithm and another strategy and explain how both approaches lead to the same answer.

In lesson 34,” Interpret Pictographs,” students apply conceptual understanding of data organization and pictographs to new situations. During guided instruction, students use pictographs to answer questions about quantities that are represented by symbols and apply their understanding of keys to determine totals. In the “Critical Thinking” section, students analyze and solve data-based problems involving home runs, favorite sports, and survey results, which requires them to apply pictograph concepts in unfamiliar contexts. The “Learn Together: Build and Compare Class Pictographs” activity requires students to collect, organize, represent, and analyze class survey data using a pictograph and key. Additionally, the “Extension: Same Data, Different Keys Challenge” activity asks students to create new pictographs using different keys and explain how the representation changes while the underlying data remains the same. Together, these opportunities require students to transfer and apply their conceptual understanding of pictographs, keys, and data analysis to new problem 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 Labs” sections are designed to build students’ automaticity and fluency in numbers and operations. For example, “Fluency Lab 3A” prompts students to compute addition and subtraction facts within 20 and compare which strategy choice is faster in solving each problem.

In lesson 16, “Solve Multistep Problems,” students develop automaticity and fluency through activities that require efficient computation and application of previously learned skills. During the “Bridge: From One Step to Two Steps” activity in the Teacher Edition, students review and solve one-step addition and subtraction problems before extending those skills to multistep situations. The “Integrate Prior Skills” section guides educators in having students apply place-value strategies and the standard algorithm to compute accurately and efficiently when solving multistep problems. Additionally, the “Differentiation: Model the Standard Algorithm” activity provides opportunities for students to practice computational procedures using equations and representations. Together, these experiences strengthen students’ fluency in addition and subtraction while supporting successful completion of grade-level mathematical tasks that involve multistep problem-solving.

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 for lesson 13, “Subtract Two-Digit Numbers,” prompts students to use both mental math and a place-value chart to solve subtraction problems. The challenge question in the sidebar of the Teacher Edition asks students to “find the difference between 56 and 29 using mental math and the standard algorithm, and explain how both strategies show the same difference.” “Fluency Lab 3C” is paired with this lesson. Students must solve two-digit subtraction problems and evaluate which strategy helped in solving those problems more easily. Students also conduct an error analysis and reflection on efficiency to further develop their accuracy and efficiency in subtracting two-digit numbers.

In lesson 16, “Solve Multi-Step Problems,” students apply efficient, flexible, and accurate procedures while solving multistep problems. During guided instruction, students determine which operations are needed at each stage of a problem and use equations to represent and solve the situation. The “Integrate Prior Skills” section prompts educators to require students to apply previously learned place-value strategies and the standard algorithm to compute accurately and efficiently. Additionally, the “Differentiation: Use a Step Table to Organize Information” activity encourages students to organize information strategically before selecting procedures to solve a specific problem. In contrast, the “Differentiation: Model the Standard Algorithm” activity provides opportunities for students to apply standard computational procedures within a meaningful context. Together, these experiences provide repeated opportunities for students to practice and refine efficient, flexible, and accurate mathematical procedures throughout the lesson.

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

Opportunities are provided throughout the lessons to evaluate representations, models, strategies, and solutions for efficiency and accuracy. For example, the “Critical Thinking” activity for lesson 12, “Add Up to Four Two-Digit Numbers,” prompts students to evaluate whether the sum of number sentences is affected by the order of the numbers. The “Learn Together” section that follows prompts students to evaluate grouping strategies for efficiency. “Fluency Lab 3B: Add Multi-Digit Numbers” is paired with this lesson. In “Fluency Lab” activities, students receive opportunities to choose strategies and evaluate solutions for efficiency and accuracy. While students can be flexible in the strategies they use, “Fluency Lab” activities are provided for only six of the 42 lessons.

In lesson 16, “Solve Multi-Step Problems,” students evaluate representations and solution strategies throughout the lesson. During guided instruction, students analyze multistep-problem situations by determining how each equation represents a specific action within the story. Then, they evaluate whether the solution from one step appropriately supports the next step in the process. In the second problem, students use a table to organize information and evaluate how the representation helps identify the operations that are needed to solve the problem accurately. Additionally, the “Differentiation: Use a Step Table to Organize Information” activity requires students to compare information that is presented in a visual organizer with corresponding equations. The “Differentiation: First, Next, Last Cards” activity encourages students to evaluate the sequence of events and determine whether their mathematical representation accurately reflects the problem situation. Together, these opportunities require students to analyze and evaluate mathematical representations, models, strategies, and solutions for efficiency and accuracy throughout the lesson.

Evaluation for 5.2d
Materials contain guidance to support students in selecting increasingly efficient approaches to solve mathematics problems.

Each “Fluency Lab” provides guidance to help students select the most efficient approaches to operations with whole numbers. For example, “Fluency Lab 3B” prompts students to consider more efficient strategies by asking, “Can you break apart the numbers or add tens first to make it easier?” and “When would adding tens and ones be easier than using the standard algorithm?” Students actively reflect on when decomposing numbers into tens and ones provides a faster mental pathway and when the formal standard algorithm is a more helpful and efficient tool.

In lesson 34, “Interpret Pictographs,” students receive guidance for selecting efficient approaches when interpreting and representing data. During guided instruction, students are taught to first identify the title, categories, and key before interpreting quantities that are represented by symbols, providing a systematic process for analyzing pictographs. “Monitor Student Thinking” prompts in the Teacher Edition guide educators to help students focus on the key as an efficient tool for determining quantities rather than counting individual items. In the “Compare Strategies” section, students examine pictographs that use different keys and discuss how the choice of key affects the efficiency of representing and interpreting data. Additionally, the “Extension: Same Data, Different Keys Challenge” activity encourages students to consider how different keys can make a pictograph easier to create and interpret while still accurately representing data. Together, these supports help students select increasingly efficient approaches for solving problems involving data representations.

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

The “Purpose of the Chapter” section 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, “Represent, Compare, and Analyze Whole Numbers,” states, “Students build a coherent understanding of whole numbers up to 1,200 by composing and decomposing numbers, representing numbers in multiple forms, comparing and ordering values, locating numbers on number lines, identifying numbers that are 10 more, 10 less, 100 more, and 100 less, and determining whether numbers are even or odd.” Additionally, this section indicates that students “use place-value charts, base 10 models, number lines, equal-group representations, and symbolic notation to explain their thinking.”

In chapter 8, “Data Analysis,” the overview includes statements for both conceptual and procedural elements of the TEKS that are included in the lessons for this chapter. The “Purpose of the Chapter” section states, “Students develop a connected understanding of data by creating and interpreting pictographs and bar graphs, using graph data to solve one-step problems, and drawing conclusions and making predictions from the graphs.” Additionally, this section indicates that the chapter “strengthens students’ ability to compare categories, choose operations based on questions, and distinguish between what data shows now and what it may suggest for the future.”

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

The materials provide opportunities for students to use concrete models, pictorial representations, and abstract models, as required by the TEKS. In the overview for chapter 4, “Multi-Step Addition and Subtraction,” in the Teacher Edition, the “TEKS Support” section indicates that students can engage with a variety of representations, including counters, base 10 models, step tables, start-change-result organizers, part-part-whole diagrams, and equations. These supports provide opportunities for students to move among concrete, pictorial, and abstract representations as they develop an understanding of multistep addition and subtraction situations.

Students use concrete, pictorial, and abstract models throughout lesson 16, “Solve Multi-Step Problems.” During the “Activating Prior Knowledge” and “Differentiation” activities, students use counters to model quantities and actions within story problems. Then, students use pictorial representations, such as step tables and organizational charts, to represent relationships among quantities and sequence the steps that are required to solve a problem. During guided instruction and independent problem-solving activities, students transition to abstract representations by writing and solving equations that model each step of a multistep situation. Additionally, the “Differentiation: Model the Standard Algorithm” and “Differentiation: Use a Step Table to Organize Information” activities connect concrete and pictorial models to symbolic equations. Together, these opportunities require students to use concrete, pictorial, and abstract representations in alignment with the grade 2 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 to help students connect, create, define, and explain representational models to abstract concepts. For example, the “Critical Thinking” activity for lesson 11, “Recall Basic Addition and Subtraction Facts,” prompts students to “create a pictorial model to find the difference between 18 and 6.” Students use a part-part-whole table to connect to the number sentence. Additionally, the challenge question asks students to “write two different subtraction sentences that have a difference of 12.” Then, students explain how they know those facts are correct. Before the lesson, the Teacher Edition includes a hands-on task that uses counters and ten frames to activate students’ prior knowledge of making 10 to support the learning of addition facts. While “Activating Prior Knowledge” activities help students activate prior knowledge, they do not support students in connecting, creating, defining, or explaining concrete models to abstract concepts, as required by the TEKS.

The “Guided Instruction” section for each lesson is designed so students can work with educators to connect representational models to abstract concepts. For example, in lesson 34, “Interpret Pictographs,” students explain how the symbols in a pictograph correspond to numerical values and use the key to determine abstract quantities that are represented by the graph. “Critical Thinking,” “Practice,” “Assessment,” and “Exit Ticket” activities in the student pages for each lesson provide further support for students to meaningfully connect, create, define, and explain representational models to abstract concepts. For example, the “Critical Thinking” activity for lesson 34 prompts students to make a pictograph from a tally chart and “explain how the pictograph shows which sport is the favorite.” In addition to the student pages, the Teacher Edition wraparound provides activities that include support in connecting concepts with representational models. While the materials include concrete activities that are designed specifically for struggling students, the tasks in the Teacher Edition wraparound are not structured to connect concepts for students using a concrete-pictorial-abstract progression.

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

The “ELPS Language and Discourse Support” sections that are included before each lesson in the Teacher Edition guide educators in facilitating mathematical discourse and supporting language development. For example, in lesson 27, “Compose Three-Dimensional Solids,” this section prompts students to explain new solids they build by “stacking, joining, and combining solids such as cubes, prisms, cylinders, cones, and pyramids.” As students build these solids and become more comfortable, educators encourage them to “explain what stays the same about each solid; what changes in the new figure; and how they know whether the composed figure includes a cube, cylinder, cone, prism, or pyramid.” Additionally, this section provides sentence stems and questions to guide educators in helping students develop academic mathematical language. For example, educators can prompt justification by asking, “Why does stacking cubes make a rectangular prism?” or “How do curved surfaces help identify the solids used?” When asking these questions, educators are guided to require students to connect solid names, attributes, and composition clearly.

In lesson 35, “Interpret Bar Graphs,” 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 describe graphs using appropriate mathematical vocabulary and explain comparisons between categories. The “Home Language and Cognates” and “Differentiated Language Support” sections within the table provide sentence stems, structured questioning, and opportunities for students at varying language proficiency levels to use vocabulary terms such as data, category, title, scale, equal intervals, greatest, fewest, compare, and interpret in oral and written explanations. Within the lesson, the “Understand the TEKS” section connects academic vocabulary to graph features and demonstrates how titles, labels, scales, and equal intervals communicate mathematical information. Guided instruction uses bar graphs, tally charts, questioning, and visual models to help students explain relationships among categories and justify interpretations using precise mathematical language. Additionally, activities in the lesson continue to reinforce mathematical vocabulary as students explain their reasoning, justify their conclusions, and communicate their interpretations of data. For example, the “Extension: Compare Two Bar Graphs” activity prompts students to draw two bar graphs with different sets of data using the same scale and “explain how the bar lengths help them compare the two sets of data.”

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

The sidebar in the Teacher Edition includes guidance for educators to scaffold, support, and extend students’ use of academic mathematical vocabulary in context. For example, the “EBL (Emergent Bilingual Learners) Tip” box in the “Guided Instruction” section of lesson 9, “Count Fractions Beyond One Whole,” provides sentence frames for different student proficiency levels using academic language such as whole, equal parts, and eighths. The “SL/EBL (Striving Learners/Emergent Bilingual Learners) Tip” box for the lesson assessment also provides sentence frames and guidance so educators can help students justify their answers using academic mathematical vocabulary. This box directs educators to ask students who demonstrate lower levels of language proficiency to point to each part, count the fractional parts, and provide sentence stems so students can describe the fraction that is represented by the model. For students who demonstrate higher levels of language proficiency, this box directs educators to “have students explain how they counted the parts across the models and justify their answers using vocabulary such as whole, equal parts, halves, and fourths.”

In lesson 35, “Interpret Bar Graphs,” embedded educator guidance supports students in using academic mathematical vocabulary throughout instruction. The “ELPS Language and Discourse Support” section in the Teacher Edition explicitly directs educators to encourage students to describe and interpret bar graphs using terms such as title, category, scale, equal intervals, data, compare, greatest, and fewest while explaining how graph features support their conclusions. The “Home Language and Cognates” section helps students connect familiar language to new mathematical vocabulary, while the “From Oral Reasoning to Written Justification” section encourages educators to move students from verbal explanations to written mathematical justifications using precise academic language. This progression from oral to written justification demonstrates how the materials extend students’ vocabulary beyond initial scaffolding. These embedded supports scaffold, reinforce, and extend students’ use of academic mathematical vocabulary during communication with both peers and educators.

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

The “Understand the TEKS” section of lesson 2, “Represent Numbers,” defines the vocabulary terms digits, standard form, word form, expanded form, and place value. This section includes examples of these terms plus some guidance on how they are related. For example, the text states, “Place value helps you write numbers in expanded form.” A place-value chart with an example is provided, plus an explanation for how to read the number and write it in each defined form.

Additionally, the Teacher Edition sidebar includes guiding questions to support students in developing academic language. One question states, “What is the connection between the word digit and the three forms of a number?” Following guided instruction, students are given opportunities throughout the lesson to work with their peers and discuss the connection between place value and different number forms. For example, during the “Learn Together: Write It Three Ways Relay” activity, students work together to write a number in different forms, and they are encouraged to “explain how they use place value to move between forms.” In the “Extension: Create the Conflict” activity, students create one correct and one incorrect expanded form of a number. Then, they explain to a partner “why the incorrect form does not match the standard form and identify the misconception.”

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 included before each lesson in the Teacher Edition guides educators on including partner talk and “Think-Pair-Share” opportunities for students to 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 11, “Recall Basic Addition and Subtraction Facts,” students work in pairs or small groups for the first “Learn Together” activity. They “discuss how changing the order of the addends keeps the same sum and how related subtraction facts connect to the same whole.” The second “Learn Together” activity asks students to work in small groups and “state a related subtraction fact that matches their addition fact.”

In lesson 17, “Solve for the Unknown,” 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 engage in partner talk to explain how they identified missing numbers and discuss what unknown values represent in story problems and equations. The “ELPS Language and Discourse Support” section encourages students to explain whether the unknown represents the start, change, or result, and discuss how numbers and operations relate to the story problem using mathematical vocabulary. “Differentiation,” “Learn Together,” and “Critical Thinking” activities require students to explain solution strategies, compare equations, and justify their reasoning with classmates using academic mathematical vocabulary. The materials 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” sections that are included before lessons in the Teacher Edition guide educators in anticipating students’ responses. For example, in lesson 1, “Compose and Decompose Numbers,” this section states, “Acknowledge correct reasoning and prompt students to explain why trading 10 ones for one ten or 10 tens for one hundred keeps the value the same.” This section also provides questions for when students demonstrate understanding, such as “How can the same number be shown in two different ways?” Also included before the lesson, the “Bridge: Getting Ready for Hundred” activity includes a set of three expected answers to a “Think-Pair-Share” prompt in which students build 120 in multiple ways. Additionally, educators are provided with a response to each guiding question in the Teacher Edition sidebar. Student inset pages for “Critical Thinking” and “Exit Ticket” activities provide one exemplar response for each question.

The “Monitoring Understanding and Feedback” section guides educators in supporting and redirecting inaccurate student responses. In lesson 1, this section states, “Listen for misconceptions such as confusing a digit with its value, miscounting base 10 blocks, or regrouping in a way that changes the number.” This section also provides questions for when students make errors, such as “If you trade one hundred for tens, what changes in the place-value chart?” Additionally, the Teacher Edition sidebar for the “Practice” activity provides a common error for each practice question plus a hint that educators can use to help guide struggling students.

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

The TEKS process standards are appropriately integrated into the materials. The lesson planner that is included before each lesson in the Teacher Edition describes how the lesson’s process standards are incorporated into learning objectives. The sidebar for the “Guided Instruction” section includes these same process standard numbers for the lesson. For example, in lesson 1, “Compose and Decompose Numbers,” the sidebar indicates that TEKS “2.1E: Organize and communicate ideas” and TEKS “2.1F: Analyze relationships” should guide students through each problem. During the second problem, educators are guided to prompt students to analyze place-value relationships by asking, “After composing 10 hundreds into one thousand, how can you figure out what is left without counting the blocks one by one? How can you use what you know about hundreds and thousands to reason it out?” Additionally, the “Building Stamina” chapter assessments and practice assessments indicate the process standard 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 1, “Compose and Decompose Numbers,” indicates that TEKS 2.1E and TEKS 2.1F are the mathematical processes included in that lesson. This section states that students will “use place-value models and representations to organize and record their thinking”; “analyze relationships between hundreds, tens, and ones when composing and decomposing numbers”; and “explain how different groupings can represent the same number.” While this section describes how the process standards are incorporated into the lesson, it does not explain how they are connected throughout the learning pathways.

The “Guided Instruction” section sidebar in the Teacher Edition includes the process standard numbers for specific lessons. For example, in lesson 10, “Recognize Examples and Non-Examples of Fractions,” the section states that TEKS “2.1F: Analyze relationships” and TEKS “2.1G: Justify ideas using precise mathematical language” should be incorporated to guide students through each problem. The “Learn Together: Create Examples and Non-Examples” activity in lesson 10 prompts students to divide a square into two equal parts and divide another square into two unequal parts. Then, students explain to a partner “which drawing is an example of halves and which is a non-example.” While this activity asks students to analyze relationships, there is no description of how TEKS 2.1F 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 2 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, along with the corresponding lessons. Each lesson planner includes a section that identifies the process standards that are incorporated in the lesson. For example, lesson 11, “Recall Basic Addition and Subtraction Facts,” includes these mathematical processes: TEKS 2.1B and TEKS 2.1F. These same process standards are indicated in the sidebar for the “Guided Instruction” section to “guide students through each problem using mathematical processes.”

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

Lessons provide opportunities for students to think mathematically, persevere through problem solving, and make sense of mathematics. In lesson 4, “Find Numbers on a Number Line,” “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 asks questions such as, “Why do landmark numbers usually end in 0, and how does that help you locate numbers faster?” and “How can you explain 480’s location using greater than and less than words?” Additionally, the “Critical Thinking” activity prompts students to explain their thinking when locating a value on a number line and when drawing their own model. Challenge questions for this activity prompt students to persevere and extend their thinking for each problem. For example, a challenge question in lesson 4 asks students to “continue the pattern for two more days and describe the rule in words and with a number sentence.” At the end of the lesson, the exit ticket provides an opportunity for students to independently utilize an open number line and landmark numbers to locate the number 275 and demonstrate their understanding of the lesson.

In lesson 35, “Interpret Bar Graphs,” students engage in problem-solving that promotes perseverance and mathematical reasoning. During the “Activate Prior Knowledge” section in the Teacher Edition, students collect class data, organize it into a bar graph, and analyze the completed graph to answer questions about the information that is presented. The “Understand the TEKS” and “Guided Instruction” sections require students to interpret titles, category labels, scales, and equal intervals before making comparisons and drawing conclusions from that data. Rather than simply reading values from the graph, students analyze relationships among categories and explain how the graph supports their answers. Additionally, the “Monitoring Understanding and Feedback” section encourages educators to ask probing questions that help students reconsider their thinking, justify conclusions, and persist when interpreting unfamiliar graphs or resolving misconceptions. “Critical Thinking,” “Practice,” “Assessment,” and “Exit Ticket” activities continue to require students to analyze data, justify interpretations, and verify the reasonableness of their conclusions.

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 multiple ways to solve problems and complete tasks are available. In lesson 1, “Compose and Decompose Numbers,” students are encouraged to compose and decompose numbers in more than one way. For example, the “Critical Thinking” activity, along with challenge questions, prompts students to explain and justify multiple ways to represent numbers to demonstrate their understanding. One challenge question asks students to “represent the total using base 10 blocks or a number sentence and explain how they know their answer is reasonable.” Additionally, the “Learn Together” activity that follows prompts students to work in pairs to draw base 10 models in both standard and nonstandard ways to decompose numbers. Partners are expected to explain to each other how their drawings show the same number.

In Lesson 17, “Solve for the Unknown,” students are encouraged to recognize and justify multiple solution strategies when solving unknown-value problems. During guided instruction, students represent the same problem using equations, drawings, and manipulatives while explaining why a particular operation or representation is appropriate. The “Monitoring Understanding and Feedback” section in the Teacher Edition prompts educators to ask students how they solved a problem, whether another strategy could work as well, and why their solution is reasonable. These questions encourage students to explain and justify different approaches rather than rely on a single method. Additionally, the “Learn Together” activity requires students to collaborate with peers, compare solution strategies, and explain how different representations can be used to solve the same problem. “Critical Thinking” tasks prompt students to analyze multiple problem situations, determine an unknown quantity, and defend their reasoning using mathematical evidence. “Practice,” “Assessment,” and “Exit Ticket” activities continue to reinforce flexible thinking by allowing students to apply and justify different approaches to solving problems with unknown values.

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, in lesson 7, “Identify Halves, Fourths, and Eighths,” the “Critical Thinking” activity involves dividing and creating models of fractional pieces. With a partner or the educator, students are expected to explain the name of each part and how the model helps solve the problem. Both “Learn Together” activities in this lesson ask students to create or sort fractional parts and explain their reasoning with a partner, utilizing vocabulary from the lesson. Additionally, “Extension” activities prompt students to create and compare fractional models and write about their thinking. In the second “Extension” activity, students are expected to “write or explain which parts are larger or smaller and why the size of the parts changes when the number of equal parts increases.”

In lesson 22, “Classify and Sort Polygons,” students make sense of mathematics by drawing, describing, and discussing attributes of polygons throughout the instructional sequence. In the “Activate Prior Knowledge” section in the Teacher Edition, students sort shapes by attributes and classify polygons by the number of sides and vertices. The “Understand the TEKS” and “Guided Instruction” sections require students to classify polygons by the number of sides and number of vertices, identify special shapes by other attributes, and justify comparisons among polygons through educator questioning and discussion. Additionally, “Learn Together” and “Differentiation” activities require students to draw and label polygons, sort shapes into categories based on attributes, describe how categories can be created using a shape’s attributes, and write a sentence that describes how a drawing matches a given description. “Critical Thinking” tasks prompt students to draw and label various shapes, explain the attributes of a shape, and compare shapes using words or diagrams. “Practice,” “Assessment,” and “Exit Ticket” activities continue to require students to identify polygons, record answers, explain their reasoning, and explain polygon attributes 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, and justifications.

The “ELPS Language and Discourse Support” sections that are included before each lesson in the Teacher Edition help educators guide students to share and reflect on their problem-solving approaches. For example, in lesson 5, “Identify More or Less,” students are expected to orally explain how to find 10 more, 10 less, 100 more, or 100 less than a given number, and educators prompt them to “describe which digit changes, which digits stay the same, and how place value shows the change.” Educators are also guided to ask students to present an argument by explaining “why only one place changes in each example.” Prompts for justification include, “Why does 10 more change the tens place and not the ones place?” and “How does the number line show 10 less?” Additionally, “How Am I Doing?” boxes in both student pages and the sidebar of the Teacher Edition guide students and educators to reflect on the lesson. The educator is prompted to “circulate and have them explain how they determined 10 more, 10 less, 100 more, and 100 less.”

In lesson 20, “Explore Foundations of Multiplication,” educators are provided with embedded guidance to facilitate student explanations, arguments, and justifications during problem solving. During guided instruction, prompts in the Teacher Edition sidebar encourage students to explain how repeated addition, skip counting, or using equal groups can help them find a total. The “Monitoring Understanding and Feedback” section that is included before the lesson provides questioning strategies that prompt students to explain their reasoning, demonstrate understanding, and reflect on whether their answers make sense in the context of the problem. The “From Oral Reasoning to Written Justification” section further guides educators in helping students transition from verbal explanations to written mathematical justifications. Additionally, “Learn Together” activities require students to collaborate with their peers, create real-world multiplication situations, and explain which real-world contexts are most common. Differentiation activities encourage students to model and discuss different multiplicative models and scenarios and justify how the models and scenarios align. “Critical Thinking” tasks require students to defend their mathematical decisions using evidence from the problem, and “Practice,” “Assessment,” and “Exit Ticket” activities continue to provide opportunities for students to explain and justify their thinking.

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 include prompts and guidance to support educators in providing explanatory feedback based on students’ responses and anticipated misconceptions. For example, in lesson 6, “Explore Even and Odd Numbers,” this section guides educators to listen to students’ explanations and “acknowledge correct reasoning and prompt students to explain whether there are zero leftovers or one leftover after making equal groups of 2.” Additionally, this section provides questions based on whether students make errors or demonstrate understanding. For errors, educators can ask questions such as, “What happens when you make pairs of 2?,” “Is there a counter left without a partner?,” and/or “What does the ones digit tell you?” To extend students’ thinking, educators can ask, “Why are numbers with the same ones digit always either even or odd?” and “How does the ones-digit rule match what you see when you make pairs?”

In lesson 36, “Use Data to Solve Problems,” embedded educator guidance supports explanatory feedback through the “Monitoring Understanding and Feedback” section in the Teacher Edition. Educators are prompted to listen to students’ explanations as they read the title, labels, key, and scale on a pictograph or bar graph. The materials identify anticipated misconceptions, including reading numbers from a graph without connecting them to a specific question, confusing “how many more” with “how many in all,” ignoring a key or scale, and misleading intervals of one. Educators are guided to address these misconceptions by asking probing questions such as how the title describes what the graph is about, whether the question is asking for a total or a difference, and which amounts should be added or subtracted from a graph. Additionally, the “Instructional Support for Student Needs” section provides tier 1, tier 2, and tier 3 guidance for addressing errors in operational choice, misreading a key or scale, and/or failing to connect numbers from a graph to a specific question. 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 continue to provide opportunities for educators to observe students’ reasoning, identify misconceptions, and guide students toward accurate interpretations through questioning and discussion.